{"id":16233,"date":"2020-10-17T20:16:17","date_gmt":"2020-10-17T20:16:17","guid":{"rendered":"https:\/\/uni.hi.is\/einar\/?p=16233"},"modified":"2020-10-17T20:16:17","modified_gmt":"2020-10-17T20:16:17","slug":"stjarnedlisfraedi-og-heimsfraedi-a-islandi-2-timabilid-1780-1870-c-thyngdarfraedi-newtons","status":"publish","type":"post","link":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/?p=16233","title":{"rendered":"Stjarne\u00f0lisfr\u00e6\u00f0i og heimsfr\u00e6\u00f0i \u00e1 \u00cdslandi 2: T\u00edmabili\u00f0 1780-1870 (c) \u00deyngdarfr\u00e6\u00f0i Newtons"},"content":{"rendered":"<p style=\"text-align: right\"><a href=\"https:\/\/uni.hi.is\/einar\/2021\/05\/02\/greinaflokkur-um-stjarnedlisfraedi-og-heimsfraedi-a-islandi\/\">Yfirlit um greinaflokkin<\/a><\/p>\n<p>Enginn raunv\u00edsindama\u00f0ur hefur fengi\u00f0 jafn mikla umfj\u00f6llun \u00ed ritu\u00f0u m\u00e1li og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Isaac_Newton\">Newton<\/a>, nema ef vera skyldi <a href=\"https:\/\/en.wikipedia.org\/wiki\/Albert_Einstein\">Einstein<\/a>. Fyrir utan s\u00edvaxandi fj\u00f6lda b\u00f3ka og n\u00e6r \u00f3teljandi greinar um \u00feennan fyrsta \u201en\u00fat\u00edma\u201c stjarne\u00f0lisfr\u00e6\u00f0ing, \u00e6vi hans og v\u00edsindaafrek, pers\u00f3nuleika, ranns\u00f3knir \u00ed <a href=\"https:\/\/en.wikipedia.org\/wiki\/Isaac_Newton%27s_occult_studies\">efnaspeki og bibl\u00edufr\u00e6\u00f0um<\/a>, sem og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Later_life_of_Isaac_Newton\">opinber emb\u00e6ttisst\u00f6rf<\/a>, er hans geti\u00f0 \u00ed \u00f6llum almennum alfr\u00e6\u00f0iritum og flestum ef ekki \u00f6llum byrjendakennslub\u00f3kum \u00ed e\u00f0lisfr\u00e6\u00f0i og st\u00e6r\u00f0fr\u00e6\u00f0i fyrir framhaldssk\u00f3la og h\u00e1sk\u00f3la.<\/p>\n<p>\u00cd fyrri f\u00e6rslum \u00feessa greinaflokks var fjalla\u00f0 stuttlega um Newton og verk hans \u00e1 v\u00f6ldum st\u00f6\u00f0um. H\u00e9r ver\u00f0ur athyglinni fyrst og fremst beint a\u00f0 \u00feyngdarfr\u00e6\u00f0i hans og hvernig uppl\u00fdsingar um hana b\u00e1rust \u00edslenskri al\u00fe\u00fd\u00f0u \u00e1 s\u00ednum t\u00edma. \u00deeim lesendum, sem vilja kafa d\u00fdpra en h\u00e9r er gert, m\u00e1 benda \u00e1 eftirfarandi heimildir:<\/p>\n<ul>\n<li>W. Newman: <a href=\"https:\/\/fivebooks.com\/best-books\/isaac-newton-william-newman\/\">The best books on Isaac Newton<\/a><\/li>\n<li>J. Gleick, 2003: <a href=\"https:\/\/www.amazon.co.uk\/Isaac-Newton-James-Gleick\/dp\/0007163185\/ref=sr_1_5?dchild=1&amp;keywords=james+gleick&amp;qid=1598369787&amp;s=books&amp;sr=1-5\">Isaac Newton<\/a>.<\/li>\n<li>I. B. Cohen &amp; G. S. Smith ritstj., 2002: <a href=\"http:\/\/strangebeautiful.com\/other-texts\/cambridge-companion-newton.pdf\">The Cambridge Companion to Newton<\/a>. (<a href=\"https:\/\/books.google.is\/books?id=se27CwAAQBAJ&amp;source=gbs_navlinks_s\">2. \u00fatg. endurb\u00e6tt, 2016<\/a>).<\/li>\n<li>G. Gjertsen, 1987: <a href=\"https:\/\/www.amazon.com\/Newton-Handbook-Gerek-Gjertsen\/dp\/0710202792\">The Newton Handbook<\/a>.<\/li>\n<\/ul>\n<figure id=\"attachment_14729\" aria-describedby=\"caption-attachment-14729\" style=\"width: 384px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-14729\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/05\/GodfreyKneller-IsaacNewton-1689-218x300.jpg\" alt=\"\" width=\"384\" height=\"529\" \/><figcaption id=\"caption-attachment-14729\" class=\"wp-caption-text\"><a href=\"https:\/\/en.wikipedia.org\/wiki\/Isaac_Newton\"><span style=\"font-size: 10pt\">\u00cdsak Newton<\/span><\/a><span style=\"font-size: 10pt\">\u00a01689, tveimur \u00e1rum eftir a\u00f0 meistaraverki\u00f0 <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1l n\u00e1tt\u00faruspekinnar<\/em> kom \u00fat. M\u00e1lverk eftir G. Kneller.<\/span><\/figcaption><\/figure>\n<p>\u00deyngdarfr\u00e6\u00f0i Newtons var upphaflega sett\u00a0 fram \u00ed \u00feri\u00f0ja hluta <a href=\"https:\/\/en.wikipedia.org\/wiki\/Philosophi%C3%A6_Naturalis_Principia_Mathematica\">St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1la n\u00e1tt\u00faruspekinnar<\/a> \u00e1ri\u00f0 1687. &#8211; \u00cd fyrsta hlutanum er hins vegar lag\u00f0ur grunnur a\u00f0 s\u00edgildri aflfr\u00e6\u00f0i, sem er nau\u00f0synleg undirsta\u00f0a, \u00feegar beita skal \u00feyngdarl\u00f6gm\u00e1li Newtons, auk \u00feess sem h\u00fan hefur mikilv\u00e6gt og almennt notagildi \u00ed e\u00f0lisfr\u00e6\u00f0i, verkfr\u00e6\u00f0i, daglegu l\u00edfi og v\u00ed\u00f0ar. \u00dear er jafnframt fjalla\u00f0 um mi\u00f0l\u00e6ga krafta, einkum \u00fe\u00f3 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Centripetal_force\">mi\u00f0s\u00f3knarkraftinn<\/a>. S\u00fdnt er fram \u00e1, a\u00f0 \u00feegar sl\u00edkur kraftur breytist \u00ed \u00f6fugu hlutfalli vi\u00f0 fjarl\u00e6g\u00f0ina fr\u00e1 kraftmi\u00f0junni \u00ed \u00f6\u00f0ru veldi, eru brautir agna \u00ed kraftsvi\u00f0inu\u00a0 keilusni\u00f0 og bent \u00e1 tengsl \u00feeirrar ni\u00f0urst\u00f6\u00f0u vi\u00f0 l\u00f6gm\u00e1l Keplers. \u00de\u00e1 er \u00fear a\u00f0 finna fyrstu \u00feekktu tilraunina til a\u00f0 gl\u00edma vi\u00f0 \u00feraut, sem n\u00fa gengur undir nafninu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Three-body_problem\">\u00feriggja-hnatta vandam\u00e1li\u00f0<\/a>.<\/p>\n<p>Annar hluti b\u00f3karinnar fjallar svo a\u00f0 mestu um \u00e1hrif vi\u00f0n\u00e1ms gegn hreyfingu og \u00fdmsa \u00fe\u00e6tti \u00far straumfr\u00e6\u00f0i, sem Newton notar \u00ed lokin til a\u00f0 s\u00fdna fram \u00e1, a\u00f0 hvirflakenning Descartes getur alls ekki \u00fatsk\u00fdrt hreyfingar himintunglanna.<\/p>\n<p>\u00deess ber a\u00f0 geta, a\u00f0 \u00feetta merka t\u00edmam\u00f3taverk Newtons er a\u00f0 hluta byggt \u00e1 ranns\u00f3knum forvera hans, einkum \u00fe\u00f3 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Johannes_Kepler\">Keplers<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Galileo_Galilei\">Gal\u00edle\u00f3s<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Ren%C3%A9_Descartes\">Descartes<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Christiaan_Huygens\">Huygens<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Robert_Hooke\">Hookes<\/a>. Afrek h\u00f6fundarins f\u00f3lst me\u00f0al annars \u00ed \u00fev\u00ed a\u00f0 taka saman gagnlegustu \u00fe\u00e6ttina \u00far verkum fyrrnefndra spekinga, innlei\u00f0a n\u00fd hugt\u00f6k og reiknia\u00f0fer\u00f0ir og jafnframt a\u00f0 m\u00f3ta n\u00fdja a\u00f0fer\u00f0afr\u00e6\u00f0i \u00ed n\u00e1tt\u00faruspeki, sem notu\u00f0 er enn \u00feann dag \u00ed dag.<\/p>\n<ul>\n<li>I. Newton, 1687: <a href=\"https:\/\/books.google.is\/books?id=XJwx0lnKvOgC&amp;pg=PP2&amp;redir_esc=y#v=onepage&amp;q&amp;f=false\">Philosophiae naturalis principia mathematica<\/a>.\u00a0 &#8211;\u00a0 <a href=\"https:\/\/www.e-rara.ch\/zut\/wihibe\/content\/titleinfo\/338618\">\u00d6nnur \u00fatg\u00e1fa<\/a> 1713\u00a0 &#8211;\u00a0 \u00a0<a href=\"https:\/\/www.e-rara.ch\/zut\/wihibe\/content\/titleinfo\/338026\">\u00deri\u00f0ja \u00fatg\u00e1fa<\/a> 1726.\u00a0 &#8211;\u00a0 Ensk \u00fe\u00fd\u00f0ing 3ju \u00fatg\u00e1fu eftir A. Motte, 1729: <a href=\"https:\/\/books.google.is\/books?id=Tm0FAAAAQAAJ&amp;source=gbs_navlinks_s\">Vol 1<\/a>; <a href=\"https:\/\/archive.org\/details\/bub_gb_6EqxPav3vIsC\/page\/n7\/mode\/2up\">Vol 2 og Vol 3<\/a> (vol 3 hefst \u00e1 bls. 200).\u00a0 &#8211;\u00a0 N\u00fdjasta enska \u00fe\u00fd\u00f0ingin \u00e1samt \u00edtarlegri umfj\u00f6llun kom \u00fat 1999: I. Newton, I. B. Cohen and A. Whitman: <a href=\"https:\/\/books.google.is\/books?id=k_NgQgAACAAJ&amp;source=gbs_navlinks_s\">The Principia: Mathematical Principles of Natural Philosophy<\/a>.<\/li>\n<li>S. Chandrasekhar, 1995: <a href=\"https:\/\/books.google.is\/books?id=qfJVNPQVHbsC&amp;source=gbs_navlinks_s\">Newton&#8217;s Principia for the Common Reader<\/a>.<\/li>\n<li>G. Smith, 2007: <a href=\"https:\/\/plato.stanford.edu\/entries\/newton-principia\/\">Newton\u2019s Philosophiae Naturalis Principia Mathematica<\/a>.<\/li>\n<li>C. Smeenk &amp; E. Schliesser, 2013: <a href=\"https:\/\/www.academia.edu\/8536212\/Newtons_Principia_with_Eric_Schliesser_?email_work_card=minimal-title\">Newton\u2019s Principia<\/a>.<\/li>\n<li>S. D. Snobelen, 1998: <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S016093279801148X\">On reading Isaac Newton&#8217;s Principia in the 18th century<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center\"><span style=\"font-size: 14pt\"><strong>\u00d6rf\u00e1 or\u00f0 um aflfr\u00e6\u00f0i<br \/>\n<\/strong><\/span><\/h3>\n<p>E\u00f0lisfr\u00e6\u00f0i fyrir byrjendur \u00ed framhalds- og h\u00e1sk\u00f3lum hefst yfirleitt \u00e1 umfj\u00f6llun um grundvallaratri\u00f0i aflfr\u00e6\u00f0innar. Oftast er nemendum tj\u00e1\u00f0, a\u00f0 n\u00e1msefni\u00f0 s\u00e9 byggt \u00e1 hugmyndum Newtons, eins og \u00fe\u00e6r voru settar fram \u00ed fyrsta hluta <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1la n\u00e1tt\u00faruspekinnar<\/em>. Hins vegar er venjulega sleppt a\u00f0 geta \u00feess, a\u00f0 hin st\u00e6r\u00f0fr\u00e6\u00f0ilega framsetning Newtons \u00e1 aflfr\u00e6\u00f0inni er \u00e1kaflega torskilin og a\u00f0 \u00fea\u00f0 var ekki fyrr en <a href=\"https:\/\/en.wikipedia.org\/wiki\/Leonhard_Euler\">L. Euler<\/a> kom til s\u00f6gunnar um mi\u00f0ja \u00e1tj\u00e1ndu \u00f6ld, sem a\u00f0rir en fremstu st\u00e6r\u00f0fr\u00e6\u00f0ingar uppl\u00fdsingarinnar g\u00e1tu n\u00fdtt s\u00e9r hugmyndir meistarans a\u00f0 einhverju gagni.<\/p>\n<p>S\u00fa framsetning \u00e1 aflfr\u00e6\u00f0inni, sem kennd er \u00ed h\u00e1sk\u00f3lum, er a\u00f0 mestu komin fr\u00e1 Euler og byggir \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Calculus\">\u00f6rsm\u00e6\u00f0areikningi<\/a>, \u00fear sem <a href=\"https:\/\/en.wikipedia.org\/wiki\/Leibniz%27s_notation\">hi\u00f0 \u00fe\u00e6gilega t\u00e1knm\u00e1l Leibniz<\/a> er nota\u00f0 \u00ed sta\u00f0 <a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/j.1600-0498.1998.tb00536.x\">r\u00famfr\u00e6\u00f0ilegra reiknia\u00f0fer\u00f0a Newtons<\/a>. Sem d\u00e6mi m\u00e1 nefna, a\u00f0 <a href=\"https:\/\/www.math24.net\/newtons-second-law-motion\/\">anna\u00f0 hreyfingarl\u00f6gm\u00e1l Newtons<\/a> f\u00e9kk \u00fea\u00f0 form, sem n\u00fa er nota\u00f0, \u00ed <a href=\"https:\/\/scholarlycommons.pacific.edu\/euler-works\/177\/\">mikilv\u00e6gri grein<\/a> eftir Euler \u00e1ri\u00f0 1752 (sj\u00e1 n\u00e1nar um \u00feetta efni <a href=\"https:\/\/hal.archives-ouvertes.fr\/hal-00415933\/document\">h\u00e9r<\/a>).<\/p>\n<p>\u00cd \u00feessari f\u00e6rslu ver\u00f0ur ekki fjalla\u00f0 frekar um hina margslungnu s\u00f6gu aflfr\u00e6\u00f0innar sem sl\u00edkrar, en \u00feeim, sem hafa \u00e1huga \u00e1 efninu, er bent \u00e1 eftirfarandi heimildir:<\/p>\n<ul>\n<li>Wikipedia: <a href=\"https:\/\/en.wikipedia.org\/wiki\/History_of_classical_mechanics\">History of Classical Mechanics<\/a>.<\/li>\n<li>R. Dugas, 1988: <a href=\"http:\/\/www.bibotu.com\/books\/Philosophy\/History%20and%20Philosophy%20of%20Science\/Dugas%20-%20A%20History%20of%20Mechanics%20(Routledge,%201955).pdf\">A History of Mechanics<\/a>.<\/li>\n<li>E. Mach, 1919: <a href=\"https:\/\/archive.org\/details\/scienceofmechani005860mbp\/page\/n5\/mode\/2up\">The Science of Mechanics: A Critical and Historical Account of Its Development<\/a> (4. \u00fatg.).<\/li>\n<li>C. Truesdell, 1960: <a href=\"https:\/\/www.jstor.org\/stable\/41133208?seq=2#metadata_info_tab_contents\">A Program toward Rediscovering the Rational Mechanics of the Age of Reason<\/a>.<\/li>\n<li>C. Truesdell, 1976: <em>History of Classical Mechanics<\/em>. <a href=\"http:\/\/home.iitk.ac.in\/~ag\/ESO202\/Truesdell1.pdf\">Part 1, to 1800<\/a> &#8211; <a href=\"https:\/\/link.springer.com\/article\/10.1007\/BF00600486\">Part 2, The 19. and 20. centuries<\/a>.<\/li>\n<li>M. J. Crowe, 2007: <a href=\"https:\/\/www.amazon.com\/Mechanics-Aristotle-Einstein-Michael-Crowe\/dp\/1888009322\">Mechanics from Aristotle to Einstein<\/a>.<\/li>\n<li>C. Rovelli, 2014: <a href=\"https:\/\/arxiv.org\/abs\/1312.4057\">Aristotle&#8217;s Physics: a Physicist&#8217;s Look<\/a>.<\/li>\n<li>Mikael M. Karlsson, 1988: <a href=\"https:\/\/timarit.is\/page\/4964542#page\/n5\/mode\/2up\">\u00deungir \u00feankar \u2013 um aflfr\u00e6\u00f0i Arist\u00f3telesar<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center\"><strong><span style=\"font-size: 14pt\">\u00deyngdarl\u00f6gm\u00e1li\u00f0<\/span><\/strong><\/h3>\n<p>\u00cd <a href=\"https:\/\/en.wikipedia.org\/wiki\/Geocentric_model#Geocentrism_and_rival_systems\">jar\u00f0mi\u00f0juheimi<\/a> fornaldar og mi\u00f0alda gengu n\u00e1tt\u00faruspekingar n\u00e6r undantekningarlaust \u00fat fr\u00e1 \u00fev\u00ed sem v\u00edsu, a\u00f0 l\u00f6gm\u00e1l stj\u00f6rnuheimsins v\u00e6ru allt \u00f6nnur en \u00feau, sem r\u00edktu \u00e1 j\u00f6r\u00f0u ni\u00f0ri. \u00deegar <a href=\"https:\/\/en.wikipedia.org\/wiki\/Copernican_heliocentrism\">s\u00f3lmi\u00f0jukenning K\u00f3pern\u00edkusar<\/a> f\u00f3r fyrir alv\u00f6ru a\u00f0 ry\u00f0ja s\u00e9r til r\u00fams \u00e1 sautj\u00e1ndu \u00f6ld, var\u00f0 j\u00f6r\u00f0in sm\u00e1m saman hluti af stj\u00f6rnuheiminum \u00ed hugum l\u00e6rd\u00f3msmanna og nokkrir \u00feeirra t\u00f3ku a\u00f0 velta fyrir s\u00e9r \u00feeim m\u00f6guleika, a\u00f0 ef til vill v\u00e6ru l\u00f6gm\u00e1lin ekki svo \u00f3l\u00edk \u00e1 himni og j\u00f6r\u00f0u. \u00dear voru fremstir \u00ed flokki \u00feeir Kepler og Descartes, sem b\u00e1\u00f0ir settu fram e\u00f0lisfr\u00e6\u00f0ileg afbrig\u00f0i af s\u00f3lmi\u00f0jukenningunni, \u00e1n \u00feess \u00fe\u00f3 a\u00f0 hafa erindi sem erfi\u00f0i. Um \u00feetta var fjalla\u00f0 <a href=\"https:\/\/uni.hi.is\/einar\/2020\/08\/30\/stjarnedlisfraedi-og-heimsfraedi-a-islandi-2-timabilid-1780-1870-b-stjarnedlisfraedi-fyrir-daga-newtons\/\">\u00ed s\u00ed\u00f0ustu f\u00e6rslu<\/a>, en frekari kynningu \u00e1 vangaveltum fyrri t\u00edma um \u00feyngdina m\u00e1 me\u00f0al annars finna \u00ed eftirfarandi heimildum:<\/p>\n<ul>\n<li>Wikipedia: <a href=\"https:\/\/en.wikipedia.org\/wiki\/History_of_gravitational_theory\">History of Gravitational Theory<\/a>.<\/li>\n<li>J. J. O&#8217;Connor &amp; E. F. Robertson, 2003: <a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Gravitation\/\">Theories of Gravitation<\/a>.<\/li>\n<li>Alberto Cappi, 2012: <a href=\"http:\/\/www.cultureandcosmos.org\/pdfs\/16\/Cappi_INSAPVII_Gravity_before_Newton.pdf\">The concept of gravity before Newton.<\/a><\/li>\n<li>E. Hecht, 2019: <a href=\"https:\/\/aapt.scitation.org\/doi\/abs\/10.1119\/1.5089751?\">Kepler and the origins of the theory of gravity<\/a>.<\/li>\n<\/ul>\n<p>Eins og allir vita, h\u00e9lt Newton \u00fev\u00ed r\u00e9ttilega fram, a\u00f0 beita m\u00e6tti framsetningu hans \u00e1 aflfr\u00e6\u00f0inni hvar sem er \u00ed s\u00f3lkerfinu og a\u00f0 \u00feyngdarl\u00f6gm\u00e1l hans g\u00e6fi ekki a\u00f0eins r\u00e9tta mynd af \u00e1hrifum \u00feyngdarinnar \u00e1 j\u00f6r\u00f0inni, heldur \u00fatsk\u00fdr\u00f0i \u00fea\u00f0 jafnframt hreyfingar himintungla \u00ed s\u00f3lkerfinu. \u00deessar ni\u00f0urst\u00f6\u00f0ur birti hann \u00ed <a href=\"https:\/\/en.wikipedia.org\/wiki\/Philosophi%C3%A6_Naturalis_Principia_Mathematica#Book_3,_De_mundi_systemate\">De mundi systemate<\/a> (<span id=\"Book_3,_De_mundi_systemate\" class=\"mw-headline\"><em>Um heimskerfi\u00f0<\/em>), sem er \u00feri\u00f0ji hluti <a href=\"https:\/\/en.wikipedia.org\/wiki\/Philosophi%C3%A6_Naturalis_Principia_Mathematica\">St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1la n\u00e1tt\u00faruspekinnar<\/a>.<\/span><\/p>\n<p>Me\u00f0 \u00fev\u00ed a\u00f0 nota n\u00fat\u00edma or\u00f0alag m\u00e1 setja <a href=\"https:\/\/en.wikipedia.org\/wiki\/Newton%27s_law_of_universal_gravitation\">\u00feyngdarl\u00f6gm\u00e1li\u00f0<\/a> fram \u00e1 eftirfarandi h\u00e1tt: Tveir punktmassar, m<sub>1<\/sub> og m<sub>2<\/sub>, dragast hvor a\u00f0 \u00f6\u00f0rum me\u00f0 jafnst\u00f3rum gagnst\u00e6\u00f0um kr\u00f6ftum, F<sub>1<\/sub> og F<sub>2<\/sub>, me\u00f0 stefnu eftir tengil\u00ednu massanna. Ef fjarl\u00e6g\u00f0in milli punktanna er r, gildir a\u00f0 F<sub>1<\/sub> = F<sub>2<\/sub> = Gm<sub>1<\/sub>m<sub>2<\/sub>\/r<sup>2<\/sup>, \u00fear sem G er stu\u00f0ull, sem kenndur er vi\u00f0 Newton. Til a\u00f0 form\u00falan komi a\u00f0 fullum notum \u00fearf til vi\u00f0b\u00f3tar a\u00f0 beita \u00f6\u00f0ru hreyfingarl\u00f6gm\u00e1li Newtons, <strong>F<\/strong> = m<strong>a<\/strong>, \u00fear sem <strong>a<\/strong> er hr\u00f6\u00f0un (umfj\u00f6llun um a\u00f0fer\u00f0afr\u00e6\u00f0ina m\u00e1 finna \u00ed aflfr\u00e6\u00f0ib\u00f3kum). Form\u00fala Newtons fyrir \u00feyngdina gildir einnig fyrir tvo hnetti me\u00f0 k\u00falalaga massadreifingu, ef r er n\u00fa sett jafnt fjarl\u00e6g\u00f0inni milli mi\u00f0ju hnattanna.<\/p>\n<figure id=\"attachment_13410\" aria-describedby=\"caption-attachment-13410\" style=\"width: 418px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-13410\" src=\"https:\/\/uni.hi.is\/einar\/files\/2019\/11\/Naturl\u00e6rens-mechaniske-deel-300x279.png\" alt=\"\" width=\"418\" height=\"389\" \/><figcaption id=\"caption-attachment-13410\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Hluti af s\u00ed\u00f0u 170 \u00ed fyrstu kennslub\u00f3kinnni \u00ed n\u00e1tt\u00faruspeki, sem notu\u00f0 var \u00ed \u00edslenskum sk\u00f3la, <em><a href=\"https:\/\/books.google.is\/books?id=kCdPAAAAYAAJ&amp;hl=da&amp;source=gbs_navlinks_s\">Naturl\u00e6rens mechaniske Deel<\/a><\/em> (1844) eftir <a href=\"https:\/\/uni.hi.is\/einar\/2019\/09\/09\/h-c-orsted-bein-og-obein-ahrif-hans-a-islendinga-og-upphaf-kennslu-i-edlisfraedi-og-stjornufraedi-vid-reykjavikurskola\/\">H. C. \u00d6rsted<\/a>. \u00dearna f\u00e6rir h\u00f6fundurinn r\u00f6k fyrir \u00fev\u00ed, a\u00f0 \u00feyngdar\u00e1hrif hnattar me\u00f0 k\u00falusamhverfa massadreifingu (BDEF) \u00e1 punktmassa A hafi stefnu eftir l\u00ednunni ABCE, \u00fear sem punkturinn C er mi\u00f0ja hnattarins. \u00c1 n\u00e6stu s\u00ed\u00f0um b\u00f3karinnar er svo sagt fr\u00e1 \u00fev\u00ed (en ekki r\u00f6kstutt), a\u00f0 krafturinn s\u00e9 hinn sami og ef allur massi hnattarins v\u00e6ri \u00ed C. Eins og fr\u00e6gt er or\u00f0i\u00f0, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Shell_theorem\">sanna\u00f0i Newton \u00feetta fyrstur manna<\/a> \u00ed <em>St\u00e6r\u00f0fr\u00e6\u00f0i-l\u00f6gm\u00e1lum n\u00e1tt\u00faruspekinnar<\/em> og n\u00fa m\u00e1 au\u00f0veldlega finna s\u00f6nnunina \u00ed aflfr\u00e6\u00f0in\u00e1msefni h\u00e1sk\u00f3lanema \u00ed raunv\u00edsindum.<\/span><\/figcaption><\/figure>\n<figure id=\"attachment_13970\" aria-describedby=\"caption-attachment-13970\" style=\"width: 326px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-13970\" src=\"http:\/\/uni.hi.is\/einar\/files\/2019\/12\/2008_NYR_02013_0270_000-183x300.jpg\" alt=\"\" width=\"326\" height=\"534\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/12\/2008_NYR_02013_0270_000-183x300.jpg 183w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/12\/2008_NYR_02013_0270_000-625x1024.jpg 625w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/12\/2008_NYR_02013_0270_000-768x1258.jpg 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/12\/2008_NYR_02013_0270_000-938x1536.jpg 938w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/12\/2008_NYR_02013_0270_000.jpg 1053w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><figcaption id=\"caption-attachment-13970\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">\u00deessi skemmtilega sk\u00fdringarmynd Newtons er \u00far verkinu <a href=\"https:\/\/books.google.is\/books?id=rEYUAAAAQAAJ&amp;source=gbs_navlinks_s\">A Treatise of the System of the World<\/a>, sem hann samdi \u00e1ri\u00f0 1685, en kom ekki \u00e1 prenti fyrr en a\u00f0 honum l\u00e1tnum, \u00e1ri\u00f0 1728. Myndin \u00e1 a\u00f0 s\u00fdna, hvernig \u00feyngdin \u00e1kvar\u00f0ar flugbraut hluta \u00ed loftt\u00e6mi. \u00dea\u00f0 er l\u00e1r\u00e9ttur upphafshra\u00f0i fallbyssuk\u00falu \u00e1 fjallstoppnum V, sem r\u00e6\u00f0ur braut k\u00falunnar. Ef skothra\u00f0inn er yfir \u00e1kve\u00f0nu l\u00e1gmarki (en \u00fe\u00f3 ekki of mikill), fer k\u00falan \u00e1 sporbraut um j\u00f6r\u00f0ina, annars fellur h\u00fan til jar\u00f0ar. Ef hra\u00f0in er hins vegar jafn lausnarha\u00f0a e\u00f0a meiri, losnar k\u00falan fr\u00e1 j\u00f6r\u00f0inni og hverfur \u00fat \u00ed geiminn, anna\u00f0hvort eftir fleygboga- e\u00f0a brei\u00f0bogabraut. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Newton%27s_cannonball\">Sj\u00e1 n\u00e1nari \u00fatsk\u00fdringar h\u00e9r<\/a>.<br \/><\/span><\/figcaption><\/figure>\n<p>\u00cd <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lunum<\/em> s\u00fdnir Newton me\u00f0al annars fram \u00e1 tengslin milli \u00feyngdar-l\u00f6gm\u00e1lsins og l\u00f6gm\u00e1la Keplers og fjallar um truflanir \u00e1 brautum reikistjarna og fylgihnatta \u00feeirra vegna \u00feyngdar\u00e1hrifa fr\u00e1 \u00f6\u00f0rum himintunglum en s\u00f3linni. \u00de\u00e1 gefur hann fyrstu r\u00e9ttu sk\u00fdringuna \u00e1 sj\u00e1varf\u00f6llum, \u00fatsk\u00fdrir hvers vegna j\u00f6r\u00f0in er flatari \u00e1 p\u00f3lsv\u00e6\u00f0unum en um mi\u00f0baug og leysir g\u00e1tuna um frams\u00f3kn vorpunktsins. Um allt \u00feetta og fleira ver\u00f0ur fjalla\u00f0 n\u00e1nar h\u00e9r \u00e1 eftir.<\/p>\n<p>Sagan af \u00fev\u00ed, hvernig Newton t\u00f3kst a\u00f0 m\u00f3ta heildarkenningu um \u00feyngdina, sem n\u00e6r til allra hluta, hvar sem er \u00ed alheimi, hefur veri\u00f0 s\u00f6g\u00f0 \u00ed fj\u00f6lda b\u00f3ka og t\u00edmaritsgreina. Geti\u00f0 er um nokkur sl\u00edk rit \u00ed heimildaskr\u00e1m \u00ed \u00feessari f\u00e6rslu, b\u00e6\u00f0i h\u00e9r a\u00f0 framan og \u00ed \u00feessum kafla. Fr\u00e6gust er \u00fe\u00f3 sagan af Newton og eplinu, sem finna m\u00e1 \u00ed m\u00f6rgum mismunandi \u00fatg\u00e1fum \u00ed al\u00fe\u00fd\u00f0uritum v\u00ed\u00f0a um heim. \u00cd <a href=\"https:\/\/uni.hi.is\/einar\/2019\/11\/25\/edlisfraedi-fischers-fyrsta-edlisfraedibokin-sem-kom-ut-a-islensku\/\">E\u00f0lisfr\u00e6\u00f0i<\/a> Fischers fr\u00e1 1852 er fr\u00e1s\u00f6gnin svona (bls. 24):<\/p>\n<blockquote><p>Sagan segir, a\u00f0 <em>[Newton]<\/em> hafi einusinni veri\u00f0 a\u00f0 ganga um g\u00f3lf \u00ed aldingar\u00f0i nokkrum, og hafi \u00fe\u00e1 dotti\u00f0 epli ofan \u00far eik einni og komi\u00f0 \u00ed h\u00f6fu\u00f0 honum. Honum kom \u00feetta ekki \u00e1 \u00f3vart, \u00fev\u00ed hann vissi a\u00f0 \u00fea\u00f0 var \u00fe\u00fdngdin, sem kn\u00fa\u00f0i epli\u00f0 ni\u00f0ur \u00e1 j\u00f6r\u00f0ina, en n\u00fa datt honum s\u00fa spurning \u00ed hug, hvort epli\u00f0 mundi hafa dotti\u00f0 eins fyrir \u00fea\u00f0, \u00fe\u00f3 eikin hef\u00f0i veri\u00f0 m\u00f6rgum sinni h\u00e6rri. Hann efa\u00f0ist ekki um a\u00f0 svo hef\u00f0i fari\u00f0.\u00a0 &#8211;\u00a0 \u201dEn ef eikin hef\u00f0i n\u00e1\u00f0 upp \u00ed t\u00fangli\u00f0 ?\u201d\u00a0 &#8211;\u00a0 \u00dar \u00feessari spurningu gat hann ekki leyst, og kom \u00fea\u00f0 honum til a\u00f0 gj\u00f6ra \u00fdmsar athuganir og tilraunir um \u00feetta efni, og \u00e1lyktun s\u00fa, er hann komst a\u00f0, var undrunarver\u00f0. Hann uppg\u00f6tva\u00f0i \u00fe\u00e1 hi\u00f0 mikilv\u00e6ga l\u00f6gm\u00e1l \u00fe\u00fdngdarinnar, a\u00f0 a\u00f0dr\u00e1ttarafli\u00f0 m\u00ednkar eptir fert\u00f6lum fjarl\u00e6g\u00f0arinnar.<\/p><\/blockquote>\n<ul>\n<li>L. Rosenfeld, 1965: <a href=\"https:\/\/uni.hi.is\/einar\/files\/2020\/05\/Rosenfeld_1965.pdf\">Newton and the Law of Gravitation<\/a>.<\/li>\n<li>M. Nauenberg, 2015: <a href=\"https:\/\/arxiv.org\/pdf\/1503.06861.pdf\">The Reception of Newton&#8217;s Principia<\/a>.<\/li>\n<li>M. Nauenberg, 2005: <a href=\"https:\/\/link.springer.com\/content\/pdf\/10.1007%2Fs00016-004-0226-y.pdf\">Robert Hooke\u2019s Seminal Contribution to Orbital Dynamics<\/a>.<\/li>\n<li>K. Maglo, 2003: <a href=\"http:\/\/www.chss.uqam.ca\/Portals\/0\/docs\/hps5002\/Perspectives_on%20Science_v11n2_p135-169.pdf\">The Reception of Newton\u2019s Gravitational Theory by Huygens, Varignon and Maupertuiis: How Normal Science may be Revolutionary<\/a>.<\/li>\n<li>F.\u00a0 H. Lunteren, 1988: <a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-94-009-2809-1_9\">Gravitation and Nineteenth-Century Physical Worldviews<\/a>.<\/li>\n<li>F. van Lunteren, 1991: <a href=\"https:\/\/www.academia.edu\/28425222\/Framing_hypotheses_Conceptions_of_gravity_in_the_18th_and_19th_centuries\">Framing Hypotheses: Conceptions of gravity in the 18th and 19th centuries<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center\"><span style=\"font-size: 14pt\"><b>\u201eHypotheses non fingo\u201c<\/b> <\/span><\/h3>\n<p>\u00deeir evr\u00f3psku st\u00e6r\u00f0fr\u00e6\u00f0ingar og n\u00e1tt\u00faruspekingar, sem \u00e1 anna\u00f0 bor\u00f0 g\u00e1tu lesi\u00f0 <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1l n\u00e1tt\u00faruspekinnar<\/em> s\u00e9r a\u00f0 gagni, voru samm\u00e1la um \u00fea\u00f0, a\u00f0 riti\u00f0 v\u00e6ri st\u00e6r\u00f0fr\u00e6\u00f0ilegt meistaraverk. Hins vegar gagnr\u00fdndu \u00fdmsir hinar heimspekilegu undirst\u00f6\u00f0ur, sem verki\u00f0 hv\u00edldi \u00e1, me\u00f0al annars hugmyndir Newtons um t\u00f3m og kraftverkun.<\/p>\n<p>Sem d\u00e6mi m\u00e1 nefna, a\u00f0 margir l\u00e6rd\u00f3msmenn uppl\u00fdsingaraldar, s\u00e9rstaklega \u00fe\u00f3 \u00e1 meginlandinu, voru samm\u00e1la\u00a0 Arist\u00f3telesi um \u00fea\u00f0, a\u00f0 kraftur g\u00e6ti ekki verka\u00f0 milli hluta \u00e1n snertingar af einhverju tagi, anna\u00f0hvort beint e\u00f0a \u00ed gegnum einhverskonar vaka (aether). Newton var hins vegar at\u00f3mhyggjuma\u00f0ur og hin \u00f3deilanlegu at\u00f3m hans hreyf\u00f0ust \u00ed t\u00f3mar\u00fami. Hreyfingar\u00e1stand \u00feeira gat a\u00f0 sj\u00e1lfs\u00f6g\u00f0u breyst vi\u00f0 \u00e1rekstra og \u00feau g\u00e1tu sameinast vegna samlo\u00f0unar, en \u00feyngdarkrafturinn milli \u00feeirra bygg\u00f0ist \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Action_at_a_distance\">fjarhrifum<\/a> og hi\u00f0 sama \u00e1tti vi\u00f0 um a\u00f0skilda st\u00f3ra hluti eins og himintungl. \u00deetta \u00fe\u00f3tti m\u00f6nnum eins og Leibniz og Huygens algj\u00f6rlega \u00f3kiljanlegt og m\u00f3tm\u00e6ltu hugmyndinni um fjarhrif har\u00f0lega, b\u00e6\u00f0i \u00ed r\u00e6\u00f0u og riti.<\/p>\n<p>Vita\u00f0 er, a\u00f0 Newton ger\u00f0i \u00fdmsar tilraunir til a\u00f0 finna \u00e1s\u00e6ttanlegar lei\u00f0ir til a\u00f0 losna vi\u00f0 fjarhrifin, en \u00e1n \u00e1rangurs. \u00cd vi\u00f0auka e\u00f0a eftirm\u00e1la (l. <em>Scholium generale<\/em>; e. <em>General Scholium<\/em>), sem hann b\u00e6tti vi\u00f0 a\u00f0ra \u00fatg\u00e1fu <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lanna<\/em> \u00e1ri\u00f0 1713 (og aftur \u00f6rl\u00edti\u00f0 breyttan vi\u00f0 \u00feri\u00f0ju \u00fatg\u00e1funa 1726) tekur hann svona til or\u00f0a \u00ed \u00e1ttundu efnisgrein:<\/p>\n<figure id=\"attachment_16470\" aria-describedby=\"caption-attachment-16470\" style=\"width: 545px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16470\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/09\/BFranzs-Newton-copy-3-256x300.jpg\" alt=\"\" width=\"545\" height=\"639\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/BFranzs-Newton-copy-3-256x300.jpg 256w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/BFranzs-Newton-copy-3-874x1024.jpg 874w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/BFranzs-Newton-copy-3-768x899.jpg 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/BFranzs-Newton-copy-3-1312x1536.jpg 1312w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/BFranzs-Newton-copy-3.jpg 1538w\" sizes=\"auto, (max-width: 545px) 100vw, 545px\" \/><figcaption id=\"caption-attachment-16470\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">\u00deessi \u00edslenska \u00fe\u00fd\u00f0ing Bj\u00f6rns Franzsonar birtist \u00e1ri\u00f0 1945 \u00ed b\u00f3kinni <em>Undur veraldar<\/em> (ritstj. H. Shapley, S. Rapport &amp; H. Wright). Sj\u00e1 einnig\u00a0 b\u00f3k \u00deorsteins Vilhj\u00e1mssonar, <em>Heimsmynd II<\/em>, 1987, bls. 247-53.<br \/><\/span><\/figcaption><\/figure>\n<p>R\u00e9tt fyrir ne\u00f0an mi\u00f0ju m\u00e1 sj\u00e1 hina fr\u00e6gu fullyr\u00f0ingu \u201etilg\u00e1tur sm\u00ed\u00f0a \u00e9g ekki\u201c, sem er \u00fe\u00fd\u00f0ing \u00e1 \u201ehypotheses non fingo\u201c.\u00a0 Eftirm\u00e1linn \u00ed heild er sennilega \u00fea\u00f0 af verkum Newtons, sem flestir hafa lesi\u00f0 og heimspekingar og sagnfr\u00e6\u00f0ingar v\u00edsa hva\u00f0 mest \u00ed. \u00cd \u00feessum greinaflokki hefur \u00feegar komi\u00f0 fram, a\u00f0 \u00fea\u00f0 var Stef\u00e1n Bj\u00f6rnsson reiknimeistari, sem fyrstur \u00cdslendinga kynnti s\u00e9r \u00feyngdarfr\u00e6\u00f0i Newtons og \u00ed einni af disp\u00fat\u00edum s\u00ednum vitnar hann beint \u00ed <em>Scolium generale<\/em>. Um \u00fea\u00f0 ver\u00f0ur n\u00e1nar r\u00e6tt \u00ed n\u00e6sta kafla.<\/p>\n<p>\u00cd samr\u00e6mi vi\u00f0 \u00feessa yfirl\u00fdsingu breytti Newton v\u00ed\u00f0ast hvar <em>tilg\u00e1tum<\/em> (hypotheses) fyrstu \u00fatg\u00e1funnar \u00ed r<em>eglur<\/em> (regulae philosophandi) e\u00f0a <em>fyrirb\u00e6ri<\/em> (phaenomena) \u00ed seinni \u00fatg\u00e1fum <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lanna<\/em>. A\u00f0fer\u00f0afr\u00e6\u00f0i hans breyttist \u00fe\u00f3 l\u00edti\u00f0 me\u00f0 n\u00fdju n\u00f6fnunum.<\/p>\n<p>\u00der\u00e1tt fyrir mikla gagnr\u00fdni \u00ed fyrstu, hlutu fjarhrifin sm\u00e1m saman sam\u00feykki l\u00e6rd\u00f3msmanna \u00e1 meginlandi Evr\u00f3pu og \u00feyngdarl\u00f6gm\u00e1li\u00f0 var \u00f3spart nota\u00f0 til reikninga \u00e1 hreyfingum himintungla. \u00c1hyggjur manna af hinum heimspekilega grundvelli f\u00f3ru og st\u00f6\u00f0ugt minnkandi, ekki s\u00edst eftir a\u00f0 hugtaki\u00f0 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gravitational_field\">\u00feyngdarsvi\u00f0<\/a> kom til s\u00f6gunnar.\u00a0 Almenn umfj\u00f6llun um s\u00edgilda \u00feyngdarfr\u00e6\u00f0i hefur og byggt \u00e1 \u00feeirri hugmyndafr\u00e6\u00f0i alla t\u00ed\u00f0 s\u00ed\u00f0an.<\/p>\n<ul>\n<li>I. Newton, 1726: <a href=\"https:\/\/newtonprojectca.files.wordpress.com\/2013\/06\/newton-general-scholium-1729-english-text-by-motte-a4.pdf\">General scholium<\/a>. Ensk \u00fe\u00fd\u00f0ing fr\u00e1 1729. Sj\u00e1 n\u00e1nar <a href=\"https:\/\/isaacnewton.ca\/newtons-general-scholium\/\">h\u00e9r<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/General_Scholium\">h\u00e9r<\/a>.<\/li>\n<li>C. Smeenk, 2016: <a href=\"http:\/\/publish.uwo.ca\/~csmeenk2\/files\/SmeenkGSDraftWeb.pdf\">Cosmology and Physical Astronomy in Newton\u2019s General Scholium. <\/a><\/li>\n<li>I. Newton, H. S. Thayer, 1953: <a href=\"http:\/\/publish.uwo.ca\/~csmeenk2\/files\/SmeenkGSDraftWeb.pdf\">Newton&#8217;s Philosophy of Nature: Selections from His Writings.<\/a><\/li>\n<li>A. Janiak 2014: <a href=\"https:\/\/plato.stanford.edu\/entries\/newton-philosophy\/\">Newton\u2019s Philosophy<\/a>.<\/li>\n<li>L. Rosenfeld, 1969: <a href=\"https:\/\/www.jstor.org\/stable\/41133293?seq=1#metadata_info_tab_contents\">Newton&#8217;s Views on Aether and Gravitation<\/a>.<\/li>\n<li>J. Henry, 2011: <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0039368110001044\">Gravity and De gravitatione: the development of Newton\u2019s ideas on action at a distance<\/a>.<\/li>\n<li>J. Henry, 2020: <a href=\"https:\/\/link.springer.com\/content\/pdf\/10.1007%2F978-3-319-20791-9_39-1.pdf\">Action at a Distance in Early Modern Natural Philosophy<\/a>.<\/li>\n<li>M. B. Hesse, 1955: <a href=\"https:\/\/www.jstor.org\/stable\/227576?seq=1#metadata_info_tab_contents\">Action at a Distance in Classical Physics<\/a>.<\/li>\n<li>M. B. Hesse, 1962: <a href=\"https:\/\/archive.org\/details\/forcesfieldsconc0000hess\/page\/n5\">Forces and Fields: The Concept of Action at a Distance in the History of Physics<\/a>. Einkum kaflar V til VII.<\/li>\n<\/ul>\n<h3 style=\"text-align: center\"><span style=\"font-size: 14pt\"><strong>\u00a0<\/strong><\/span><\/h3>\n<h3 style=\"text-align: center\"><span style=\"font-size: 14pt\"><strong>Stef\u00e1n Bj\u00f6rnsson &#8211; F<\/strong><strong><span style=\"font-size: 14pt\">yrsti \u00edslenski nj\u00fatonistinn?<\/span><br \/>\n<\/strong><\/span><\/h3>\n<p>\u00c1ri\u00f0 1758 disp\u00fatera\u00f0i <a href=\"http:\/\/uni.hi.is\/einar\/2017\/10\/18\/aflfraedi-i-verkum-stefans-bjornssonar\/\">Stef\u00e1n Bj\u00f6rnsson<\/a> reiknimeistari einu sinni sem oftar vi\u00f0 Hafnarh\u00e1sk\u00f3la. Heiti fyrirlestrarins \u00fea\u00f0 \u00e1ri\u00f0 var <a href=\"https:\/\/notendur.hi.is\/einar\/SAGA\/SB_cometae_1758.pdf\">De Effectu Cometarum Descendentium in Systema Nostrum Planetarium<\/a> (<em>Um verkan halastjarna sem ganga ni\u00f0ur \u00ed reikistj\u00f6rnukerfi vort<\/em>) og framsetningin s\u00fdnir fram\u00farskarandi skilning h\u00f6fundarins \u00e1 aflfr\u00e6\u00f0i og \u00feyngdarfr\u00e6\u00f0i Newtons.<\/p>\n<p>\u00c1 \u00feessum t\u00edma var sp\u00e1 <a href=\"http:\/\/adsbit.harvard.edu\/\/full\/1986JHA....17....1W\/0000001.000.html?high=59678436d723218\">E. Halleys<\/a> um fyrstu endurkomu halastj\u00f6rnunnar, sem n\u00fa er vi\u00f0 hann kennd, <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00033798400200271?journalCode=tasc20\">miki\u00f0 til umr\u00e6\u00f0u<\/a> v\u00ed\u00f0a um heim, ekki s\u00edst vegna \u00feess, a\u00f0 sp\u00e1in var bygg\u00f0 \u00e1 \u00feyngdarfr\u00e6\u00f0i Newtons (sj\u00e1 n\u00e1nar s\u00ed\u00f0ar \u00ed \u00feessari f\u00e6rslu). \u00dea\u00f0 er \u00fev\u00ed ekki \u00f3sennilegt, a\u00f0 s\u00e1 almenni \u00e1hugi hafi r\u00e1\u00f0i\u00f0 vali Stef\u00e1ns \u00e1 umfj\u00f6llunarefni.<\/p>\n<figure id=\"attachment_14686\" aria-describedby=\"caption-attachment-14686\" style=\"width: 433px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-14686\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/04\/SB_cometae_1758-Bls_1-241x300.png\" alt=\"\" width=\"433\" height=\"539\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/04\/SB_cometae_1758-Bls_1-241x300.png 241w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/04\/SB_cometae_1758-Bls_1-824x1024.png 824w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/04\/SB_cometae_1758-Bls_1-768x954.png 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/04\/SB_cometae_1758-Bls_1.png 1014w\" sizes=\"auto, (max-width: 433px) 100vw, 433px\" \/><figcaption id=\"caption-attachment-14686\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Fyrsta s\u00ed\u00f0an \u00ed disp\u00fatat\u00edu <a href=\"https:\/\/uni.hi.is\/einar\/2017\/10\/18\/aflfraedi-i-verkum-stefans-bjornssonar\/\">Stef\u00e1ns Bj\u00f6rnssonar<\/a> <a href=\"https:\/\/notendur.hi.is\/einar\/SAGA\/SB_cometae_1758.pdf\">Um verkan halastjarna, sem ganga ni\u00f0ur \u00ed reikistj\u00f6rnukerfi vort<\/a> fr\u00e1 1758. H\u00f6fundurinn byrjar \u00e1 \u00fev\u00ed a\u00f0 setja fram \u00feyngdarl\u00f6gm\u00e1li\u00f0 me\u00f0 or\u00f0unum \u201e<em>Allir hlutir \u00ed heimi dragast gagnkv\u00e6mt hver a\u00f0 \u00f6\u00f0rum og toga gagnkv\u00e6mt hver \u00ed annan \u00ed samsettu hlutfalli, beinu vi\u00f0 efnismagn og \u00f6fugu vi\u00f0 kva\u00f0rat fjarl\u00e6g\u00f0anna milli mi\u00f0punkta \u00feeirra.<\/em>\u201c S\u00ed\u00f0an f\u00e6rir hann r\u00f6k fyrir \u00fev\u00ed, a\u00f0 halastj\u00f6rnur s\u00e9u himintungl og l\u00fati \u00fev\u00ed \u00feyngdarl\u00f6gm\u00e1linu.<br \/><\/span><\/figcaption><\/figure>\n<p>Disp\u00fatat\u00edan, sem \u00f6ll er bygg\u00f0 \u00e1 n\u00e1tt\u00faruspeki og heimsmynd Newtons, fjallar \u00edtarlega um \u00feyngdarl\u00f6gm\u00e1li\u00f0 og l\u00fdsir \u00fev\u00ed \u00ed nokkrum sm\u00e1atri\u00f0um, hvernig halastj\u00f6rnur hreyfast vegna \u00feyngdarhrifa s\u00f3larinnar. Jafnframt r\u00e6\u00f0ir Stef\u00e1n truflandi \u00e1hrif halastjarna \u00e1 hreyfingu s\u00f3lar og reikistjarna og einnig um sj\u00e1varf\u00f6ll af \u00feeirra v\u00f6ldum sem og \u00fdmislegt anna\u00f0 \u00e1hugavert. R\u00e9tt er a\u00f0 geta \u00feess, a\u00f0 Stef\u00e1n nefnir \u00fea\u00f0 oftar en einu sinni, a\u00f0 \u00feyngdarhrif halastjarnanna s\u00e9u reyndar mj\u00f6g l\u00edtil og sennilega \u00f3m\u00e6lanleg. Einnig m\u00e1 nefna, a\u00f0 \u00ed 6. grein disp\u00fatat\u00edunnar setur hann fram markhyggjur\u00f6k fyrir tilviljankenndri dreifingu halastj\u00f6rnubrauta og v\u00edsar \u00fear beint \u00ed 3. efnisgreinina \u00ed eftirm\u00e1la (Scolium generale) <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1la n\u00e1tt\u00faruspekinnar<\/em>.<\/p>\n<p>Eftir \u00feessa l\u00fdsingu, kynnu lesendur a\u00f0 halda, a\u00f0 Stef\u00e1n hafi veri\u00f0 gallhar\u00f0ur nj\u00fatonisti. Svo vir\u00f0ist \u00fe\u00f3 ekki hafa veri\u00f0, \u00fev\u00ed \u00fe\u00f3tt hann s\u00e9 s\u00e1ttur vi\u00f0 \u00feyngdarl\u00f6gm\u00e1li\u00f0 og notkun \u00feess, sam\u00feykkir hann ekki fjarhrif a\u00f0 h\u00e6tti Newtons. \u00dea\u00f0 vi\u00f0horf kemur fram \u00ed n\u00fdrri disp\u00fat\u00edu hans \u00e1ri\u00f0 1759, sem ber hi\u00f0 s\u00e9rkennilega heiti, <a href=\"https:\/\/uni.hi.is\/einar\/files\/2020\/09\/SB-Stjo\u0308_L\u00e6knisl_1759.pdf\">De usu astronomi\u00e6 in medicina cujus pr\u00e6liminaria de influxu corporum c\u00e6lestium systemmatis nostri solaris in tellurem nostram mediante illuminaria et magnetica<\/a> (<em>Um gagnsemi stj\u00f6rnufr\u00e6\u00f0i \u00ed l\u00e6knislist: Inngangur um \u00e1hrif himinhnatta s\u00f3lkerfis vors \u00e1 j\u00f6r\u00f0 vora me\u00f0 lj\u00f3safli og segulafli<\/em>).<\/p>\n<p>\u00cd disp\u00fat\u00edunni afneitar Stef\u00e1n fjarhrifum strax \u00ed upphafi og segir:<\/p>\n<blockquote><p>Af \u00fev\u00ed lei\u00f0ir a\u00f0 \u00f3rav\u00edddir himins \u00ed \u00f6llu s\u00f3lkerfi voru, allt fr\u00e1 yfirbor\u00f0i s\u00f3lar vorrar, ekki a\u00f0eins \u00fat fyrir Sat\u00farnus, heldur einnig fjarl\u00e6gustu halastj\u00f6rnur, eru gagnteknar og fylltar einhverju afar f\u00ednger\u00f0u efni, og me\u00f0 \u00feeim mi\u00f0li hafa allir hlutir \u00ed kerfi voru gagnkv\u00e6m \u00e1hrif hver \u00e1 annan. \u00deetta efni nefnist almennt vaki og er skipt ni\u00f0ur \u00ed \u00f6nnur fleiri, t.d.\u00a0 lj\u00f3svaka, og <em>[&#8230;]<\/em> a\u00f0dr\u00e1ttarvaka, og a\u00f0rir b\u00e6ta vi\u00f0 \u00feyngdarvaka og varmavaka.<\/p><\/blockquote>\n<p>S\u00ed\u00f0an b\u00e6tir hann vi\u00f0:<\/p>\n<blockquote><p>En hvort v\u00edddir himins s\u00e9u \u00fe\u00e9ttfylltar vaka me\u00f0 hreint engu t\u00f3mar\u00fami, e\u00f0a fyrir komi \u00ed v\u00ed\u00f0\u00e1ttunni eitthvert t\u00f3m \u00e1 v\u00ed\u00f0 og dreif, og hinga\u00f0 og \u00feanga\u00f0 s\u00e9u dreif\u00f0ar gloppur gj\u00f6rsamlega \u00e1n vaka, er atri\u00f0i sem h\u00e9r ver\u00f0ur l\u00e1ti\u00f0 liggja \u00e1 milli hluta. Fylgismenn Newtons verja kenninguna um t\u00f3m, og henni til stu\u00f0nings f\u00e6rir hinn virti <a href=\"https:\/\/en.wikipedia.org\/wiki\/Willem_%27s_Gravesande\">Gravesande<\/a> afar kn\u00fdjandi r\u00f6k \u00ed 12. kafla 6. b\u00f3kar ritsins <em>[<a href=\"https:\/\/books.google.is\/books?id=U7c-AAAAcAAJ&amp;source=gbs_navlinks_s\">Physices elementa mathematica: sive introductio ad philosophiam Newtonianam<\/a>]<\/em>. Leibniz og fylgismenn hans verja kenninguna um efnisfyllingu.<\/p><\/blockquote>\n<p>\u00cd framhaldinu fjallar Stef\u00e1n svo \u00ed talsvert l\u00f6ngu m\u00e1li um eiginleika s\u00f3larlj\u00f3ssins og \u00e1hrif \u00feess \u00e1 j\u00f6r\u00f0ina og \u00edb\u00faa hennar. \u00cd \u00fev\u00ed sambandi vitnar hann me\u00f0al annars \u00ed <a href=\"https:\/\/en.wikipedia.org\/wiki\/Opticks\">Lj\u00f3sfr\u00e6\u00f0i<\/a> Newtons, <a href=\"https:\/\/books.google.is\/books?id=vJvk8UJDiBAC&amp;source=gbs_navlinks_s\">Efnafr\u00e6\u00f0i<\/a> eftir <a href=\"https:\/\/en.wikipedia.org\/wiki\/Herman_Boerhaave\">H. Boerhaave<\/a> og \u00fdmis fleiri rit.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center\"><strong><span style=\"font-size: 14pt\">\u00deyngdin \u00ed fyrstu \u00edslensku fr\u00e6\u00f0sluritunum<\/span><\/strong><\/h3>\n<p>Eins og \u00e1\u00f0ur hefur veri\u00f0 minnst \u00e1, var\u00f0 \u00feyngdarfr\u00e6\u00f0i Newtons fyrst hluti af n\u00e1msefni Hafnarh\u00e1sk\u00f3la eftir a\u00f0 <a href=\"https:\/\/da.wikipedia.org\/wiki\/Thomas_Bugge\">Thomas Bugge<\/a> var\u00f0 pr\u00f3fessor \u00ed stj\u00f6rnufr\u00e6\u00f0i \u00e1ri\u00f0 1777. \u00de\u00f3tt \u00edtarlega s\u00e9 um hana fjalla\u00f0 \u00ed <span class=\"fn\"><span dir=\"ltr\"><a href=\"https:\/\/books.google.is\/books?id=eoVaAAAAcAAJ&amp;hl=is&amp;source=gbs_navlinks_s\">kennslub\u00f3k<\/a><\/span><\/span> hans fr\u00e1 1796 (sj\u00e1 umfj\u00f6llunina fr\u00e1 og me\u00f0 bls. 128) er ekki lj\u00f3st, hversu n\u00e1kv\u00e6mlega hann f\u00f3r \u00ed efni\u00f0 \u00ed kennslunni. Hins vegar er vita\u00f0 um \u00fdmsa st\u00fadenta og l\u00e6rd\u00f3msmenn \u00ed Danaveldi, til d\u00e6mis Stef\u00e1n Bj\u00f6rnsson, sem kynntu s\u00e9r\u00a0 \u00feyngdarfr\u00e6\u00f0ina \u00e1 eigin sp\u00fdtur, \u00e1\u00f0ur en Bugge var\u00f0 pr\u00f3fessor.<\/p>\n<ul>\n<li>H. Kragh, 2012: <a href=\"http:\/\/css.au.dk\/fileadmin\/reposs\/reposs-019.pdf\">Newtonianism in the Scandinavian Countries, 1690\u20131790<\/a><\/li>\n<\/ul>\n<p>H\u00e9r heima, birtist fyrsta al\u00fe\u00fd\u00f0lega umfj\u00f6llunin um \u00feyngdina \u00ed <a href=\"https:\/\/timarit.is\/page\/964484\">N\u00e1tt\u00faruhistor\u00edu<\/a> B\u00fcschings \u00e1ri\u00f0 1782 (bls. 240):<\/p>\n<blockquote><p>Hvar sem men standa \u00e1 jardarhnettinum, finiz \u00feat \u00e6tid vera \u00e1 \u00feeim hlutanum, sem upp sn\u00fdr, en skilja eigi, at f\u00f3lk megi standa undir j\u00f6rdunni ser andsp\u00e6nis; \u00fev\u00ed svo \u00feykir, sem h\u00f6fudin h\u00e1ngi, og mundi ski\u00f3tt detta nidr; en \u00fev\u00ed er eigi svo varit, helldr er j\u00f6rdin l\u00edk st\u00f3rri segulsteinsk\u00falu; \u00fe\u00e1 henni er vellt \u00ed j\u00e1rnsvarfi, \u00fe\u00e1 dregr h\u00fan \u00feat til s\u00edn, svo kornin h\u00e1nga vid hana, b\u00e6di at ofan og nedanverdu; \u00e1 sama h\u00e1tt dregr og j\u00f6rdin alla hluti til s\u00edn, sem um hana eru. Hvar sem madr er staddr, hefir hann himininn yfir h\u00f6fdi, og j\u00f6rdina undir f\u00f3tum ser; ber \u00feessi jardarinnar sk\u00f6pun li\u00f3sliga vitni um Guds v\u00edsd\u00f3m; \u00fev\u00ed \u00feessvegna kunna men b\u00e6di at ferdaz \u00ed kr\u00edngum hana alla, sem t\u00eddum hefir gi\u00f6rt verit, og gi\u00f6riz, en t\u00e6kiz \u00f3m\u00f6guliga, ef h\u00fan eigi v\u00e6ri hn\u00f6tt\u00f3tt; og \u00fear med kann j\u00f6rdin si\u00e1lf \u00fev\u00ed audvelldar at sn\u00faaz svo sem \u00e1 \u00feolinm\u00f3di, og g\u00e1nga umhverfis s\u00f3lina.<\/p><\/blockquote>\n<p>\u00de\u00f3tt \u00ed lok tilvitnunarinnar komi sk\u00fdrt fram, a\u00f0 B\u00fcsching s\u00e9 s\u00e1ttur vi\u00f0 s\u00f3lmi\u00f0jukenninguna og \u00feekki til m\u00f6ndulsn\u00fanings jar\u00f0ar, er umfj\u00f6llun hans um \u00feyngdina frekar forneskjuleg. Auk \u00feess er ekki minnst \u00e1 \u00fea\u00f0 \u00ed b\u00f3kinni, a\u00f0 \u00feyngdin r\u00edki l\u00edka \u00e1 \u00f6\u00f0rum hn\u00f6ttum og milli himintungla.<\/p>\n<p>Svipa\u00f0a, en gagnlegri umfj\u00f6llun, er a\u00f0 finna hj\u00e1 Magn\u00fasi Stephensen \u00ed <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=970277\">Alstirnda himninum<\/a> fr\u00e1 1797 (bls. 34-35). Til vi\u00f0b\u00f3tar hefur Magn\u00fasi e\u00f0lilega \u00fe\u00f3tt mikilv\u00e6gt a\u00f0 sannf\u00e6ra landsmenn um hnattl\u00f6gun jar\u00f0arinnar (bls. 36-38) og notar til \u00feess r\u00f6ksemdaf\u00e6rslu, sem haf\u00f0i veri\u00f0 vel \u00feekkt \u00ed Evr\u00f3pu fr\u00e1 \u00fev\u00ed \u00e1 d\u00f6gum Forn-Grikkja. Henni er reyndar enn beitt \u00ed al\u00fe\u00fd\u00f0legum fr\u00e6\u00f0sluritum og kennslub\u00f3kum fyrir byrjendur.<\/p>\n<figure id=\"attachment_16439\" aria-describedby=\"caption-attachment-16439\" style=\"width: 353px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16439\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/09\/Sacrobosco-1550-B3r-203x300.jpg\" alt=\"\" width=\"353\" height=\"522\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Sacrobosco-1550-B3r-203x300.jpg 203w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Sacrobosco-1550-B3r-691x1024.jpg 691w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Sacrobosco-1550-B3r-768x1138.jpg 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Sacrobosco-1550-B3r-1037x1536.jpg 1037w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Sacrobosco-1550-B3r.jpg 1080w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\" \/><figcaption id=\"caption-attachment-16439\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">S\u00ed\u00f0a \u00far kennslub\u00f3k <a href=\"https:\/\/en.wikipedia.org\/wiki\/Johannes_de_Sacrobosco\">Sacroboscos<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/De_sphaera_mundi\">De Spheara<\/a> (<em>Um k\u00faluna<\/em>), fr\u00e1 1550. \u00dearna er, me\u00f0 hj\u00e1lp sk\u00fdringarmynda,\u00a0 fjalla\u00f0 um r\u00f6kin fyrir hnattl\u00f6gun jar\u00f0ar. Efst til vinstri m\u00e1 sj\u00e1 menn \u00e1 mismunandi st\u00f6\u00f0um \u00e1 yfirbor\u00f0i jar\u00f0k\u00falunnar. Strikin, sem tengja \u00fe\u00e1 vi\u00f0 stj\u00f6rnur \u00e1\u00a0 himink\u00falunni, s\u00fdna a\u00f0 \u00feeir sj\u00e1 ekki allir s\u00f6mu stj\u00f6rnurnar. \u00cd efra horninu til h\u00e6gri m\u00e1 sj\u00e1 tunglmyrkva. Af bogadregnum skugga jar\u00f0ar \u00e1 tunglyfir-bor\u00f0inu m\u00e1 \u00e1lykta a\u00f0 j\u00f6r\u00f0in s\u00e9 k\u00fala. Ne\u00f0st er svo s\u00fdnt, hvernig sj\u00e1 m\u00e1 hnattl\u00f6gun jar\u00f0ar me\u00f0 \u00fev\u00ed a\u00f0 fylgjast me\u00f0 hvarfi skips, sem siglir yfir sj\u00f3ndeildarhringinn. &#8211;\u00a0 Svipa\u00f0a umfj\u00f6llun fr\u00e1 13. \u00f6ld er a\u00f0 finna \u00ed <a href=\"http:\/\/baekur.is\/bok\/000331679\/0\/7\/Rimbegla\">R\u00edmbeglu<\/a>-\u00fatg\u00e1fu Stef\u00e1ns Bj\u00f6rnssonar fr\u00e1 1780 (IV. partur, \u00a751-53, bls. 466-468. &#8211; Sj\u00e1 einnig \u00ed <a href=\"https:\/\/rafhladan.is\/handle\/10802\/4962\">Alfr\u00e6\u00f0i \u00edslenzkri II<\/a>, bls. 104-105).<br \/><\/span><\/figcaption><\/figure>\n<p>Fj\u00f3rt\u00e1n \u00e1rum \u00e1\u00f0ur en <em>Alstirni himinninn<\/em> kom \u00fat, fjalla\u00f0i Magn\u00fas stuttlega um \u00feyngarkraftinn \u00ed ritger\u00f0inni <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=964679\">Um meteora<\/a>, \u00fe\u00e1 n\u00fdb\u00fainn a\u00f0 l\u00e6ra n\u00e1tt\u00faruspeki hj\u00e1 Kratzenstein og stj\u00f6rnufr\u00e6\u00f0i hj\u00e1 Bugge. \u00dear segir hann \u00e1 bls. 154:<\/p>\n<blockquote><p>Allir himinknettir hafa, nockurskonar <span style=\"text-decoration: underline\"><em>dr\u00e1ttarkrapt<\/em><\/span> (vim attractivam), ecki \u00f3l\u00edkt segulsteininum, \u00feat er: ad draga hverr annann til s\u00edn, edr eins og N\u00e1tt\u00faruspekingar segia: \u00fe\u00fdngia hv\u00f6rr \u00e1 m\u00f3ti \u00f6drum, \u00feat er: s\u00fdna vidleitni til at falla hv\u00f6rr \u00e1 annann, af eiginn \u00fe\u00fanga s\u00ednum, eins og til d\u00e6mis steinn, sem kastat er \u00ed lopt upp, s\u00e6kir \u00f3dum nidr til jardar.<\/p>\n<p>\u00c1 \u00feenna h\u00e1tt \u00fe\u00fdngir j\u00f6rdin \u00e1 m\u00f3ti s\u00f3lu og t\u00fangli, og s\u00f3l og t\u00fangl aptr \u00ed m\u00f3ti j\u00f6rdunni; en \u00fear s\u00f3lin er hartn\u00e6r 500 sinnum lengra burt fr\u00e1 j\u00f6rdunni, enn t\u00fanglit, \u00fe\u00e1 er einninn <span style=\"text-decoration: underline\"><em>\u00fe\u00fdng\u00edng <\/em><\/span>(gravitatio) hennar \u00ed m\u00f3ti j\u00f6rdunni l\u00e1ngtum minni en t\u00fanglsins; \u00fe\u00f3 m\u00e1 hverki s\u00f3l ne t\u00fangl hamla, edur kippa henna til muna \u00fat af g\u00e1ngveg s\u00ednum, en fl\u00f3di og fi\u00f6ru meiga \u00feau til leidar koma.<\/p><\/blockquote>\n<p>A\u00f0 \u00fev\u00ed \u00e9g best veit, er \u00feetta fyrsta tilraun \u00edslensks h\u00f6fundar til a\u00f0 \u00fatsk\u00fdra \u00feyngdarhugtak Newtons fyrir l\u00f6ndum s\u00ednum \u00e1 m\u00f3\u00f0urm\u00e1linu.\u00a0 \u00deetta var \u00e1ri\u00f0 1783, 96 \u00e1rum eftir a\u00f0 <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1l n\u00e1tt\u00faruspekinnar<\/em> komu \u00fat. Newton er \u00fe\u00f3 hvergi nefndur, hvorki h\u00e9r, n\u00e9 \u00ed greinum Magn\u00fasar um stj\u00f6rnufr\u00e6\u00f0i \u00e1ri\u00f0 1797. \u00dear minnist hann \u00fe\u00f3 \u00e1 nokkra \u00feekkta stjarnv\u00edsindamenn, sem uppi voru eftir daga Newtons.<\/p>\n<figure id=\"attachment_13666\" aria-describedby=\"caption-attachment-13666\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-13666\" src=\"http:\/\/uni.hi.is\/einar\/files\/2019\/11\/MagnusSteph-186x300.jpg\" alt=\"\" width=\"310\" height=\"500\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/11\/MagnusSteph-186x300.jpg 186w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/11\/MagnusSteph.jpg 418w\" sizes=\"auto, (max-width: 310px) 100vw, 310px\" \/><figcaption id=\"caption-attachment-13666\" class=\"wp-caption-text\"><a href=\"https:\/\/uni.hi.is\/einar\/2017\/11\/05\/magnus-stephensen-og-natturunnar-yndislegu-fraedi\/\"><span style=\"font-size: 10pt\">Magn\u00fas Stephensen<\/span><\/a>, Fyrsti \u00cdslendingurinn, sem ger\u00f0i tilraun til a\u00f0 \u00fatsk\u00fdra \u00feyngdina fyrir almenningi \u00e1 \u00cdslandi. &#8211;\u00a0<span style=\"font-size: 10pt\"> Teikning eftir m\u00e1lverki C. A. Jensen fr\u00e1 1826.<\/span><\/figcaption><\/figure>\n<p>Nafn Newtons kemur fyrst fyrir \u00ed \u00edslensku al\u00fe\u00fd\u00f0uriti \u00ed ne\u00f0anm\u00e1lsgrein\u00a0 J\u00f3ns l\u00e6r\u00f0a J\u00f3nssonar \u00ed <a href=\"http:\/\/baekur.is\/bok\/000380271\/0\/5\/Sa_gudlega_thenkjandi_Bls_5\">N\u00e1tt\u00farusko\u00f0ara<\/a> Suhms \u00e1ri\u00f0 1798. \u00dear segir hann um hnattl\u00f6gun jar\u00f0ar \u00e1 bls. 7-8 og v\u00edsar b\u00e6\u00f0i \u00ed <em>Astro- et physico-Theologie<\/em> eftir <a href=\"https:\/\/en.wikipedia.org\/wiki\/William_Derham\">W. Derham<\/a> og fyrsta hlutann af <a href=\"https:\/\/books.google.is\/books?id=9Nui3zGEyhIC&amp;source=gbs_similarbooks\">Naturlehre<\/a> eftir <a href=\"https:\/\/de.wikipedia.org\/wiki\/Johann_Gottlob_Kr%C3%BCger\">J. G. Kr\u00fcger<\/a>:<\/p>\n<blockquote><p>Ad j\u00f6rdin hn\u00f6tt\u00f3tt er, heldur enn \u00ed annari mind, leidir Newton \u00fe\u00e1 ors\u00f6k til, ad allir partar jardar s\u00e6kja ad hennar midp\u00fankti, og ad \u00feessi dr\u00e1ttar-kraptur s\u00e9 \u00ed \u00f6llum hlutum, sj\u00e1um vjer medal annars af vatns- og regn-dropunum, sem \u00e1valt hn\u00f6tt\u00f3ttir eru medan \u00feeir falla \u00edgegnum loptid, hv\u00f6rri mind \u00feeir halda eins \u00ed lopt-t\u00f3mu r\u00fami sem ella, er vottar, ad \u00feryck\u00edngar kraptur loptsins ollir \u00fev\u00ed ecki einskostar. En hinu, ad j\u00f6rdin er \u00fe\u00f3 ecki rett hn\u00f6tt\u00f3tt, heldur flatari undir heims-endunum, enn bruna-beltinu, \u00fev\u00ed veldur, n\u00e6rst hita s\u00f3larinnar, hennar daglegi sn\u00faningur, sem verkar \u00fead, ad partar hennar vilja losna og hristast \u00ed sundur framar um midbik hennar, enn undir skautunum og\u00a0 reikna \u00fev\u00ed meistarar a\u00f0 j\u00f6rdin se fimm m\u00edlum l\u00e6gri undir \u00feeim enn brunabeltinu.<\/p><\/blockquote>\n<p>\u00cd <a href=\"https:\/\/uni.hi.is\/einar\/2020\/08\/30\/stjarnedlisfraedi-og-heimsfraedi-a-islandi-2-timabilid-1780-1870-b-stjarnedlisfraedi-fyrir-daga-newtons\/\">s\u00ed\u00f0ustu f\u00e6rslu<\/a> var geti\u00f0 um\u00a0 tilraun J\u00f3ns \u00ed <em>N\u00e1tt\u00farusko\u00f0ara<\/em> til a\u00f0 \u00fatsk\u00fdra \u00feyngdarkraftinn, me\u00f0 \u00fev\u00ed a\u00f0 notast vi\u00f0 ellefu \u00e1ra gamla b\u00f3k\u00a0 Bastholms, <a href=\"https:\/\/books.google.is\/books?id=A943ngEACAAJ&amp;source=gbs_navlinks_s\">Philosophie for Ul\u00e6rde<\/a>. \u00cd einni af ne\u00f0anm\u00e1lsgreinum s\u00ednum segir J\u00f3n (bls. 96-97):<\/p>\n<blockquote><p>Hvad \u00fev\u00ed valdi ad s\u00f3lin dregur pl\u00e1neturnar \u00ed kr\u00edng um sig, er ad s\u00f6nnu tors\u00f3tt ad skilja, \u00fe\u00f3 f\u00e6rir Basth\u00f3lm \u00feessa saml\u00edkingu \u00fear til: steinn \u00ed sl\u00f6ngu einni leitast \u00e1 allar siddur ad flj\u00faga \u00fat fr\u00e1 hendi manns, sem er hans midp\u00fanktur. \u00deannig fylgir og pl\u00e1netunum nockurskonar kraptur, ad fl\u00fdja \u00fat fr\u00e1 s\u00ednum midp\u00fankti, sem er s\u00f3lin. En \u00fear er \u00fe\u00e1 annar gagnst\u00e6dur kraptur, sem heldur \u00feeim aptur; og hv\u00f6rr er hann? allir l\u00edkamir hafa einskonar krapt \u00feann \u00ed ser ad draga hv\u00f6rn annann til s\u00edn, t.d. \u00feegar tveir dropar vatns snerta hv\u00f6rr annann, hlaupa \u00feeir saman \u00ed einn dropa. Tveir hnettir \u00ed sama vatni, draga hv\u00f6rr annann til s\u00edn, seu \u00feeir ecki ofl\u00e1ngt hv\u00f6rr fr\u00e1 \u00f6drum. \u00deetta r\u00eds \u00fe\u00f3 af vatninu, sem er \u00ed millum hnattanna, \u00fev\u00ed annadhv\u00f6rt hlj\u00f3ta l\u00edkamirnir ad snerta hv\u00f6rr annann fyrir medal eda medalslaust, skuli \u00feeir hv\u00f6rr annann til s\u00edn draga. \u00c1 \u00feann h\u00e1tt dregur hn\u00f6tturinn \u00fead n\u00e6sta vatn til s\u00edn, \u00feetta vatn aptur \u00fead n\u00e6rsta vatn ser, og s. fr. \u00deannig s\u00fdnist \u00fev\u00ed varid um \u00fe\u00e1 himnesku l\u00edkami. \u00dear er til, sem sagt er <em>[\u00ed 3. ne\u00f0anm\u00e1lsgrein, bls. 11]<\/em> rennandi \u00e6theriskt efni, \u00ed hv\u00f6rju s\u00f3lin og allar hennar pl\u00e1netur sveima. S\u00f3lin dregur \u00feetta efni til s\u00edn, og \u00fead aptur pl\u00e1neturnar. \u00deegar \u00feessi kraptur er jafnst\u00f3r \u00feeim kraptinum, sem dr\u00edfa vill pl\u00e1neturnar \u00fat fr\u00e1 s\u00ednum midp\u00fankti, hlj\u00f3ta \u00fe\u00e6r vafalaust ad flj\u00faga \u00ed kr\u00edngum s\u00f3lina, eins og steinninn \u00ed slaungunni um kr\u00edng h\u00f6ndina.<\/p><\/blockquote>\n<p>\u00dearna er blanda\u00f0 saman hugmyndafr\u00e6\u00f0i Descartes og Newtons \u00e1 d\u00e1l\u00edti\u00f0 skondinn og ruglandi h\u00e1tt.\u00a0 Sl\u00edkt mun v\u00edst hafa veri\u00f0 algengt \u00ed al\u00fe\u00fd\u00f0uritum \u00e1 \u00e1tj\u00e1ndu \u00f6ld og eldurspegl-ar \u00e1n efa, hversu erfitt \u00fea\u00f0 var \u00e1 s\u00ednum t\u00edma a\u00f0 n\u00e1 t\u00f6kum \u00e1 kenningum Newtons um aflfr\u00e6\u00f0i og \u00feyngd. Eins og sj\u00e1 m\u00e1 hj\u00e1 J\u00f3ni l\u00e6r\u00f0a, gripu h\u00f6fundar e\u00f0lilega oft til \u00feess r\u00e1\u00f0s a\u00f0 tala um <a href=\"https:\/\/en.wikipedia.org\/wiki\/History_of_centrifugal_and_centripetal_forces\">mi\u00f0fl\u00f3tta- og mi\u00f0s\u00f3knarkrafta<\/a> til a\u00f0 au\u00f0velda skilning. Anna\u00f0 d\u00e6mi um sl\u00edkt er a\u00f0 finna \u00ed <a href=\"https:\/\/baekur.is\/bok\/000144122\/Almenn\">Almennri landaskipunarfr\u00e6di<\/a> (bls. 13):<\/p>\n<blockquote><p>Ad manneskiur og adrir hlutir \u00e1 hnettinum ecki hvirflast \u00fat \u00ed buskan, k\u00e9mur af \u00fev\u00ed, ad allir hlutir leita nidur ad midp\u00fankti jardar, og \u00feessi addr\u00e1ttarkraptur jardar (vis centripetalis) yfirgeingur mi\u00f6g framfararflugid (flegis edur slaungukraptinn vis centrifuga) sem sn\u00faningurinn k\u00e9mur til leidar \u00feegar eckert hindrar, og sem mundi f\u00e6ra hlutina \u00fat \u00ed loptid first n\u00e6rri j\u00f6rdunni, og s\u00eddan meira og meira \u00fat fr\u00e1 hveli hennar eptir beinni svokalladri snertil\u00ednu (tangent). <em>[Ne\u00f0anm\u00e1ls:]<\/em> \u00deessi \u00f3dfluga sn\u00faningr (fr\u00e1flugskraptr) veldur \u00fev\u00ed ad j\u00f6rdin er ekki \u00f6ld\u00fangis hn\u00f6tt\u00f3tt, heldur ein\u00fangis hnattarl\u00edk, og digrari um midbikid.<\/p><\/blockquote>\n<p>Um \u00feetta m\u00e1 segja, a\u00f0 h\u00f6fundum al\u00fe\u00fd\u00f0uurita \u00e1 \u00e1runum um og upp\u00far 1800 tekst misvel upp, hva\u00f0 \u00fatsk\u00fdringar var\u00f0ar. \u00dea\u00f0 m\u00e6tti jafnvel spyrja, hvort umfj\u00f6llunin hafi yfirleitt komi\u00f0 lesendum a\u00f0 gagni, e\u00f0a bara rugla\u00f0 \u00fe\u00e1 enn frekar \u00ed r\u00edminu.<\/p>\n<p>N\u00e6st \u00e1 eftir Stef\u00e1ni Bj\u00f6rnssyni er \u00fea\u00f0 Bj\u00f6rn Gunnlaugsson, sem fyrstur \u00cdslendinga \u00f6\u00f0la\u00f0ist fullan skilning \u00e1 \u00feyngdarfr\u00e6\u00f0i Newtons. \u00dev\u00ed mi\u00f0ur liggur l\u00edti\u00f0 eftir hann um efni\u00f0 \u00e1 prenti, en auglj\u00f3st er af \u00feeim verkum, sem hann \u00fe\u00f3 birti, a\u00f0 hann hefur kunna\u00f0 a\u00f0 beita \u00feyngdarl\u00f6gm\u00e1linu vi\u00f0 \u00fatreikninga (sj\u00e1 n\u00e1nar h\u00e9r \u00e1 eftir og f\u00e6rsluna <a href=\"https:\/\/uni.hi.is\/einar\/2018\/06\/24\/halastjarnan-mikla-arid-1858-maelingar-og-hughrif-i-upphafi-nyrra-tima-i-stjornufraedi\/\">um halastj\u00f6rnuna 1858<\/a> &#8211; \u00ddmsa a\u00f0ra reikninga Bj\u00f6rns \u00ed \u00feyngdarfr\u00e6\u00f0i m\u00e1 finna \u00ed handritum).<\/p>\n<p>\u00dea\u00f0 kom \u00fev\u00ed \u00ed hlut nemanda Bj\u00f6rns, J\u00f3nasar Hallgr\u00edmssonar, a\u00f0 f\u00e6ra \u00edslenskum almenningi fyrstu n\u00e1kv\u00e6mu uppl\u00fdsingarnar um \u00feyngdarfr\u00e6\u00f0i Newtons. Segja m\u00e1, a\u00f0 me\u00f0 \u00fe\u00fd\u00f0ingum s\u00ednum og ritger\u00f0um hafi hann teki\u00f0 vi\u00f0 keflinu af Magn\u00fasi Stephensen, sem mikilv\u00e6gasti al\u00fe\u00fd\u00f0ufr\u00e6\u00f0ari \u00cdslendinga um raunv\u00edsindaleg efni \u00e1 fyrri hluta \u00e1tj\u00e1ndu aldar.<\/p>\n<p>J\u00f3nas fjallar \u00ed fyrsta sinn um \u00feyngdina innan um anna\u00f0 efni \u00ed ritger\u00f0inni <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=2012172\">Um e\u00f0li og uppruna jar\u00f0arinnar<\/a> \u00e1ri\u00f0 1835. Um gu\u00f0, n\u00e1tt\u00farul\u00f6gm\u00e1l og \u00feyngd hefur hann \u00feetta a\u00f0 segja (bls. 111):<\/p>\n<blockquote><p>Hva\u00f0 \u00f6blum n\u00e1tt\u00farunnar og e\u00fdl\u00edfa l\u00f6gm\u00e1li vi\u00f0v\u00edkur, \u00fe\u00e1 sj\u00e1 menn einnig vi\u00f0 n\u00e1kv\u00e6mari \u00edhugun, a\u00f0 \u00feau reyndar eru in endanlega mind, er oss au\u00f0nast a\u00f0 sj\u00e1 vilja gu\u00f0s og hina e\u00fdl\u00edfu skynsemi \u00ed; enn hj\u00e1 sj\u00e1lfum gu\u00f0i er eingin umbre\u00fdting n\u00e9 umbreit\u00edngarskuggi, so gu\u00f0r\u00e6kileg sko\u00f0un hlutanna hl\u00fdtur, ekki s\u00ed\u00f0ur enn heimspekilegar rans\u00f3knir, a\u00f0 lei\u00f0a menn \u00e1 \u00fe\u00e1 sannf\u00e6r\u00edngu, a\u00f0 l\u00f6gm\u00e1l n\u00e1tt\u00farunnar se e\u00fdl\u00edft og \u00f3umbreytanlegt. \u00dev\u00ed fer so fj\u00e6rri a\u00f0 alm\u00e6tti gu\u00f0s og frj\u00e1lsu vizku s\u00e9 neita\u00f0 fyrir \u00fea\u00f0, a\u00f0 einmitt af \u00fev\u00ed inn frj\u00e1lsi gu\u00f0 er fullkominn og \u00f3takmarka\u00f0ur, hlj\u00f3ta hans gj\u00f6r\u00f0ir fyrir vorum augum a\u00f0 l\u00edta \u00fat sem e\u00fdl\u00edf og obifanleg l\u00f6g, er allir hlutir ver\u00f0i a\u00f0 hl\u00fd\u00f0a, T\u00f6kum til d\u00e6mis \u00fe\u00fdngdina. \u00cd fyrstunni kemur h\u00fan oss fyrir sj\u00f3nir einsog almennt l\u00f6gm\u00e1l fyrir hlutina h\u00e9r \u00e1 j\u00f6r\u00f0u; vi\u00f0 n\u00e1kv\u00e6mari \u00edgrundun sj\u00e1 menn, a\u00f0 h\u00fan er a\u00f0dr\u00e1ttar kraftur allra skapa\u00f0ra hluta s\u00edn \u00e1 milli; ennfremur, a\u00f0 h\u00fan er s\u00e1 ablfj\u00f6tur, sem tengir saman alheiminn, og loksins birtist h\u00fan oss sem s\u00e1 gu\u00f0legur vilji, er vi\u00f0heldur hnattakerfum heimsins \u00ed s\u00ednu fagra og undrunarver\u00f0a sambandi. H\u00e9r h\u00f6fum vi\u00f0 hafi\u00f0 oss sm\u00e1tt og sm\u00e1tt fr\u00e1 einni sko\u00f0un til annarar h\u00e1leitari, og komum \u00fear einsog annarsta\u00f0ar til \u00fee\u00edrrar \u00e1liktunar, a\u00f0 <span style=\"text-decoration: underline\"><em>upphaf allra hluta s\u00e9 gu\u00f0<\/em><\/span>.<\/p><\/blockquote>\n<p>Nokkrum s\u00ed\u00f0um aftar l\u00fdsir J\u00f3nas \u00ed nokkrum sm\u00e1atri\u00f0um hinni svok\u00f6llu\u00f0u <a href=\"https:\/\/www.fossilhunters.xyz\/inner-solar-system\/the-kantlaplace-nebular-hypothesis.html\">Kant-Laplace kenningu<\/a> um myndun s\u00f3lkerfisins, \u00fear sem \u00feyngdarafli\u00f0 kemur mj\u00f6g vi\u00f0 s\u00f6gu (kenningin ver\u00f0ur n\u00e1nar r\u00e6dd \u00ed n\u00e6stu f\u00e6rslu).<\/p>\n<p>\u00deegar tilvitnunin h\u00e9r fyrir ofan er lesin, fer ekki hj\u00e1 \u00fev\u00ed, a\u00f0 h\u00e6gt s\u00e9 a\u00f0 sj\u00e1 \u00e1kve\u00f0na saml\u00edkingu vi\u00f0 hugmyndir Newtons og \u00fdmissa annarra l\u00e6rd\u00f3msmanna um gu\u00f0 og sk\u00f6punarverki\u00f0. \u00cd \u00fev\u00ed sambandi m\u00e1 nefna, a\u00f0 v\u00ed\u00f0a er \u00fev\u00ed haldi\u00f0 fram, a\u00f0 hinn tr\u00faa\u00f0i Newton hafi innleitt hugmyndina um s\u00f3lkerfi\u00f0 sem hina fullkomnu klukku e\u00f0a sigurverk skaparans. \u00deetta er sannanlega rangt, \u00fev\u00ed fullyr\u00f0inguna m\u00e1 rekja til Descartes. Newton \u00e1tta\u00f0i sig hins vegar flj\u00f3tlega \u00e1 \u00fev\u00ed, a\u00f0 himintunglin hafa \u00feyngdar\u00e1hrif hvert \u00e1 anna\u00f0 og vi\u00f0 \u00fea\u00f0 geta\u00a0 brautir \u00feeirra truflast. Hann taldi \u00fev\u00ed, a\u00f0 ef \u00ed \u00f3efni stefndi, myndi gu\u00f0 gr\u00edpa \u00ed taumana, lei\u00f0r\u00e9tta hreyfinguna og halda s\u00f3lkerfinu st\u00f6\u00f0ugu.<\/p>\n<p>Leibniz, einn helsti gagnr\u00fdnandi Newtons, var \u00e1 \u00f6\u00f0ru m\u00e1li. \u00cd s\u00ednu fyrsta br\u00e9fi \u00ed hinum \u00feekktu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Leibniz%E2%80%93Clarke_correspondence\">br\u00e9faskiptum vi\u00f0 S. Clarke<\/a> segir hann me\u00f0al annars, a\u00f0 Newton og fylgismenn hans hafi hinar fur\u00f0ulegustu hugmyndir um verk gu\u00f0s. \u00deeir telji, a\u00f0 gu\u00f0 \u00feurfi a\u00f0 trekkja upp klukku s\u00edna \u00f6\u00f0ru hverju til a\u00f0 koma \u00ed veg fyrir a\u00f0 h\u00fan stoppi.\u00a0 Hann hafi sem sagt ekki veri\u00f0 n\u00e6gjanlega frams\u00fdnn til a\u00f0 skapa hana sem eil\u00edf\u00f0arv\u00e9l, nokku\u00f0 sem Leibniz taldi \u00f3hj\u00e1kv\u00e6milegt \u00ed hinum besta heimi allra hugsanlegra heima.<\/p>\n<p>Stuttlega ver\u00f0ur fjalla\u00f0 um st\u00f6\u00f0ugleika s\u00f3lkerfisins s\u00ed\u00f0ar \u00ed f\u00e6rslunni.<\/p>\n<ul>\n<li>S. Clarke ritstj., 1717: <a href=\"https:\/\/books.google.is\/books?id=l8WMIJEvpBAC&amp;source=gbs_navlinks_s\">A collection of papers, which passed between the late learned Mr. Leibnitz , and Dr. Clarke, in the years 1715 and 1716<\/a>.<\/li>\n<li>S. D. Snobelen, 2012: <a href=\"https:\/\/isaacnewtonstheology.files.wordpress.com\/2013\/06\/the-myth-of-the-clockwork-universe.pdf\">The Myth of the Clockwork Universe: Newton, Newtonianism, and the Enlightenment<\/a>.<\/li>\n<li>J. Henry, 2019: <a href=\"https:\/\/link.springer.com\/referenceworkentry\/10.1007\/978-3-319-20791-9_1-1\">Laws of Nature<\/a>.<\/li>\n<\/ul>\n<figure id=\"attachment_12591\" aria-describedby=\"caption-attachment-12591\" style=\"width: 309px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-12591\" src=\"http:\/\/uni.hi.is\/einar\/files\/2019\/09\/Jonash-195x300.jpg\" alt=\"\" width=\"309\" height=\"476\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/09\/Jonash-195x300.jpg 195w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2019\/09\/Jonash.jpg 325w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><figcaption id=\"caption-attachment-12591\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">V\u00edsindama\u00f0urinn og sk\u00e1ldi\u00f0 <a href=\"https:\/\/jonashallgrimsson.is\/index.php?page=visindamadurinn-jonas\">J\u00f3nas Hallgr\u00edmsson<\/a>. Teikning fr\u00e1 1845.<\/span><\/figcaption><\/figure>\n<p>\u00de\u00fd\u00f0ing og endurs\u00f6gn J\u00f3nasar Hallgr\u00edmssonar \u00e1 ritinu <a href=\"https:\/\/books.google.is\/books?id=89YyAQAAMAAJ&amp;hl=is&amp;source=gbs_navlinks_s\">Popul\u00e6rt Foredrag over Astronomien<\/a> eftir <a href=\"https:\/\/da.wikipedia.org\/wiki\/G.F._Ursin\">G. F. Ursin<\/a> kom \u00fat undir nafninu <a href=\"https:\/\/baekur.is\/bok\/000402495\/Stjornufraedi__lett_og_handa\">Stj\u00f6rnufr\u00e6\u00f0i<\/a> \u00e1ri\u00f0 1842. H\u00fan var fyrsta b\u00f3kin \u00e1 \u00edslensku, sem algj\u00f6rlega var helgu\u00f0 \u00feeirri v\u00edsindagrein.\u00a0 Danska frum\u00fatg\u00e1fan var me\u00f0al bestu al\u00fe\u00fd\u00f0urita, sem \u00fat komu \u00ed Danm\u00f6rku \u00e1 fyrri hluta \u00e1tj\u00e1ndu aldar, og hi\u00f0 sama \u00e1 vi\u00f0 h\u00e9r \u00e1 landi um snilldar\u00fe\u00fd\u00f0ingu J\u00f3nasar. B\u00f3kin er kannski ekki miki\u00f0 lesin \u00ed dag, en vi\u00f0 notum enn fj\u00f6ldann allan af <a href=\"http:\/\/timarit.is\/view_page_init.jsp?gegnirId=000508643\">n\u00fdyr\u00f0um<\/a>, sem fyrst litu dagsins lj\u00f3s \u00ed \u00fe\u00fd\u00f0ingunni.<\/p>\n<p>B\u00f3k Ursins er almennt og vanda\u00f0 yfirlit yfir sj\u00f6rnufr\u00e6\u00f0i s\u00edns t\u00edma, en h\u00e9r munum vi\u00f0 fyrst og fremst beina athyglinni a\u00f0 umfj\u00f6lluninni um \u00feyngdina. H\u00fan hefst \u00ed <em>sj\u00f6undu grein<\/em> b\u00f3karinnar (bls. 87-100) me\u00f0 stuttum inngangi um hreyfifr\u00e6\u00f0i hluta a\u00f0 h\u00e6tti Newtons.\u00a0 S\u00ed\u00f0an er r\u00e6tt um slaungulei\u00f0ina, \u00fea\u00f0 er hinn bogna veg (fleygboga), sem l\u00edkamir er sl\u00f6ngva\u00f0 er, fara vi\u00f0 yfirbor\u00f0 jar\u00f0ar. \u00de\u00e1 er fjalla\u00f0\u00a0 um hringhreyfingu og mi\u00f0fl\u00f3ttakraft og jafnframt um mi\u00f0s\u00f3knarkraftinn, \u00fea\u00f0 er a\u00f0dr\u00e1ttarkraftinn e\u00f0a \u00feyngdina.<\/p>\n<p>\u00deyngdarl\u00f6gm\u00e1l Newtons er teki\u00f0 fyrir \u00e1n allrar st\u00e6r\u00f0fr\u00e6\u00f0i \u00e1 bls. 95-96, og mun \u00fea\u00f0 vera \u00ed fyrsta sinn, sem \u00fea\u00f0 er sett fram \u00e1 \u00edslensku.<\/p>\n<p>\u00cd <em>\u00e1ttundu greininni<\/em> (bls. 100-114) er fjalla\u00f0 um \u00fea\u00f0 hvernig \u00feyngdarl\u00f6gm\u00e1li\u00f0 er nota\u00f0 til a\u00f0 \u00fatsk\u00fdra \u00fdmis fyrirb\u00e6ri \u00ed s\u00f3lkerfinu, til d\u00e6mis brautir himintungla.<\/p>\n<figure id=\"attachment_16613\" aria-describedby=\"caption-attachment-16613\" style=\"width: 408px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16613\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/09\/Ursin_Fig.20_orig-277x300.jpg\" alt=\"\" width=\"408\" height=\"442\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Ursin_Fig.20_orig-277x300.jpg 277w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Ursin_Fig.20_orig-768x831.jpg 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Ursin_Fig.20_orig.jpg 842w\" sizes=\"auto, (max-width: 408px) 100vw, 408px\" \/><figcaption id=\"caption-attachment-16613\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Mynd, sem fylgir umfj\u00f6lluninni \u00ed<em> Stj\u00f6rnufr\u00e6\u00f0i<\/em> Ursins\u00a0 um brautir hnatta \u00ed s\u00f3lkerfinu (bls. 101-105). <em>&#8211; <\/em>H\u00e9r er<em> S<\/em> mi\u00f0hn\u00f6ttur. Ef fylgihn\u00f6ttur \u00ed <em>P <\/em>hreyfist me\u00f0 \u00e1kve\u00f0num hra\u00f0a, <em>Pm<\/em>, hornr\u00e9tt \u00e1 stefnuna til <em>S, <\/em>fer hann eftir <em>hringbraut<\/em> me\u00f0 <em>S<\/em> \u00ed mi\u00f0ju. S\u00e9 hra\u00f0inn <em>PM &gt;<\/em> <em>Pm<\/em>, en samt ekki of mikill (<em>PM<\/em> &lt; \u221a2 <em>Pm<\/em>), ver\u00f0ur brautin <em>sporbaugur<\/em> me\u00f0 <em>S<\/em> \u00ed \u00feeim brennipunkti, sem er n\u00e6r <em>P<\/em>. Fir\u00f0in er \u00ed <em>A<\/em> og n\u00e1ndin \u00ed <em>P<\/em> (\u00feetta er s\u00fdnt \u00e1 myndinni). Ef <em>PM &lt; Pm<\/em> ver\u00f0ur brautin sporbaugur innan \u00ed hringnum me\u00f0 <em>S<\/em> \u00ed \u00feeim brennipunkti, sem er fj\u00e6r <em>P<\/em> og <em>P<\/em> ver\u00f0ur n\u00fa fir\u00f0arpunktur.\u00a0 Ef <em>PM<\/em> = \u221a2 <em>Pm <\/em>er brautin <em>fleygbogi<\/em>, en <em>brei\u00f0bogi<\/em> ef <em>PM<\/em> &gt; \u221a2 <em>Pm.\u00a0<\/em> &#8211;\u00a0 \u00cd s\u00f3lkerfinu hreyfast reikistj\u00f6rnurnar eftir sporbaugum um s\u00f3lina og s\u00f6mulei\u00f0is tunglin um reikistj\u00f6rnur-nar. \u00de\u00e6r halastj\u00f6rnur, sem\u00a0 ekki eru \u00e1 \u00edl\u00f6ngum sporbaugum um s\u00f3l, hreyfast \u00fdmist eftir fleygbogum s\u00f0a brei\u00f0bogum.<br \/><\/span><\/figcaption><\/figure>\n<p>\u00c1 bls.105-106 segir Ursin fr\u00e1 \u00fev\u00ed, a\u00f0 \u00feyngdarl\u00f6gm\u00e1li\u00f0 gildi \u00f3breytt um um \u201er\u00e9ttmynda\u00f0a hnetti\u201c, ef gert er r\u00e1\u00f0 fyrir, a\u00f0 allt efni \u00feeirra s\u00e9 samankomi\u00f0 \u00ed mi\u00f0punktunum. \u00de\u00e1 fer hann nokkrum or\u00f0um um \u00feriggja-hnatta vandam\u00e1li\u00f0 og truflanareikning almennt, s\u00fdnir hvernig \u00e1kvar\u00f0a m\u00e1 massa reikistjarna, fjallar um sj\u00e1varf\u00f6ll og \u00e1hrif m\u00f6ndulsn\u00fanings \u00e1\u00a0 l\u00f6gun jar\u00f0ar. \u00d6ll \u00feessi atri\u00f0i ver\u00f0a tekin betur fyrir s\u00ed\u00f0ar \u00ed f\u00e6rslunni.<\/p>\n<p>Segja m\u00e1, a\u00f0 me\u00f0 <em>Stj\u00f6rnufr\u00e6\u00f0i<\/em> Ursins hafi \u00f6llum \u00cdslendingum veri\u00f0 trygg\u00f0ur a\u00f0gangur a\u00f0 tilt\u00f6lulega a\u00f0gengilegri fr\u00e6\u00f0slu um stjarnv\u00edsindi, \u00fear \u00e1 me\u00f0al \u00feyngdarfr\u00e6\u00f0i Newtons. Fr\u00e1 og me\u00f0 1846 g\u00e1tu sk\u00f3lapiltar \u00ed Reykjav\u00edkursk\u00f3la einnig\u00a0 lesi\u00f0 s\u00e9r til um\u00a0 \u00feyngdina \u00ed kennslub\u00f3kinni <a href=\"https:\/\/books.google.is\/books?id=kCdPAAAAYAAJ&amp;hl=da&amp;source=gbs_navlinks_s\">Naturl\u00e6rens mechaniske Deel<\/a> eftir H. C. \u00d6rsted (bls. 165-220) og Bj\u00f6rn Gunnlaugsson hefur \u00e1n efa fjalla\u00f0 um \u00feyngdarfr\u00e6\u00f0ina \u00ed stj\u00f6rnufr\u00e6\u00f0it\u00edmum.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><em><strong>Sj\u00e1varf\u00f6ll<\/strong><\/em><\/p>\n<p>Tilvitnunin h\u00e9r a\u00f0 framan \u00ed vi\u00f0auka <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1la n\u00e1tt\u00faruspekinnar <\/em>hefst \u00e1 or\u00f0unum \u201eT<em>il \u00feessa h\u00f6fum vi\u00f0 beitt \u00feyngdarkraftinum til sk\u00fdringar \u00e1 fyrirb\u00e6rum himinsins og hafsins, \u00e1n \u00feess a\u00f0 nokkur sko\u00f0un hafi veri\u00f0 l\u00e1tin uppi enn\u00fe\u00e1 um ors\u00f6k\u00a0 \u00feessa krafts<\/em>.\u201c \u00dearna er Newton\u00a0 greinilega a\u00f0 v\u00edsa til \u00feess, sem hann sj\u00e1lfur taldi merkustu ni\u00f0urst\u00f6\u00f0ur \u00feyngdarfr\u00e6\u00f0i sinnar, nefnilega \u00fatsk\u00fdringarnar \u00e1 hreyfingum himintungla annars vegar, og ors\u00f6kum fl\u00f3\u00f0s og fj\u00f6ru hins vegar.<\/p>\n<ul>\n<li>Wikipedia: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Tidal_force\">Tidal force<\/a>.<\/li>\n<li>Wikipedia: <a href=\"https:\/\/en.wikipedia.org\/wiki\/Tide\">Tide<\/a>.<\/li>\n<\/ul>\n<p>Fr\u00e1 upphafi vega hafa sj\u00f3menn og a\u00f0rir \u00feeir sem vi\u00f0 strendur b\u00faa, fylgst n\u00e1i\u00f0 me\u00f0 fl\u00f3\u00f0i og fj\u00f6ru og velt v\u00f6ngum yfir ors\u00f6kum \u00feeirra. \u00cdslendingar eru \u00fear engin undanteking, eins og sj\u00e1 m\u00e1 \u00e1 \u00edslenskum mi\u00f0aldahandritum fr\u00e1 13. \u00f6ld, sem me\u00f0al annars fjalla um g\u00f6ngu tungls og s\u00f3lar og sj\u00e1varf\u00f6ll. Sj\u00e1 til d\u00e6mis <a href=\"http:\/\/baekur.is\/bok\/000331679\/0\/7\/Rimbegla\">R\u00edmbeglu<\/a>-\u00fatg\u00e1fu Stef\u00e1ns Bj\u00f6rnssonar (IV. partur, \u00a710-31, bls. 438-452 og \u00a767-68, bls. 478) og s\u00f6mu greinar \u00ed <a href=\"https:\/\/rafhladan.is\/handle\/10802\/4962\">Alfr\u00e6\u00f0i \u00edslenzkri II<\/a>.<\/p>\n<p>\u00c1ri\u00f0 1783 fjalla\u00f0i Magn\u00fas Stephensen all \u00edtarlega um fl\u00f3\u00f0 og fj\u00f6ru \u00ed hinni miklu grein sinni <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=964679\">Um meteora<\/a> (\u00a718, bls. 154-158) og vitnar me\u00f0al annars \u00ed ritger\u00f0ina <a href=\"https:\/\/dibiki.ub.uni-kiel.de\/viewer\/object\/PPN680063811\/1\/\">Theoriam Cursus Oceani<\/a> eftir fyrrum kennara sinn, C. G. Kratzenstein. \u00c1n \u00feess a\u00f0 nefna Newton \u00e1 nafn, greinir hann fr\u00e1 \u00fev\u00ed, a\u00f0 sj\u00e1varf\u00f6ll stafi af \u00feyngdarkr\u00f6ftum t\u00fangls og s\u00f3lar, fjallar um st\u00f3rstreymi og sm\u00e1streymi og r\u00e6\u00f0ir almennt um heg\u00f0un sj\u00e1varfalla v\u00ed\u00f0a um heim.<\/p>\n<p>\u00der\u00e1tt fyrir gagnlegar l\u00fdsingar, er lj\u00f3st, a\u00f0 Magn\u00fas hefur ekki fullan skilning \u00e1 \u00feyngdarfr\u00e6\u00f0i Newtons og \u00fatsk\u00fdringar hans \u00e1 \u00feyngdar\u00e1hrifum eru \u00f3fulln\u00e6gjandi, a\u00f0 minnsta kosti s\u00e9\u00f0 fr\u00e1 sj\u00f3narh\u00f3li n\u00fat\u00edmans.\u00a0 \u00deetta kemur \u00fe\u00f3 ekki \u00e1 \u00f3vart, \u00fev\u00ed sj\u00e1varfallafr\u00e6\u00f0i er ekki eins au\u00f0veld vi\u00f0ureignar og sumir kunna a\u00f0 halda. A\u00f0ra gagnlega, en jafnframt \u00f3fullkomna umfj\u00f6llun um efni\u00f0, er a\u00f0 finna \u00ed <a href=\"https:\/\/baekur.is\/bok\/000144122\/Almenn\">Almennri landaskipunarfr\u00e6di<\/a> fr\u00e1 1821 (\u00a740, bls. 143-148). \u00dear, eins og hj\u00e1 Magn\u00fasi, g\u00e6tir nokkurs misskilnings um \u00fea\u00f0, hvernig \u00feyngdafli\u00f0 veldur sj\u00e1varf\u00f6llum.<\/p>\n<p>\u00dea\u00f0 er fyrst me\u00f0 <a href=\"https:\/\/baekur.is\/bok\/000402495\/Stjornufraedi__lett_og_handa\">Stj\u00f6rnufr\u00e6di<\/a> Ursins, \u00e1ri\u00f0 1842, sem \u00edslenskir lesendur f\u00e1 nokkurn veginn fulln\u00e6gjandi l\u00fdsingu \u00e1 ors\u00f6kum sj\u00e1varfalla (bls. 109-111). J\u00f3nasi Hallgr\u00edmssyni, hefur \u00fe\u00f3 ekki \u00fe\u00f3tt n\u00f3g a\u00f0 gert, \u00fev\u00ed \u00e1ri\u00f0 eftir birti hann \u00ed <a href=\"https:\/\/is.wikipedia.org\/wiki\/Fj%C3%B6lnir_(t%C3%ADmarit)\">Fj\u00f6lni<\/a> \u00fe\u00fd\u00f0ingu s\u00edna \u00e1 greininni <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=2012829\">Um fl\u00f3\u00f0 og fj\u00f6ru<\/a> eftir danska al\u00fe\u00fd\u00f0ufr\u00e6\u00f0arann <a href=\"https:\/\/da.wikipedia.org\/wiki\/C.A._Schumacher\">C. A. Schumacher<\/a>. \u00de\u00f3tt \u00fear g\u00e6ti sums sta\u00f0ar misskilnings um \u00e1hrif \u00feyngdar og mi\u00f0fl\u00f3ttakrafta, er umfj\u00f6llunin til muna myndr\u00e6nni en fyrri l\u00fdsingar \u00e1 \u00edslensku. Sj\u00e1lfur skrifa\u00f0i J\u00f3nas svo s\u00ed\u00f0asta hluta greinarinnar (aftan vi\u00f0 \u00feverstriki\u00f0 \u00e1 bls. 51), \u00fear sem fjalla\u00f0 er um sj\u00e1varf\u00f6ll \u00e1 \u00cdslandi me\u00f0 a\u00f0sto\u00f0 fl\u00f3\u00f0at\u00f6flu.<\/p>\n<figure id=\"attachment_16695\" aria-describedby=\"caption-attachment-16695\" style=\"width: 483px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16695\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/09\/Fjo\u0308lnir1843-300x199.jpeg\" alt=\"\" width=\"483\" height=\"320\" \/><figcaption id=\"caption-attachment-16695\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Fyrsta sk\u00fdringarmyndin af \u00feremur \u00ed greininni <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=2012829\">Um fl\u00f3\u00f0 og fj\u00f6ru<\/a> fr\u00e1 1843. Me\u00f0 teikningunni h\u00e6gra megin og me\u00f0fylgjadi texta \u00ed greininni, er ger\u00f0 tilraun til a\u00f0 \u00fatsk\u00fdra \u00fe\u00e1tt tunglsins \u00ed sj\u00e1varf\u00f6llum \u00e1 j\u00f6r\u00f0inni. Tungli\u00f0 er statt \u00e1 sta\u00f0num L&#8217; og mi\u00f0ja jar\u00f0ar er \u00ed C&#8217;. L\u00f6gun v\u00f6kvahj\u00fapsins (heimshafanna) N&#8217;m&#8217;Z&#8217;n&#8217;, sem umlykur fasta j\u00f6r\u00f0ina, stafar af \u00feyngdarkrafti tunglsins, enda er \u00fea\u00f0 \u201e<em>l\u00f6gm\u00e1l \u00fe\u00edngdarinnar, a\u00f0 a\u00f0dr\u00e1ttarafli\u00f0 m\u00ednkar eptir sama hlutfalli og fjarl\u00e6g\u00f0 hlutanna eikst margf\u00f6ldu\u00f0 me\u00f0 sj\u00e1lfri sjer<\/em>.\u201c \u00datlistun \u00e1 sj\u00e1varfallahrifum s\u00f3lar fylgir svo \u00ed kj\u00f6lfari\u00f0.<br \/><\/span><\/figcaption><\/figure>\n<ul>\n<li>A. Griffin, 2008: <a href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/0031-9120\/43\/2\/F05\/pdf\">Tides, as explained by Newton<\/a>.<\/li>\n<li>D. E. Simanek, 2020: <a href=\"https:\/\/lockhaven.edu\/~dsimanek\/scenario\/tides.htm\">Tidal Misconceptions<\/a>.<\/li>\n<li>G. Tabarroni, 1989: <a href=\"http:\/\/adsabs.harvard.edu\/full\/1989MmSAI..60..769T\">The Tides and Newton<\/a>.<\/li>\n<li>D. E. Cartwright, 2000: <a href=\"https:\/\/books.google.is\/books?id=78bE5U7TVuIC&amp;hl=is&amp;source=gbs_navlinks_s\">Tides: A Scientific History<\/a>.<\/li>\n<li>\u00deorsteinn S\u00e6mundsson, 2000: <a href=\"http:\/\/www.almanak.hi.is\/flodspar.pdf\">Um sj\u00e1varfallasp\u00e1r<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><em><strong>L\u00f6gun jar\u00f0ar, hreyfing og p\u00f3lvelta<br \/>\n<\/strong><\/em><\/p>\n<p>\u00dea\u00f0 voru ekki a\u00f0eins fjarhrifin og e\u00f0li \u00feyngdarkrafts Newtons, sem \u00ed fyrstu v\u00f6f\u00f0ust fyrir m\u00f6rgum uppl\u00fdsingarm\u00f6nnum \u00e1 meginlandi Evr\u00f3pu. S\u00e9rstaklega \u00e1ttu franskir fylgismenn Descartes erfitt me\u00f0 a\u00f0 skilja \u00fe\u00e1 r\u00f6ksemdaf\u00e6rslu Newtons, a\u00f0 m\u00f6ndulsn\u00faningur jar\u00f0ar \u00e1samt \u00e1hrifum \u00feyngdarinnar ger\u00f0u \u00fea\u00f0 a\u00f0 verkum, a\u00f0 j\u00f6r\u00f0in v\u00e6ri heldur flatari \u00e1 p\u00f3lunum en vi\u00f0 mi\u00f0baug. \u00de\u00f3 haf\u00f0i Huygens \u00e1\u00f0ur nota\u00f0 kartes\u00edskar hugmyndir um mi\u00f0fl\u00f3ttaafli\u00f0 til a\u00f0 setja fram svipa\u00f0a hugmynd og Newton.<\/p>\n<p>S\u00fa ni\u00f0ursta\u00f0a Newtons, a\u00f0 j\u00f6r\u00f0in v\u00e6ri \u00ed laginu eins og <a href=\"https:\/\/simple.wikipedia.org\/wiki\/Oblate_spheroid\">flattur sporv\u00f6lusn\u00fa\u00f0ur<\/a> (e. oblate spheroid) var \u00fev\u00ed har\u00f0lega gagnr\u00fdnd \u00ed Frakklandi, enda h\u00f6f\u00f0u <a href=\"https:\/\/en.wikipedia.org\/wiki\/History_of_geodesy#Europe\">m\u00e6lingar og \u00fatreikningar Cassini fe\u00f0ganna<\/a> \u00e1\u00f0ur bent til \u00feess, a\u00f0 j\u00f6r\u00f0in l\u00edktist frekar <a href=\"https:\/\/en.wikipedia.org\/wiki\/Spheroid\">\u00edl\u00f6ngum sporv\u00f6lusn\u00fa\u00f0<\/a> (e. prolate spheroid), l\u00f6gun, sem var \u00ed samr\u00e6mi vi\u00f0 hvirflakenningu Descartes.<\/p>\n<figure id=\"attachment_14659\" aria-describedby=\"caption-attachment-14659\" style=\"width: 391px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-14659\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/04\/Ursin_earth_shape-300x212.png\" alt=\"\" width=\"391\" height=\"277\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/04\/Ursin_earth_shape-300x212.png 300w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/04\/Ursin_earth_shape.png 484w\" sizes=\"auto, (max-width: 391px) 100vw, 391px\" \/><figcaption id=\"caption-attachment-14659\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">\u00cd <em>Stj\u00f6rnufr\u00e6\u00f0i<\/em> Ursins er \u00fatsk\u00fdrt (bls. 113-114), hvernig \u00feyngdar-afli\u00f0 og m\u00f6ndulsn\u00faningur reikistjarnanna veldur \u00fev\u00ed, a\u00f0 \u201e<em>\u00fe\u00e6r eru flatvagsnar, r\u00e9tt eins og hno\u00f0a undir l\u00e9ttu fargi, flatastar um m\u00f6ndulendana, e\u00f0ur skautin og h\u00e6star um mi\u00f0biki\u00f0<\/em>\u201c. \u00c1 mynd Ursins er \u00feversni\u00f0 hnattarins EFGD bori\u00f0 saman vi\u00f0 k\u00faluna PQpA me\u00f0 sameiginlega mi\u00f0ju \u00ed C. Sn\u00fanings\u00e1sinn er Pp.\u00a0 &#8211;\u00a0 Hlutfalli\u00f0 (DC-EC)\/DC er m\u00e6likvar\u00f0i \u00e1 fr\u00e1viki\u00f0 fr\u00e1 hnattl\u00f6gun.\u00a0 Samkv\u00e6mt Ursin er \u00fea\u00f0 a\u00f0eins 1\/300 fyrir j\u00f6r\u00f0ina, sem er ekki fjarri r\u00e9ttu lagi.\u00a0 Mi\u00f0baugsbungan er \u00fev\u00ed greinilega mj\u00f6g \u00fdkt \u00e1 myndinni.<br \/><\/span><\/figcaption><\/figure>\n<p>Deilurnar milli kartesista og nj\u00fatonista um r\u00e9tta l\u00f6gun jar\u00f0ar ur\u00f0u a\u00f0 lokum svo h\u00e1v\u00e6rar, a\u00f0 Franska v\u00edsindaakadem\u00edan \u00e1kva\u00f0 a\u00f0 senda \u00fat tvo lei\u00f0angra til a\u00f0 ganga endanlega \u00far skugga um l\u00f6gunina. Annar lei\u00f0angurinn var sendur til mi\u00f0baugssv\u00e6\u00f0is \u00ed Per\u00fa \u00ed Su\u00f0ur-Amer\u00edku (sem n\u00fa kallast Ekvador) en hinn nor\u00f0ur til Lapplands. Verkefni\u00f0 var a\u00f0 beita \u00fer\u00edhyrningam\u00e6lingum til a\u00f0 finna lengd einnar breiddargr\u00e1\u00f0u \u00e1 hvorum sta\u00f0 fyrir sig og bera ni\u00f0urst\u00f6\u00f0urnar saman.<\/p>\n<p>Per\u00fa-lei\u00f0angurinn lag\u00f0i af sta\u00f0 \u00e1ri\u00f0 1735 og \u00ed honum voru \u00feekktir\u00a0 v\u00edsindamenn, eins og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pierre_Bouguer\">P. Bouguer<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Charles_Marie_de_La_Condamine\">C. M. La Condamine<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Louis_Godin\">L. Godin<\/a>. \u00c1ri\u00f0 eftir h\u00f3fst svo Lapplandsf\u00f6rin, \u00fear sem nj\u00fatonistarnir <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pierre_Louis_Maupertuis\">P. L. Maupertuis<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Alexis_Clairaut\">A. Clairaut<\/a> voru me\u00f0al lei\u00f0angursmanna. \u00c1 lei\u00f0inni nor\u00f0ur b\u00e6ttist Sv\u00edinn <a href=\"https:\/\/en.wikipedia.org\/wiki\/Anders_Celsius\">A. Celcius<\/a> \u00ed h\u00f3pinn. Nor\u00f0urfararnir sneru aftur til Par\u00edsar 1738, en mi\u00f0baugsmenn ekki fyrr en sex \u00e1rum s\u00ed\u00f0ar. Eftir umfangsmikla reikninga kom \u00ed lj\u00f3s, a\u00f0 breiddargr\u00e1\u00f0an vi\u00f0 mi\u00f0baug var styttri en s\u00fa \u00ed Lapplandi \u00ed fullu samr\u00e6mi vi\u00f0 kenningu Newtons.<\/p>\n<p>\u00de\u00f3tt sumir efu\u00f0ust um n\u00e1kv\u00e6mni m\u00e6lingnna, voru langflestir s\u00e1ttir vi\u00f0 ni\u00f0urst\u00f6\u00f0una, sem var\u00f0 aftur til \u00feess, a\u00f0 eftir mi\u00f0ja \u00e1tj\u00e1ndu \u00f6ld var kenningu Newtons um l\u00f6gunina hampa\u00f0 \u00ed svo til \u00f6llum vestr\u00e6num kennslub\u00f3kum \u00ed stj\u00f6rnufr\u00e6\u00f0i, sem \u00e1 anna\u00f0 bor\u00f0 fj\u00f6llu\u00f0u um efni\u00f0. \u00deetta m\u00e1 til d\u00e6mis sj\u00e1 \u00ed <a href=\"https:\/\/books.google.is\/books?id=9rYLbpKbSkkC&amp;source=gbs_navlinks_s\">kennslub\u00f3k<\/a> C. Horrebows fr\u00e1 1762 (bls. 292-304) og <a href=\"https:\/\/books.google.is\/books?id=eoVaAAAAcAAJ&amp;hl=is&amp;source=gbs_navlinks_s\">kennslub\u00f3k<\/a> T. Bugge fr\u00e1 1796 (bls. 282-292).<\/p>\n<p>\u00cd \u00edslensku fr\u00e6\u00f0sluritunum fr\u00e1 \u00e1runum \u00ed kringum 1800 er \u00feegar fari\u00f0 a\u00f0 fjalla um mynd Newtons af j\u00f6r\u00f0inni sem sj\u00e1lfsag\u00f0an hlut og ekki minnst \u00e1 hinar hatr\u00f6mmu deilur um l\u00f6gunina, sem tr\u00f6llri\u00f0u Mi\u00f0-Evr\u00f3pu \u00e1 fyrri hluta \u00e1tj\u00e1ndu aldar. \u00dea\u00f0 eitt er greinilegt merki \u00feess, a\u00f0 hugmyndafr\u00e6\u00f0i Newtons var \u00feegar farin a\u00f0 ry\u00f0ja s\u00e9r til r\u00fams \u00e1 \u00cdslandi, jafnvel me\u00f0al \u00feeirra h\u00f6funda, sem l\u00edti\u00f0 skildu \u00ed st\u00e6r\u00f0fr\u00e6\u00f0ilegum \u00fatreikningum meistarans e\u00f0a fylgismanna hans. Sem d\u00e6mi m\u00e1 nefna umfj\u00f6llun J\u00f3ns l\u00e6r\u00f0a \u00ed <em>N\u00e1tt\u00farusko\u00f0ara<\/em> fr\u00e1 1798 (bls. 7-8):<\/p>\n<blockquote><p>Ad j\u00f6rdin hn\u00f6tt\u00f3tt er, heldur enn \u00ed annari mind, leidir Newton \u00fe\u00e1 \u00f6rs\u00f6k til, ad allir partar jardar s\u00e6kja ad hennar midp\u00fankti, og ad \u00feessi dr\u00e1ttar-kraptur s\u00e9 \u00ed \u00f6llum hlutum <em>[&#8230;]<\/em>\u00a0 En hinu, ad j\u00f6rdin er \u00fe\u00f3 ecki rett hn\u00f6tt\u00f3tt, heldur flatari undir heims-endunum, enn bruna-beltinu, \u00fev\u00ed veldur, n\u00e6rst hita s\u00f3larinnar, hennar daglegi sn\u00faningur, sem verkar \u00fead, ad partar hennar vilja losna og hristast \u00ed sundur framar um midbik hennar, enn undir skautunum.<\/p><\/blockquote>\n<p>Anna\u00f0 d\u00e6mi er \u00ed <em>Almennri landaskipunarfr\u00e6\u00f0i<\/em> fr\u00e1 1821, en \u00fear segir \u00e1 bls. 13:<\/p>\n<blockquote><p>Ad manneskiur og adrir hlutir \u00e1 hnettinum ecki hvirflast \u00fat \u00ed buskan, k\u00e9mur af \u00fev\u00ed, ad allir hlutir leita nidur ad midp\u00fankti jardar, og \u00feessi addr\u00e1ttarkraptur jardar (vis centripetalis) yfirgeingur mi\u00f6g framfararflugid (flegis edur slaungukraptinn vis centrifuga) sem sn\u00faningurinn k\u00e9mur til leidar \u00feegar eckert hindrar, og sem mundi f\u00e6ra hlutina \u00fat \u00ed loptid first n\u00e6rri j\u00f6rdunni, og s\u00eddan meira og meira \u00fat fr\u00e1 hveli hennar eptir beinni svokalladri snertil\u00ednu (tangent). <em><span style=\"text-decoration: underline\">Ne\u00f0anm\u00e1ls<\/span>:<\/em> \u00deessi \u00f3dfluga sn\u00faningr (fr\u00e1flugskraptr) veldur \u00fev\u00ed ad j\u00f6rdin er ekki \u00f6ld\u00fangis hn\u00f6tt\u00f3tt, heldur ein\u00fangis hnattarl\u00edk, og digrari um midbikid.<\/p><\/blockquote>\n<p>\u00cd myndatextanum h\u00e9r a\u00f0 ofan kom fram, a\u00f0 \u00edtarlega \u00fatsk\u00fdringu \u00e1 l\u00f6gun jar\u00f0ar er a\u00f0 finna \u00ed <a href=\"https:\/\/baekur.is\/bok\/000402495\/Stjornufraedi__lett_og_handa\">Stj\u00f6rnufr\u00e6\u00f0i<\/a> Ursins (bls. 113-114). Aftar \u00ed b\u00f3kinni (bls. 172-175) er svo fjalla\u00f0 um \u00fdmsar m\u00e6lingar, sem sty\u00f0ja kenninguna. \u00dear er stuttlega minnst \u00e1 ni\u00f0urst\u00f6\u00f0ur La Condamine og samfer\u00f0amanna hans \u00ed Ekvador, en \u00ed sta\u00f0 \u00feess a\u00f0 geta um hinar fr\u00e6gu Lapplandsm\u00e6lingar \u00feeirra Maupertuis, Clairauts og Cels\u00edusar, nefnir h\u00f6fundurinn tilsvarandi og n\u00fdlegri ni\u00f0urst\u00f6\u00f0u samt\u00edmamanns s\u00edns, <a href=\"https:\/\/sv.wikipedia.org\/wiki\/J%C3%B6ns_Svanberg\">J. Svanbergs<\/a>.<\/p>\n<ul>\n<li>J. L. Greenberg, 1995: <a href=\"https:\/\/www.jstor.org\/stable\/41134011?seq=1#metadata_info_tab_contents\">Isaac Newton and the Problem of the Earth&#8217;s Shape<\/a>.<\/li>\n<li>G. Heine, 2013: <a href=\"https:\/\/www.jstor.org\/stable\/pdf\/10.4169\/mathhorizons.21.1.25.pdf?refreqid=excelsior%3Ab2bdf439106eb9a29ca0493f5f82193d\">Euler and the Flattening of the Earth.<\/a><\/li>\n<li>J. D. Fernie, 1991-92: <em>The Shape of the Earth<\/em>. <a href=\"https:\/\/www.jstor.org\/stable\/29774318?seq=1#metadata_info_tab_contents\">Part I<\/a>, <a href=\"https:\/\/www.jstor.org\/stable\/29774472?seq=1#metadata_info_tab_contents\">Part II<\/a> og <a href=\"https:\/\/www.jstor.org\/stable\/29774598?seq=1#metadata_info_tab_contents\">Part III<\/a>.<\/li>\n<li>M. Terrall, 1992: <a href=\"https:\/\/www.jstor.org\/stable\/234505?seq=1#metadata_info_tab_contents\">Representing the Earth&#8217;s Shape: The Polemics Surrounding Maupertuis&#8217;s Expedition to Lapland<\/a>.<\/li>\n<li>R. Iliffe, 1993: <a href=\"http:\/\/articles.adsabs.harvard.edu\/\/full\/1993HisSc..31..335I\/0000335.000.html\">&#8220;Aplatisseur du Monde et de Cassini&#8221;: Maupertuis, Precision Measurement, and the Shape of the Earth in the 1730s<\/a>.<\/li>\n<\/ul>\n<p>Ekki er oft \u00e1 \u00fea\u00f0 minnst \u00ed \u00edslenskum fr\u00e6\u00f0sluritum, a\u00f0 \u00ed <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lunum<\/em> t\u00f3kst Newton, fyrstum manna, a\u00f0 \u00fatsk\u00fdra svokalla\u00f0a <a href=\"https:\/\/science.jrank.org\/pages\/5444\/Precession-Equinoxes.html\">frams\u00f3kn jafnd\u00e6grapunkta<\/a>, sem valdi\u00f0 haf\u00f0i stj\u00f6rnufr\u00e6\u00f0ingum miklum heilabrotum \u00f6ldum saman. \u00dear nota\u00f0ist meistarinn vi\u00f0 uppl\u00fdsingar um <a href=\"https:\/\/www.universetoday.com\/47176\/earths-axis\/\">m\u00f6ndulhalla jar\u00f0arinnar<\/a> og \u00e1hrif \u00feyngdarkrafta tungls og s\u00f3lar \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Equatorial_bulge\">mi\u00f0baugsbunguna<\/a> til a\u00f0 s\u00fdna fram \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Axial_precession\">p\u00f3lveltu jar\u00f0arinnar<\/a> og \u00fear me\u00f0 frams\u00f3knina (sj\u00e1 n\u00e1nar \u00ed texta vi\u00f0 n\u00e6stu tv\u00e6r myndir). \u00c1st\u00e6\u00f0an fyrir \u00fev\u00ed, a\u00f0 \u00feessu er venjulega sleppt \u00ed al\u00fe\u00fd\u00f0ufr\u00e6\u00f0slu, er sennilega s\u00fa, a\u00f0 erfitt er a\u00f0 f\u00e1st vi\u00f0 vi\u00f0fangsefni\u00f0 \u00e1n umtalsver\u00f0rar \u00feekkingar \u00ed aflfr\u00e6\u00f0i. Jafnvel Ursin sleppir \u00fev\u00ed a\u00f0 fjalla fr\u00e6\u00f0ilega um efni\u00f0.<\/p>\n<figure id=\"attachment_16816\" aria-describedby=\"caption-attachment-16816\" style=\"width: 394px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16816\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/10\/Baugahno\u0308ttur_Sacrob_Paris1507-207x300.png\" alt=\"\" width=\"394\" height=\"571\" \/><figcaption id=\"caption-attachment-16816\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">\u00deessi skemmtilega mynd er \u00far Pa\u00edsar\u00fatg\u00e1funni af <em>De Spheara<\/em> eftir Sacrobosco fr\u00e1 1507. H\u00fan s\u00fdnir svokalla\u00f0an <a href=\"https:\/\/en.wikipedia.org\/wiki\/Armillary_sphere\">baugahn\u00f6tt<\/a>, einfalt l\u00edkan af <a href=\"https:\/\/en.wikipedia.org\/wiki\/Celestial_sphere\">hvelfingunni<\/a> me\u00f0 hringjum, sem samsvara landfr\u00e6\u00f0ilegum baugum jar\u00f0k\u00falunnar (\u00ed mi\u00f0junni). <a href=\"https:\/\/en.wikipedia.org\/wiki\/Celestial_pole\">M\u00f6ndull himins<\/a>, <em>am<\/em>, er l\u00f3\u00f0r\u00e9ttur \u00e1 myndinni og liggur hornr\u00e9tt \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Celestial_equator\">mi\u00f0baug himins<\/a>, <em>fg<\/em>. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Ecliptic\">S\u00f3lbaugurinn<\/a>, <em>pq<\/em>, er umlukinn belti<a href=\"https:\/\/en.wikipedia.org\/wiki\/Zodiac\"> d\u00fdrahringsins<\/a> me\u00f0 hinum fornu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Zodiac#Twelve_signs\">t\u00e1knum<\/a> fyrir stj\u00f6rnumerkin t\u00f3lf. \u00c1 \u00feeirri hli\u00f0, sem fram sn\u00fdr, sker s\u00f3lbaugurinn mi\u00f0baug \u00ed <a href=\"https:\/\/en.wikipedia.org\/wiki\/March_equinox\">vorpunktinum<\/a>, Hann er \u00fearna s\u00fdndur \u00ed <a href=\"https:\/\/www.stjornufraedi.is\/stjornuskodun\/stjornumerkin\/hruturinn\">Hr\u00fatsmerki<\/a>\u00a0 (\u2648\ufe0e), og horni\u00f0 milli bauganna er n\u00fa um 23,5 gr\u00e1\u00f0ur. Vegna <a href=\"https:\/\/en.wikipedia.org\/wiki\/Axial_precession\">frams\u00f3knar skur\u00f0punktsins<\/a> \u201eni\u00f0ur eftir\u201c s\u00f3lbaug er vorpunkturinn n\u00fa \u00ed <a href=\"https:\/\/www.stjornufraedi.is\/stjornuskodun\/stjornumerkin\/fiskarnir\">Fiskamerki<\/a> (\u2653\ufe0e) og stefnir \u00ed \u00e1tt a\u00f0 <a href=\"https:\/\/www.stjornufraedi.is\/stjornuskodun\/stjornumerkin\/vatnsberinn\">Vatnsberanum<\/a> (\u2652\ufe0e). \u00dea\u00f0 tekur hann um 26 \u00fe\u00fasund \u00e1r a\u00f0 fara allan hringinn.<br \/><\/span><\/figcaption><\/figure>\n<figure id=\"attachment_16817\" aria-describedby=\"caption-attachment-16817\" style=\"width: 547px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16817\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/10\/Arstidir_ferguson-300x113.jpeg\" alt=\"\" width=\"547\" height=\"206\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/10\/Arstidir_ferguson-300x113.jpeg 300w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/10\/Arstidir_ferguson.jpeg 735w\" sizes=\"auto, (max-width: 547px) 100vw, 547px\" \/><figcaption id=\"caption-attachment-16817\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">M\u00f6ndulhalli jar\u00f0ar og gangur hennar um s\u00f3lu (<em>S<\/em>) er ors\u00f6k <a href=\"https:\/\/en.wikipedia.org\/wiki\/Season\">\u00e1rst\u00ed\u00f0anna<\/a>. Hallinn er n\u00fa um 23,5 gr\u00e1\u00f0ur mi\u00f0a\u00f0 vi\u00f0 l\u00f3\u00f0l\u00ednu \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Earth%27s_orbit\">jar\u00f0brautarsl\u00e9ttuna<\/a>. \u00deyngdar\u00e1hrif tungls og s\u00f3lar \u00e1 mi\u00f0baugs-bungu jar\u00f0ar valda \u00fev\u00ed, a\u00f0 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Axial_precession\">m\u00f6ndullinn veltur um l\u00f3\u00f0l\u00ednuna<\/a> og fer einn hring \u00e1 um \u00fea\u00f0 bil 26 \u00fe\u00fasund \u00e1rum. Myndin er \u00far b\u00f3k J. Fergusons, <a href=\"https:\/\/books.google.is\/books?id=riFKdOEyduwC&amp;source=gbs_navlinks_s\">An Easy Introduction to Astronomy, for Young Gentlemen and Ladies<\/a>, fr\u00e1 1769. Svip\u00f0u\u00f0 teikning haf\u00f0i \u00e1\u00f0ur birst \u00e1ri\u00f0 1756 \u00ed verkinu <a href=\"https:\/\/books.google.is\/books?id=Ji1cAAAAQAAJ&amp;source=gbs_navlinks_s\">Astronomy Explained Upon Sir Isaac Newton&#8217;s Principles, and Made Easy to Those who Have Not Studied Mathematics<\/a> eftir sama h\u00f6fund.<br \/><\/span><\/figcaption><\/figure>\n<p>\u00deegar betur var a\u00f0 g\u00e1\u00f0, leyndust villur \u00ed \u00fatlei\u00f0slu Newtons \u00e1 p\u00f3lveltunni. \u00dea\u00f0 kom \u00fev\u00ed \u00ed hlut \u00feeirra <a href=\"https:\/\/en.wikipedia.org\/wiki\/Jean_le_Rond_d%27Alembert\">J. R. d&#8217;Alemberts<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Leonhard_Euler\">L. Eulers<\/a> a\u00f0 lagf\u00e6ra framsetninguna og \u00fatsk\u00fdra \u00ed lei\u00f0inni hina svok\u00f6llu\u00f0u <a href=\"https:\/\/en.wikipedia.org\/wiki\/Nutation\">p\u00f3lri\u00f0u<\/a>, sem hinn merki stj\u00f6rnufr\u00e6\u00f0ingur <a href=\"https:\/\/en.wikipedia.org\/wiki\/James_Bradley\">J. Bradley<\/a> uppg\u00f6tva\u00f0i \u00e1 \u00e1runum 1728-1748.<\/p>\n<p>Bradley er \u00fe\u00f3 l\u00edklega \u00feekktari fyrir a\u00f0 hafa \u00e1\u00f0ur (\u00e1 \u00e1runum 1725-1728) uppg\u00f6tva\u00f0 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Aberration_(astronomy)\">lj\u00f3svilluna<\/a>, fyrirb\u00e6ri sem stafar af endanlegum hra\u00f0a lj\u00f3ssins og hreyfingu jar\u00f0ar mi\u00f0a\u00f0 vi\u00f0 fastastj\u00f6rnurnar. \u00deessa mikilv\u00e6gu uppg\u00f6tvun ver\u00f0ur a\u00f0 telja fyrstu beinu s\u00f6nnunina \u00e1 g\u00f6ngu jar\u00f0ar um s\u00f3lu. Um hana og \u00fdmislegt anna\u00f0, sem h\u00e9r hefur veri\u00f0 r\u00e6tt, er stuttlega fjalla\u00f0 \u00ed kaflanum um hreyfingu jar\u00f0ainnar \u00ed <a href=\"https:\/\/baekur.is\/bok\/000144122\/Almenn\">Almenni landaskipunarfr\u00e6di<\/a> (\u00a714, bls. 55-61) og s\u00f6mulei\u00f0is hj\u00e1 Ursin (bls. 148-152).<\/p>\n<p>Samhengisins vegna, er \u00ed lokin r\u00e9tt a\u00f0 nefna \u00fea\u00f0 h\u00e9r, a\u00f0 \u00fer\u00e1tt fyrir mikla leit, allt fr\u00e1 d\u00f6gum K\u00f3pern\u00edkusar, var \u00fea\u00f0 var ekki fyrr en \u00e1ri\u00f0 1838, sem stj\u00f6rnufr\u00e6\u00f0ingar fundu fyrsta d\u00e6mi\u00f0 um <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stellar_parallax\">\u00e1rlega hli\u00f0run fastastj\u00f6rnu<\/a> og g\u00e1tu \u00feannig \u00e1kvar\u00f0a\u00f0 fjarl\u00e6g\u00f0ina til hennar. Um var a\u00f0 r\u00e6\u00f0a stj\u00f6rnuna <a href=\"https:\/\/en.wikipedia.org\/wiki\/61_Cygni\">61 Cygni<\/a> \u00ed 11,4 lj\u00f3s\u00e1ra fjarl\u00e6g\u00f0. \u00cd vissum skilningi m\u00e1 segja, a\u00f0 s\u00e1 fundur hafi marka\u00f0 endanlegan sigur s\u00f3lmi\u00f0jukenningarinnar \u00e1 jar\u00f0mi\u00f0ju-kenningum.<\/p>\n<p>\u00cd <a href=\"https:\/\/baekur.is\/bok\/000402495\/Stjornufraedi__lett_og_handa\">Stj\u00f6rnufr\u00e6\u00f0i<\/a> Ursins er\u00a0 fjalla\u00f0 um hli\u00f0run \u00e1 bls. 141-143, en h\u00f6fundurinn hefur ekki haft t\u00edma til a\u00f0 koma fr\u00e9ttinni um n\u00fdju m\u00e6linguna \u00ed d\u00f6nsku frum\u00fatg\u00e1funa, sem birt var 1838. \u00de\u00fd\u00f0andinn vir\u00f0ist ekki heldur hafa vita\u00f0 af uppg\u00f6tvuninni, svo hennar er ekki geti\u00f0 \u00ed \u00edslensku \u00fatg\u00e1funni fr\u00e1 1842. \u00cd umfj\u00f6llun Ursins er \u00fe\u00f3 bent \u00e1, a\u00f0 \u00e1 ritunart\u00edma b\u00f3karinnar hafi engin fastastjarna enn m\u00e6lst me\u00f0 hli\u00f0run. Efri m\u00e6lingam\u00f6rk s\u00e9u um \u00fea\u00f0 bil ein bogasek\u00fanda og af \u00fev\u00ed lei\u00f0i, a\u00f0 l\u00e1gmarksfjarl\u00e6g\u00f0in til \u00feeirra hlj\u00f3ti a\u00f0 vera meiri en 3 lj\u00f3s\u00e1r. \u00cd dag vitum vi\u00f0, a\u00f0 n\u00e1l\u00e6gasta \u00feekkta fastastjarnan, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Proxima_Centauri\">Prox\u00edma \u00ed Mannf\u00e1knum<\/a>, er \u00ed 4,24 lj\u00f3s\u00e1ra fjarl\u00e6g\u00f0. N\u00e1nar ver\u00f0ur fjalla\u00f0 um fastastj\u00f6rnurnar og fjarl\u00e6g\u00f0ina til \u00feeirra \u00ed n\u00e6stu f\u00e6rslu(m).<\/p>\n<ul>\n<li>C. Wilson, 1987: <a href=\"https:\/\/www.jstor.org\/stable\/41133816?seq=1#metadata_info_tab_contents\">D&#8217;Alembert versus Euler on the Precession of the Equinoxes and the Mechanics of Rigid Bodies<\/a>.<\/li>\n<li>M. Ekman, 1993: <a href=\"https:\/\/notendur.hi.is\/~einar\/HistoireMarees.pdf\">A concise history of the theories of tides, precession-nutation and polar motion (from antiquity to 1950)<\/a>.<\/li>\n<li>J. Bradley, E. Halley &amp; G. Sarton, 1931:<a href=\"https:\/\/www.jstor.org\/stable\/224710?seq=1#metadata_info_tab_contents\"> Discovery of the Aberration of Light<\/a>.<\/li>\n<li>D. -E. Liebscher &amp; P. Brosche, 1998: <a href=\"http:\/\/articles.adsabs.harvard.edu\/\/full\/1998AN....319..309L\/0000309.000.html\">Aberration and relativity<\/a>.<\/li>\n<li>J. D. Fernie, 1975: <em>The Historical Search for Stellar Parallax<\/em>. <a href=\"http:\/\/adsabs.harvard.edu\/full\/1975JRASC..69..153F\">Part I<\/a>. <a href=\"http:\/\/adsabs.harvard.edu\/full\/1975JRASC..69..222F\">Part II<\/a>.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><em><strong>Halastjarnan 1759<\/strong><\/em><\/p>\n<p>Eitt \u00feeirra n\u00fdm\u00e6la, sem Newton birti \u00ed <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lunum <\/em>og vakti hva\u00f0 mesta athygli samt\u00edmamanna, var kenningin um \u00fea\u00f0, a\u00f0 halastj\u00f6rnur v\u00e6ru himintungl og lytu \u00fev\u00ed \u00feyngdarl\u00f6gm\u00e1linu eins og reikistj\u00f6rnurnar og tungl \u00feeirra (sj\u00e1 umfj\u00f6llunina fr\u00e1 og me\u00f0 lemmu 4 \u00ed \u00feri\u00f0ju b\u00f3k). \u00deekktasta myndin \u00ed<em> St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lunum<\/em> er einmitt teikning, sem s\u00fdnir ni\u00f0urst\u00f6\u00f0ur \u00fatreikninga meistarans \u00e1 fleygbogabraut halastj\u00f6rnunnar fr\u00e6gu \u00e1ri\u00f0 1680.<\/p>\n<figure id=\"attachment_5843\" aria-describedby=\"caption-attachment-5843\" style=\"width: 478px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-5843\" src=\"https:\/\/uni.hi.is\/einar\/files\/2018\/07\/Principia_Comet-300x155.png\" alt=\"\" width=\"478\" height=\"247\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2018\/07\/Principia_Comet-300x155.png 300w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2018\/07\/Principia_Comet.png 600w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\" \/><figcaption id=\"caption-attachment-5843\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Teikning Newtons af braut halastj\u00f6rnunnar 1680 \u00ed fleygbogan\u00e1lgun. ABC t\u00e1knar fleygbogann og D st\u00f6\u00f0u s\u00f3lar \u00ed brennipunktinum. Boginn GH er hluti af braut jar\u00f0ar, en flestir hinir b\u00f3kstafirnir gefa til kynna st\u00f6\u00f0u halastj\u00f6rnunnar \u00e1 mismunandi t\u00edmum.<br \/><\/span><\/figcaption><\/figure>\n<ul>\n<li>D. W. Hughes, 1988: <a href=\"https:\/\/www.jstor.org\/stable\/531369?seq=1#page_scan_tab_contents\">The Principia and Comets.<\/a><\/li>\n<li>J. A. Ruffner, 2010: <a href=\"https:\/\/journals.sagepub.com\/doi\/10.1177\/002182861004100401\">Isaac newton&#8217;s historia cometarum and the quest for elliptical orbits.<\/a><\/li>\n<\/ul>\n<p>Reiknia\u00f0fer\u00f0in, sem Newton nota\u00f0i til a\u00f0 finna braut halastj\u00f6rnunnar 1680, var b\u00e6\u00f0i fl\u00f3kin og t\u00edmafrek. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Edmond_Halley\">E. Halley<\/a>, sem las pr\u00f3f\u00f6rk af <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lunum<\/em> og a\u00f0sto\u00f0a\u00f0i Newton vi\u00f0 a\u00f0 b\u00faa verki\u00f0 undir prentun, var \u00ed s\u00e9rstakri a\u00f0st\u00f6\u00f0u til a\u00f0 tileinka s\u00e9r a\u00f0fer\u00f0ina og beita henni \u00e1 fleiri halastj\u00f6rnur. \u00cd kringum 1695 var hann fari\u00f0 a\u00f0 gruna, a\u00f0 halastj\u00f6rnurnar fr\u00e6gu, \u00e1rin 1531, 1607 og 1682, v\u00e6ru \u00ed raun ein og sama stjarnan. H\u00fan v\u00e6ri \u00e1 sporbaug um s\u00f3lina og f\u00e6ri eina umfer\u00f0 \u00e1 um \u00fea\u00f0 bil 76 \u00e1rum.<\/p>\n<p>\u00dea\u00f0 var \u00fe\u00f3 ekki fyrr en 1705, sem Halley birti ni\u00f0urst\u00f6\u00f0ur reikninga sinna \u00e1 brautum 24 halastjarna \u00ed handh\u00e6gri t\u00f6flu, og <a href=\"https:\/\/archive.org\/details\/synopsisofastron00hall\">setti jafnframt fram tilg\u00e1tu<\/a> \u00feess efnis, a\u00f0 halastjarnan, sem \u00e1\u00f0ur haf\u00f0i s\u00e9st 1531, 1607 og 1682, myndi birtast \u00e1 n\u00fdjan leik \u00e1ri\u00f0 1758.<\/p>\n<div id=\"attachment_7718\" class=\"wp-caption aligncenter\" style=\"width: 576px\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-7718\" src=\"https:\/\/uni.hi.is\/einar\/files\/2018\/09\/HalleyTable1705-300x196.jpg\" alt=\"\" width=\"576\" height=\"376\" aria-describedby=\"caption-attachment-7718\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2018\/09\/HalleyTable1705-300x196.jpg 300w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2018\/09\/HalleyTable1705-1024x669.jpg 1024w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2018\/09\/HalleyTable1705-768x502.jpg 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2018\/09\/HalleyTable1705.jpg 1420w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/p>\n<p id=\"caption-attachment-7718\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Hin merka tafla Halleys fr\u00e1 1705 \u00fear sem sj\u00e1 m\u00e1 l\u00edkindin me\u00f0 halastj\u00f6rnunum \u00e1rin 1531, 1607 og 1682. T\u00f6lulegar uppl\u00fdsingar um \u00feessar \u00ferj\u00e1r stj\u00f6rnur eru undirstrika\u00f0ar me\u00f0 appels\u00ednugulum lit.<\/span><\/p>\n<\/div>\n<p>\u00deegar l\u00ed\u00f0a f\u00f3r \u00e1 sj\u00f6tta \u00e1ratug \u00e1tj\u00e1ndu aldar, var endurkomu stj\u00f6rnunnar be\u00f0i\u00f0 me\u00f0 mikilli eftirv\u00e6ntingu, ekki a\u00f0eins \u00ed Englandi heldur um \u00f6ll Vesturl\u00f6nd. Eins og \u00e1\u00f0ur hefur komi\u00f0 fram, er \u00e1st\u00e6\u00f0a til a\u00f0 \u00e6tla, a\u00f0 disp\u00fatat\u00eda Stef\u00e1ns Bj\u00f6rnssonar <a href=\"https:\/\/notendur.hi.is\/einar\/SAGA\/SB_cometae_1758.pdf\">Um verkan halastjarna <\/a>fr\u00e1 \u00e1rinu 1758 hafi veri\u00f0 samin af \u00feessu tilefni.<\/p>\n<p>Sp\u00e1 Halleys var bygg\u00f0 \u00e1 \u00feeirri tilg\u00e1tu Newtons, a\u00f0 halastj\u00f6rnur v\u00e6ru h\u00e1\u00f0ar \u00feyngdinni \u00e1 sama h\u00e1tt og \u00f6nnur himintungl. Endurkoman var \u00fev\u00ed mikilv\u00e6gur pr\u00f3fsteinn fyrir \u00feyngdarl\u00f6gm\u00e1li\u00f0. \u00deegar svo stjarna Halleys birtist nokkurn veginn \u00e1 tilteknum sta\u00f0 og t\u00edma, var henni teki\u00f0 me\u00f0 miklum f\u00f6gnu\u00f0i og atbur\u00f0urinn talinn mikil sigur fyrir Newton og fylgismenn hans.<\/p>\n<figure id=\"attachment_16652\" aria-describedby=\"caption-attachment-16652\" style=\"width: 579px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-16652\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/09\/Halley_1759-300x216.jpg\" alt=\"\" width=\"579\" height=\"417\" srcset=\"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Halley_1759-300x216.jpg 300w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Halley_1759-768x552.jpg 768w, https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/wp-content\/uploads\/2020\/09\/Halley_1759.jpg 900w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><figcaption id=\"caption-attachment-16652\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">Braut Halley-stj\u00f6rnunnar \u00e1 hvelfingunni \u00ed apr\u00edl 1759. H\u00f6fundur teikningarinnar er \u00f3\u00feekktur.<br \/><\/span><\/figcaption><\/figure>\n<p>N\u00e1nari umfj\u00f6llun um \u00feetta efni og frekari bakgrunn er a\u00f0 finna \u00ed fyrstu tveimur greinum undirrita\u00f0s um <em>Halastj\u00f6rnur fyrr og n\u00fa<\/em>:<\/p>\n<ul>\n<li>Einar H. Gu\u00f0mundsson, 2018: <a href=\"https:\/\/uni.hi.is\/einar\/2018\/09\/19\/halastjornur-fyrr-og-nu-1-fra-midoldum-til-loka-sautjandu-aldar\/\">Halastj\u00f6rnur fyrr og n\u00fa &#8211; 1. Fr\u00e1 mi\u00f0\u00f6ldum til loka sautj\u00e1ndu aldar<\/a>.<\/li>\n<li>Einar H. Gu\u00f0mundsson, 2018: <a href=\"https:\/\/uni.hi.is\/einar\/2018\/09\/19\/halastjornur-fyrr-og-nu-2-atjanda-og-nitjanda-old\/\">Halastj\u00f6rnur fyrr og n\u00fa &#8211; 2. \u00c1tj\u00e1nda og n\u00edtj\u00e1nda \u00f6ld<\/a>.<\/li>\n<li>Einar H. Gu\u00f0mundsson, 2018: <a href=\"https:\/\/uni.hi.is\/einar\/2018\/09\/19\/halastjornur-fyrr-og-nu-3-tuttugasta-old\/\">Halastj\u00f6rnur fyrr og n\u00fa &#8211; 3. Tuttugasta \u00f6ld<\/a>.<\/li>\n<li>Einar H. Gu\u00f0mundsson, 2018: <a href=\"https:\/\/uni.hi.is\/einar\/2018\/09\/19\/halastjornur-fyrr-og-nu-4-upphaf-tuttugustu-og-fyrstu-aldar\/\">Halastj\u00f6rnur fyrr og n\u00fa &#8211; 4. Upphaf tuttugustu og fyrstu aldar<\/a>.<\/li>\n<li>Einar H. Gu\u00f0mundsson, 2018: <a href=\"https:\/\/uni.hi.is\/einar\/2018\/06\/24\/halastjarnan-mikla-arid-1858-maelingar-og-hughrif-i-upphafi-nyrra-tima-i-stjornufraedi\/\">Halastjarnan mikla \u00e1ri\u00f0 1858 &#8211; M\u00e6lingar og hughrif \u00ed upphafi n\u00fdrra t\u00edma \u00ed stj\u00f6rnufr\u00e6\u00f0i<\/a>.<\/li>\n<\/ul>\n<p>\u00de\u00f3tt Halley-stjarnan hafi ekki s\u00e9st fr\u00e1 \u00cdslandi vori\u00f0 1759, er hennar geti\u00f0 \u00ed \u00fdmsum \u00edslenskum al\u00fe\u00fd\u00f0uritum. Til d\u00e6mis segir svo \u00ed hugvekju Hannesar Finnssonar, <a href=\"http:\/\/baekur.is\/bok\/000160591\/2\/57\/Kvoldvokurnar_Bindi_2_Bls_57\">Um halastj\u00f6rnur<\/a>, fr\u00e1 1797 (bls. 48-49):<\/p>\n<blockquote><p>Halastj\u00f6rnurnar hafa svo vissann, reglubundinn og afmarka\u00f0ann g\u00e1ng, a\u00f0 l\u00e6r\u00f0ir menn g\u00e9ta reikna\u00f0 n\u00e6r \u00fe\u00e6r komi aftur \u00e1 sama sta\u00f0, og \u00feannig hafa \u00feeir reikna\u00f0 g\u00e1ng h\u00e9rum 80 halastjarna, sem s\u00e9st hafa s\u00ed\u00f0an 837.\u00a0 Halley, mikill Stj\u00f6rnuspekingur \u00ed Englandi, reikna\u00f0i \u00fe\u00e6r manna fyrstur fyrir 100 \u00e1rum, og \u00fe\u00e1 \u00feegar 24 af \u00feeim. Hann sag\u00f0i l\u00edka fyrir, a\u00f0 halastjarnan sem s\u00e1st 1682 mundi aftur koma 1759, og muna\u00f0i einum m\u00e1nu\u00f0i \u00ed reikningi hans, hvar til Stj\u00f6rnuspekingar hafa s\u00ed\u00f0an sagt ors\u00f6kina, svo a\u00f0 raunar skeika\u00f0i ecki reikningur hans \u00ed hinu allra minsta.<\/p><\/blockquote>\n<p>\u00dearna hefur Hannes sett \u00e1rtali\u00f0 1759 \u00ed sta\u00f0 1758, sem Halley haf\u00f0i fengi\u00f0 \u00fat \u00far n\u00e1lgunarreikningum s\u00ednum og birt 1705. \u00cd \u00e1g\u00e6tri umfj\u00f6llun um endurkomuna og a\u00f0dragandann a\u00f0 henni \u00ed <a href=\"https:\/\/baekur.is\/bok\/000402495\/0\/127\/Stjornufraedi__lett_og_handa_Bls_127\">Stj\u00f6rnufr\u00e6\u00f0i<\/a> Ursins er fjalla\u00f0 um raunverulegu \u00e1st\u00e6\u00f0una fyrir \u00feessum mun (bls. 119-120):<\/p>\n<blockquote><p>Enn hjer var stj\u00f6rnufr\u00e6\u00f0ingunum miklu \u00f6r\u00f0ugra fyrir, enn \u00fe\u00f3tt \u00feeir hef\u00f0u \u00e1tt a\u00f0 reikna sjer til brautina eptir athugunum <em>[&#8230;]<\/em> \u00dea\u00f0 var var ekki s\u00f3lin ein, mi\u00f0kn\u00f6tturinn, er rje\u00f0i fer\u00f0 halastj\u00f6rnunnar; jar\u00f0irnar allar, er halastjarnan \u00e1tti a\u00f0 fara framhj\u00e1, hlutu a\u00f0 toga \u00ed hana, hvur eptir \u00fe\u00edngd sinni, og kippa henni nokku\u00f0 \u00far lei\u00f0 og fl\u00edta e\u00f0ur seinka komu hennar \u00ed s\u00f3ln\u00e1nd, eptir kr\u00edngumst\u00e6\u00f0unum. N\u00fa var um a\u00f0 gera, a\u00f0 reikna sjer til \u00feessa hrakninga og \u00fea\u00f0 ger\u00f0u \u00feeir <a href=\"https:\/\/en.wikipedia.org\/wiki\/Alexis_Clairaut\">Clairaut<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/J%C3%A9r%C3%B4me_Lalande\">Lalande<\/a> me\u00f0 tilhj\u00e1lp l\u00e6r\u00f0rar konu, er hjet <a href=\"https:\/\/en.wikipedia.org\/wiki\/Nicole-Reine_Lepaute\">Lepaute<\/a>. <em>[&#8230;]<\/em> Clairaut sag\u00f0i \u00fev\u00ed firir, a\u00f0 <em>[halastjarnan]<\/em> mundi ekki koma \u00ed s\u00f3ln\u00e1nd firr enn um vori\u00f0 1759, og daginn t\u00f3k hann til a\u00f0 mundi ver\u00f0a 13. apr\u00edl, enn minntist hins samt jafnframt, a\u00f0 \u00feessum reikn\u00edngi gj\u00e6ti skeika\u00f0 um m\u00e1nu\u00f0 <em>[&#8230;]<\/em> \u00deessi firirs\u00f6gn kom \u00f6ll fram. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Johann_Georg_Palitzsch\">Palizsch<\/a> s\u00e1 firstur halastj\u00f6rnuna \u00e1 J\u00f3ladaginn 1758, og hjerumbil \u00e1 sama sta\u00f0 og h\u00fan \u00e1tti a\u00f0 vera eptir reikningunum; og n\u00fa t\u00f3ku fleiri vi\u00f0 og f\u00f3ru a\u00f0 athuga hana, og af \u00fev\u00ed m\u00e1tti sj\u00e1, a\u00f0 h\u00fan mundi koma \u00ed s\u00f3ln\u00e1nd 13. Marts 1759.<\/p><\/blockquote>\n<ul>\n<li>R. Wallis, 1984: <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/00033798400200271?journalCode=tasc20\">The Glory of Gravity &#8211; Halley&#8217;s Comet 1759.<\/a><\/li>\n<li>C. B. Waff, 1986:\u00a0 <a href=\"http:\/\/adsbit.harvard.edu\/\/full\/1986JHA....17....1W\/0000001.000.html?high=59678436d723218\">Comet Halley&#8217;s First Expected Return: English Public Apprehensions, 1755-58.<\/a><\/li>\n<li>P. Broughton, 1985:\u00a0 <a href=\"http:\/\/adsbit.harvard.edu\/\/full\/1985JHA....16..123B\/0000123.000.html\">The First Predicted Return of Comet Halley.<\/a><\/li>\n<li>C. Wilson, 1993: <a href=\"http:\/\/adsbit.harvard.edu\/\/full\/1993JHA....24....1W\/0000001.000.html\"> Clairaut&#8217;s Calculation of the Eighteenth-Century Return of Halley&#8217;s Comet.<\/a><\/li>\n<\/ul>\n<p>\u00cd s\u00ed\u00f0ustu tilvitnuninni h\u00e9r a\u00f0 framan nefnir Ursin d\u00e6mi um beitingu svokalla\u00f0s truflanareiknings e\u00f0a hrakningareiknings, mikilv\u00e6grar n\u00e1lgunara\u00f0fer\u00f0ar, sem Newton er upphafsma\u00f0urinn a\u00f0. R\u00e6tt ver\u00f0ur stuttlega um \u00fea\u00f0 efni \u00ed n\u00e6sta kafla, sem jafntframt er s\u00e1 s\u00ed\u00f0asti \u00ed \u00feessari f\u00e6rslu.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><em><strong>Aflfr\u00e6\u00f0i himintungla &#8211; Truflanareikningur<\/strong><\/em><\/p>\n<p>\u00cd <em>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lunum<\/em> nota\u00f0i Newton \u00feyngdarl\u00f6gm\u00e1li\u00f0 \u00e1samt hreyfingarl\u00f6gm\u00e1lunum til a\u00f0 leysa hi\u00f0 svokalla\u00f0a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Kepler_orbit#Isaac_Newton\">tveggja hnatta vandam\u00e1l<\/a>. \u00dear s\u00fdndi hann st\u00e6r\u00f0fr\u00e6\u00f0ilega fram \u00e1, a\u00f0 \u00ed einangru\u00f0u kerfi tveggja fullkomlega k\u00falusamhverfra hnatta eru brautir hnattanna keilusni\u00f0, ef eini krafturirnn sem \u00fear verkar er gagnkv\u00e6mur \u00feyngdarkraftur. \u00deegar annar hn\u00f6tturinn er mun massaminni en hinn, m\u00e1 gera \u00fe\u00e1 n\u00e1lgun, a\u00f0 st\u00e6rri hn\u00f6tturinn (t.d. s\u00f3lin) s\u00e9 kyrr. \u00de\u00e1 s\u00fdna lausnirnar, a\u00f0 ef s\u00e1 minni hreyfist ekki of hratt (t. d. reikistjarna), sn\u00fdst hann umhverfis mi\u00f0hn\u00f6ttinn \u00ed samr\u00e6mi vi\u00f0 l\u00f6gm\u00e1l Keplers. Ef hra\u00f0inn er yfir \u00e1kve\u00f0num m\u00f6rkum (t. d. sumar halastj\u00f6rnur) er brautin anna\u00f0hvort fleygbogi e\u00f0a brei\u00f0bogi.<\/p>\n<p>Newton s\u00fdndi einnig fram \u00e1, hvernig finna m\u00e1 massa reikistj\u00f6rnu me\u00f0 tungl, sem hlutfall af massa s\u00f3larinnar. \u00deetta m\u00e1 sj\u00e1 me\u00f0 \u00fev\u00ed a\u00f0 hugsa s\u00e9r tveggja hnatta kerfi, \u00fear sem fylgihn\u00f6ttur me\u00f0 l\u00edtinn massa sn\u00fdst me\u00f0 umfer\u00f0art\u00edma T um mi\u00f0hn\u00f6tt me\u00f0 massa M. Brautin er hringlaga me\u00f0 geisla R og hra\u00f0inn er v. Setjum mi\u00f0s\u00f3knarhr\u00f6\u00f0unina (a =\u00a0 v<sup>2<\/sup>\/R = 4\u03c0<sup>2<\/sup>R\/T<sup>2<\/sup>) jafna \u00feyngdarhr\u00f6\u00f0uninni (g = GM\/R<sup>2<\/sup>). \u00de\u00e1 f\u00e6st ni\u00f0ursta\u00f0an M =\u00a0 4\u03c0<sup>2<\/sup>R<sup>3<\/sup>\/GT<sup>2<\/sup>, sem m\u00e1 annars vegar nota fyrir s\u00f3l og reikistj\u00f6rnu og hins vegar fyrir reikistj\u00f6rnu og tungl hennar. Me\u00f0 \u00fev\u00ed a\u00f0 deila seinni ni\u00f0urst\u00f6\u00f0unni \u00ed \u00fe\u00e1 fyrri, f\u00e6st hlutfalli\u00f0 milli massa s\u00f3lar (M) og massa reikistj\u00f6rnunnar (m). &#8211; \u00deessu l\u00fdsir Bj\u00f6rn Gunnlaugsson svo \u00ed hinni \u00e1g\u00e6tu grein <a href=\"http:\/\/timarit.is\/view_page_init.jsp?pageId=2021474\">Um \u00fe\u00fdngd reikistjarnanna<\/a> \u00e1ri\u00f0 1849 (bls. 64-65):<\/p>\n<blockquote>\n<p style=\"text-align: left\">L\u00f6gm\u00e1li\u00f0 fyrir \u00fe\u00fdngd \u00feeirra pl\u00e1neta, sem hafa t\u00fangl me\u00f0fer\u00f0is, ver\u00f0ur framsett \u00ed \u00feessum hlutfallaj\u00f6fnu\u00f0i e\u00f0a \u00feriggjali\u00f0areglu:<br \/>\n<span style=\"color: #ffffff\">&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;.\u00a0 <\/span><em>M : m = F<sup>3<\/sup> u<sup>2<\/sup> : f<sup>3<\/sup> U<sup>2<\/sup><\/em><br \/>\nsem me\u00f0 or\u00f0um hlj\u00f3\u00f0ar \u00feannig eptir r\u00f6\u00f0. \u00de\u00fdngd s\u00f3lar <em>(M)<\/em>, m\u00f3ti \u00fe\u00fdngd pl\u00e1netunnar med hennar t\u00fanglum <em>(m)<\/em>, er sem teningur fjarl\u00e6g\u00f0ar pl\u00e1netunnar fr\u00e1 s\u00f3lunni <em>(F<sup>3<\/sup>)<\/em>, margfalda\u00f0ur med ferm\u00e1li umfer\u00f0art\u00edma t\u00fanglsins kringum pl\u00e1netuna <em>(u<sup>2<\/sup>)<\/em>, m\u00f3ti teningi fjarl\u00e6g\u00f0ar t\u00fanglsins fr\u00e1 pl\u00e1netunni <em>(f<sup>3<\/sup>)<\/em>, margf\u00f6ldu\u00f0um med ferm\u00e1li umfer\u00f0art\u00edma pl\u00e1netunnar kringum s\u00f3lina <em>(U<sup>2<\/sup>)<\/em>.<\/p>\n<\/blockquote>\n<p>Bj\u00f6rn getur \u00feess einnig, a\u00f0 finna megi massa tunglsnau\u00f0ra reikistjarna \u201e<em>me\u00f0 hrindingum \u00feeirra innbyr\u00f0is<\/em>\u201c (\u00fe.e. me\u00f0 truflanareikningi). Ursin r\u00e6\u00f0ir og um \u00feetta sama efni og fleira \u00e1 bls. 108-114 \u00ed b\u00f3k sinni.<\/p>\n<figure id=\"attachment_11422\" aria-describedby=\"caption-attachment-11422\" style=\"width: 309px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-11422\" src=\"http:\/\/uni.hi.is\/einar\/files\/2019\/07\/Bjo\u0308rn_Gunnlaugsson-232x300.jpg\" alt=\"\" width=\"309\" height=\"400\" \/><figcaption id=\"caption-attachment-11422\" class=\"wp-caption-text\"><a href=\"http:\/\/timarit.is\/view_page_init.jsp?gegnirId=000819528\"><span style=\"font-size: 10pt\">Bj\u00f6rn Gunnlaugsson<\/span><\/a><span style=\"font-size: 10pt\">, \u00e1ri\u00f0 1859. &#8211; Teikning eftir Sigur\u00f0 Gu\u00f0mundsson.<\/span><\/figcaption><\/figure>\n<p>\u00dea\u00f0 a\u00f0 \u00feekkja massa reikistjarnanna, sem hlutfall af s\u00f3larmassa, er \u00ed sj\u00e1lfu s\u00e9r \u00e1g\u00e6tt, en n\u00e1kv\u00e6mari t\u00f6lur \u00ed venjulegum einingum \u00feurftu a\u00f0 b\u00ed\u00f0a \u00fear til <a href=\"https:\/\/en.wikipedia.org\/wiki\/Henry_Cavendish\">H. Cavendish<\/a> haf\u00f0i fundi\u00f0 gildi\u00f0 \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Gravitational_constant\">\u00feyngdarstu\u00f0linum G<\/a> me\u00f0 \u00f3beinum h\u00e6tti. \u00dea\u00f0 t\u00f3kst honum \u00e1 \u00e1runum 1797-1798 \u00ed <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cavendish_experiment\">fr\u00e6gri tilraun<\/a>, sem s\u00ed\u00f0an er vi\u00f0 hann kennd, \u00fe\u00f3tt h\u00fan s\u00e9 \u00ed meginatri\u00f0um bygg\u00f0 \u00e1 hugmyndum vinar hans, hins fj\u00f6lh\u00e6fa <a href=\"https:\/\/en.wikipedia.org\/wiki\/John_Michell\">J. Michells<\/a>.<\/p>\n<p>Eins og \u00e1\u00f0ur hefur komi\u00f0 fram, vissi Newton m\u00e6ta vel, a\u00f0 j\u00f6r\u00f0in er ekki eins og fullkomin st\u00edf k\u00fala, heldur teygjanlegur hn\u00f6ttur me\u00f0 sn\u00faningi og mi\u00f0baugsbungu og tilheyrandi p\u00f3lveltu. Auk \u00feess verka gagnkv\u00e6mir sj\u00e1varfallakraftar milli tungls og jar\u00f0ar, og \u00e1hrif fr\u00e1 s\u00f3linni eru veruleg, b\u00e6\u00f0i \u00e1 sj\u00e1varf\u00f6llin og \u00f6nnur fyrirb\u00e6ri, \u00fear sem \u00feyngd kemur vi\u00f0 s\u00f6gu. Meistarinn ger\u00f0i s\u00e9r einnig fulla grein fyrir \u00fev\u00ed, a\u00f0 \u00feyngdar\u00e1frif s\u00f3lar eru \u00feess valdandi, a\u00f0 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lunar_theory#Newton\">braut tunglsins<\/a> um j\u00f6r\u00f0ina v\u00edkur talsvert fr\u00e1 sporbaugsl\u00f6gun.<\/p>\n<p>Newton ger\u00f0i margar tilraunir til a\u00f0 sp\u00e1 sem n\u00e1kv\u00e6mast fyrir um innbyr\u00f0is \u00feyngdar\u00e1hrif s\u00f3lar, tungls og jar\u00f0ar, \u00fea\u00f0 er a\u00f0 finna vi\u00f0eigandi st\u00e6r\u00f0fr\u00e6\u00f0ilega lausn \u00e1 hinu svonefnda <a href=\"https:\/\/en.wikipedia.org\/wiki\/Three-body_problem\">\u00feriggja hnatta vandam\u00e1li<\/a>. \u00dea\u00f0 t\u00f3kst \u00fe\u00f3 ekki og hann \u00e1tta\u00f0i sig flj\u00f3tlega \u00e1 \u00fev\u00ed, a\u00f0 \u00fear \u00feyrfti a\u00f0 innlei\u00f0a n\u00fdja tegund n\u00e1lgunar, a\u00f0fer\u00f0 sem n\u00fa gengur undir nafninu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Perturbation_theory#History\">truflanareikningur<\/a>. \u00deannig t\u00f3kst honum a\u00f0 finna n\u00e1lgunarlausnir, en samt ekki n\u00f3gu n\u00e1kv\u00e6mar. \u00c1 endanum l\u00fdsti hann \u00fev\u00ed yfir, a\u00f0 leitin a\u00f0 sk\u00fdringum \u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Orbit_of_the_Moon\">hreyfingum tunglsins<\/a> v\u00e6ri eina verkefni\u00f0, sem hef\u00f0i valdi\u00f0 honum h\u00f6fu\u00f0verkjum.<\/p>\n<p>\u00dea\u00f0 var ekki fyrr en um mi\u00f0bik \u00e1tj\u00e1ndu aldar, sem \u00feeim <a href=\"https:\/\/en.wikipedia.org\/wiki\/Alexis_Clairaut\">A. Clairaut<\/a>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Leonhard_Euler\">L. Euler<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Jean_le_Rond_d%27Alembert\">J. R. d&#8217;Alembert<\/a> t\u00f3kst \u00ed meginatri\u00f0um a\u00f0 leysa vandam\u00e1li\u00f0 um hreyfingu tunglsins me\u00f0 \u00fev\u00ed a\u00f0 beita n\u00e1kv\u00e6mari truflanareikningi en Newton haf\u00f0i gert \u00e1 s\u00ednum t\u00edma. \u00c1rangur \u00feeirra bygg\u00f0ist me\u00f0al annars \u00e1 hinni gagnlegu st\u00e6r\u00f0fr\u00e6\u00f0ilegu framsetningu Leibniz \u00e1 \u00f6rsm\u00e6\u00f0areikningi og ekki s\u00ed\u00f0ur \u00e1 framlagi Eulers til \u00feeirra fr\u00e6\u00f0a.<\/p>\n<ul>\n<li>A. Cook, 2000: <a href=\"http:\/\/adsabs.harvard.edu\/full\/2000A%26G....41f..21C\">Success and failure in Newton&#8217;s lunar theory<\/a>.<\/li>\n<li>S. Bodenmann, 2010: <a href=\"https:\/\/physicstoday.scitation.org\/doi\/pdf\/10.1063\/1.3293410\">The 18th-century battle over lunar motion.<\/a><\/li>\n<li>M. C. Gutzwiller, 1998: <a href=\"https:\/\/journals.aps.org\/rmp\/abstract\/10.1103\/RevModPhys.70.589\">Moon-Earth-Sun: The Oldest Three-body Problem<\/a>.<\/li>\n<\/ul>\n<p>\u00c1 seinni hluta \u00e1tj\u00e1ndu aldar fundu b\u00e6\u00f0i Euler og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Joseph-Louis_Lagrange\">J. L. Lagrange<\/a> \u00fdmsar <a href=\"https:\/\/en.wikipedia.org\/wiki\/N-body_problem#Three-body_problem\">s\u00e9rstakar lausnir<\/a> \u00e1 \u00feriggja hnatta vandam\u00e1linu og veltu me\u00f0al annars fyrir s\u00e9r kerfi, \u00fear sem massal\u00edtil \u00f6gn hreyfist \u00ed sameiginlegu \u00feyngdarsvi\u00f0i tveggja st\u00f3rra hnatta. \u00deannig uppg\u00f6tvu\u00f0u \u00feeir <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lagrange_point\">punktana<\/a>, sem n\u00fa eru eing\u00f6ngu kenndir vi\u00f0 Lagrange og miki\u00f0 nota\u00f0ir \u00ed stjarne\u00f0lisfr\u00e6\u00f0i. Sem d\u00e6mi m\u00e1 nefna, a\u00f0 fyrstu tveir \u00edslensku stj\u00f6rnufr\u00e6\u00f0ingarnir, \u00feeir <a href=\"https:\/\/uni.hi.is\/einar\/2019\/11\/14\/sturla-einarsson-stjornufraediprofessor\/\">Sturla Einarsson<\/a> og <a href=\"https:\/\/timarit.is\/page\/5457421#page\/n2\/mode\/2up\">Stein\u00fe\u00f3r Sigur\u00f0sson<\/a> fengust b\u00e1\u00f0ir vi\u00f0 \u00fatreikninga \u00e1 brautum sm\u00e1stirna \u00ed h\u00f3pi <a href=\"https:\/\/en.wikipedia.org\/wiki\/Jupiter_trojan\">Tr\u00f3jusm\u00e1stirnanna<\/a> \u00ed punktum L<sub>4<\/sub> og L<sub>5<\/sub> \u00e1 braut J\u00fap\u00edters umhverfis s\u00f3lina.<\/p>\n<p>\u00deriggja hnatta vandam\u00e1li\u00f0 er a\u00f0eins eitt hinna svok\u00f6llu\u00f0u <a href=\"https:\/\/en.wikipedia.org\/wiki\/N-body_problem\">fj\u00f6lhnatta vandam\u00e1la<\/a>. Tveggja hnatta vandam\u00e1li\u00f0 tilheyrir einnig flokknum, en \u00fea\u00f0 hefur \u00fe\u00e1 s\u00e9rst\u00f6\u00f0u, a\u00f0 til er <a href=\"https:\/\/en.wikipedia.org\/wiki\/Closed-form_expression\">almenn lausn \u00e1 loku\u00f0u formi<\/a>, nokku\u00f0 sem ekki er um a\u00f0 r\u00e6\u00f0a, ef hnettirnir eru \u00fer\u00edr e\u00f0a fleiri. \u00dea\u00f0 \u00fe\u00fd\u00f0ir, a\u00f0 \u00fe\u00e1 \u00fearf n\u00e6r undantekningalaust a\u00f0 nota s\u00e9rstakar n\u00e1lgunara\u00f0fer\u00f0ir og t\u00f6lulega reikninga vi\u00f0 leit a\u00f0 lausnum.<\/p>\n<p>\u00cd \u00edslenskum fr\u00e6\u00f0sluritum er fjalla\u00f0 um \u00fdmsa \u00fer\u00e6\u00f0i \u00feessarar s\u00f6gu, b\u00e6\u00f0i \u00ed <em>Stj\u00f6rnufr\u00e6\u00f0i<\/em> Ursins (bls. 106-124) og \u00ed grein Bj\u00f6rns Gunnlaugssonar <em>Um \u00fe\u00fdngd reikistjarnanna<\/em>.<\/p>\n<p>Fr\u00e6\u00f0igreinin, sem fjallar um fj\u00f6lhnatta vandam\u00e1li\u00f0 \u00ed stjarnv\u00edsindum gengur undir nafninu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Celestial_mechanics\">aflfr\u00e6\u00f0i himintungla<\/a> og einn mikilv\u00e6gasti hluti hennar er <a href=\"https:\/\/en.wikipedia.org\/wiki\/Perturbation_theory#History\">truflanareikningur<\/a> (hnikareikingur, hrakningareikningur). \u00cd stuttu m\u00e1li m\u00e1 segja, a\u00f0 auk Newtons hafi upphafsmennirnir veri\u00f0 \u00feeir Euler, d&#8217;Alembert og Clairaut, en greinin t\u00f3k fyrst flugi\u00f0 fyrir alv\u00f6ru me\u00f0 a\u00f0komu \u00feeirra Lagrange og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pierre-Simon_Laplace\">P. S. Laplace<\/a>. \u00dea\u00f0 var Laplace sem bj\u00f3 til hugtaki\u00f0\u00a0 <em>m\u00e9canique c\u00e9leste<\/em> (alffr\u00e6\u00f0i himintungla) og hi\u00f0 magna\u00f0a verk hans <a href=\"https:\/\/en.wikipedia.org\/wiki\/Trait%C3%A9_de_m%C3%A9canique_c%C3%A9leste\">Trait\u00e9 de M\u00e9canique C\u00e9leste<\/a> fr\u00e1 \u00e1runum 1798 til 1825 var lengi ein helsta heimild \u00feess hers stj\u00f6rnufr\u00e6\u00f0inga, sem unnu a\u00f0 n\u00e1kv\u00e6mnis\u00fatreikningum \u00e1 brautum himinhnatta \u00e1 n\u00edtj\u00e1ndu \u00f6ld og langt fram eftir \u00feeirri tuttugustu.<\/p>\n<ul>\n<li>F.R. Moulton, 1914: <a href=\"https:\/\/archive.org\/details\/introcelestial00moulrich\/page\/n7\/mode\/2up\">An Introduction to Celestial Mechanics<\/a> (2. \u00fatg). S\u00f6guyfirlit er a\u00f0 finna \u00ed lok flestra kaflanna.<\/li>\n<li>I. Peterson, 1993: <a href=\"https:\/\/books.google.is\/books?id=Ul2G5jFEejgC&amp;source=gbs_navlinks_s\">Newton&#8217;s Clock: Chaos In The Solar System<\/a>.<\/li>\n<li>R. Taton &amp; C. Wilson ritstj., 1995: <a href=\"https:\/\/www.cambridge.org\/is\/academic\/subjects\/physics\/history-philosophy-and-foundations-physics\/general-history-astronomy-volume-2?format=PB&amp;isbn=9780521120098\">The General History of Astronomy: Planetary Astronomy from the Renaissance to the Rise of Astrophysics &#8211; Part 2B: The Eighteenth and Nineteenth Centuries<\/a>.<\/li>\n<li>L. E. Doggett, 1997: <em>Celestial Mechanics<\/em>. \u00cd J. Lankford ritstj.: <a href=\"https:\/\/archive.org\/details\/historyofastrono00john\">History of Astronomy: An Encyclopedia<\/a> (bls. 131-140).<\/li>\n<li>A. E. Roy, 2004, <a href=\"https:\/\/books.google.is\/books?id=Hzv7k2vH6PgC&amp;source=gbs_navlinks_s\">Orbital Motion<\/a> (4. \u00fatg).<\/li>\n<li>A. Celletti &amp; E. Perozzi, 2007: <a href=\"https:\/\/books.google.is\/books?id=y7yar3lIj-AC&amp;source=gbs_navlinks_s\">Celestial Mechanics: The Waltz of the Planets<\/a>.<\/li>\n<\/ul>\n<p>Aflfr\u00e6\u00f0i himintungla \u00e1tti s\u00e9r bl\u00f3maskei\u00f0 \u00e1 t\u00edmabilinu fr\u00e1 \u00fev\u00ed um 1740 fram til 1860 e\u00f0a svo, \u00feegar hin n\u00fdja stjarne\u00f0lisfr\u00e6\u00f0i t\u00f3k a\u00f0 skyggja \u00e1 hana me\u00f0 litr\u00f3fs- og lj\u00f3sm\u00e6lingum, lj\u00f3smyndat\u00e6kni og n\u00fdjum hugmyndum um e\u00f0li stjarna og samband lj\u00f3ss, varma og efnis (sj\u00e1 f\u00e6rslu <span style=\"color: #00ff00\">3<\/span>). Greinin t\u00f3k \u00fe\u00f3 aftur hressilega vi\u00f0 s\u00e9r me\u00f0 tilkomu geimfer\u00f0a, ranns\u00f3kna \u00e1 n\u00fdjum svi\u00f0um rafsegulgeislunnar og st\u00f3raukinnar reiknigetu \u00e1 \u00e1runum um og upp\u00far 1960. Uppg\u00f6tvun fj\u00f6lda n\u00fdrra fyrirb\u00e6ra, \u00fear \u00e1 me\u00f0al nifteindastjarna, svarthola og \u00fe\u00e9ttst\u00e6\u00f0ra tv\u00edstirna, kalla\u00f0i \u00e1\u00a0 frekari \u00fer\u00f3un aflfr\u00e6\u00f0ireikninga, og ekki minnka\u00f0i \u00e1huginn eftir a\u00f0 menn fundu fyrstu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Exoplanet\">fjarreikistj\u00f6rnurnar<\/a> \u00e1 t\u00edunda \u00e1ratugnum.\u00a0 &#8211;\u00a0 R\u00e9tt er a\u00f0 nefna, a\u00f0 s\u00e1 \u00cdslendingur, sem hva\u00f0 mest kom a\u00f0 ranns\u00f3knum \u00ed aflfr\u00e6\u00f0i himintungla \u00e1 seinni hluta tuttugustu aldar, var stjarne\u00f0lisfr\u00e6\u00f0ingurinn <a href=\"https:\/\/uni.hi.is\/einar\/2019\/11\/14\/stjarnedlisfraedingurinn-gisli-hlodver-palsson-odru-nafni-jack-g-hills\/\">Jack G. Hills (G\u00edsli Hl\u00f6\u00f0ver P\u00e1lsson)<\/a>.<\/p>\n<p>\u00c9g l\u00fdk \u00feessari f\u00e6rslu me\u00f0 stuttri umfj\u00f6llun um nokkra \u00e1hugaver\u00f0a \u00fe\u00e6tti \u00far aflfr\u00e6\u00f0i-ranns\u00f3knum \u00e1 s\u00f3lkerfinu.<\/p>\n<p>\u00cd <em>Stj\u00f6rnufr\u00e6\u00f0i<\/em> Ursins m\u00e1 lesa eftirfarandi \u00e1 bls. 36:<\/p>\n<blockquote><p>Stj\u00f6rnuspekingar hafa leita\u00f0 svo grandgj\u00e6filega um allan himininn, a\u00f0 \u00fea\u00f0 eru l\u00edtil l\u00edkindi til nein st\u00f3r jar\u00f0stjarna og \u00f3\u00feekkt gjeti veri\u00f0 til innar, e\u00f0ur n\u00e6r s\u00f3lu, enn braut Uranusar liggur; ekki heldur l\u00edkindi til a\u00f0 nein sl\u00edk stjarna sje utar, s\u00fa er eigi heima \u00ed voru s\u00f3lkjerfi.<\/p><\/blockquote>\n<p>Ekki\u00a0 voru li\u00f0in nema fj\u00f6gur \u00e1r fr\u00e1 \u00fatkomu \u00edslensku \u00fe\u00fd\u00f0ingarinnar, \u00feegar stj\u00f6rnufr\u00e6\u00f0ing-arnir <a title=\"Johann Gottfried Galle\" href=\"https:\/\/en.wikipedia.org\/wiki\/Johann_Gottfried_Galle\">J. G. Galle<\/a> og <a title=\"Heinrich Louis d'Arrest\" href=\"https:\/\/en.wikipedia.org\/wiki\/Heinrich_Louis_d%27Arrest\">H. L. d&#8217;Arrest<\/a> komu auga \u00e1 n\u00fdja reikistj\u00f6rnu utan vi\u00f0 braut \u00daranusar. \u00deeir h\u00f6f\u00f0u fengi\u00f0 \u00e1bendingar fr\u00e1 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Urbain_Le_Verrier\">U. Le Verrier<\/a> um \u00fea\u00f0, hvar skyldi leita, en hann haf\u00f0i nota\u00f0 \u00e1\u00f0ur \u00f3\u00fatsk\u00fdr\u00f0a \u00f3reglu \u00e1 braut \u00daranusar og truflanareikning til a\u00f0 sp\u00e1 fyrir um tilvist n\u00fdju reikistj\u00f6rnunnar og st\u00f6\u00f0u hennar \u00e1 tilteknum t\u00edma.<\/p>\n<p>Hin \u00e1hugaver\u00f0a saga um <a href=\"https:\/\/en.wikipedia.org\/wiki\/Discovery_of_Neptune\">fund Nept\u00fanusar<\/a> \u00e1ri\u00f0 1846 ver\u00f0ur ekki rakin h\u00e9r, en atbur\u00f0urinn vakti g\u00edfurlega athygli \u00e1 s\u00ednum t\u00edma og var talinn mikilv\u00e6gur stu\u00f0ningur vi\u00f0 \u00feyngdarfr\u00e6\u00f0i Newtons. \u00cd greininni <em>Um \u00fe\u00fdngd reikistjarnanna<\/em> fr\u00e1 1849 fjallar Bj\u00f6rn Gunnlaugsson um truflanareikningana a\u00f0 baki og segir me\u00f0al annars \u00e1 bls. 63-65:<\/p>\n<blockquote><p>Svo eru stj\u00f6rnufr\u00e6\u00f0ingar or\u00f0nir vel a\u00f0 s\u00e9r \u00ed <em>[&#8230;]<\/em> \u00fe\u00fdngdarl\u00f6gum, a\u00f0 einn \u00feeirra hefur n\u00fa n\u00fdlega reikna\u00f0 \u00fat tilveru pl\u00e1netu, er einginn vissi af \u00e1\u00f0ur; sag\u00f0i hann fyrir hvar h\u00fan v\u00e6ri, hvernig h\u00fan geingi og hva\u00f0 \u00fe\u00fang h\u00fan v\u00e6ri, \u00e1n \u00feess a\u00f0 hafa s\u00e9\u00f0 hana, svo hann eins og v\u00f3g hana \u00f3s\u00e9na. \u00deessi ma\u00f0ur var Le Verrier, frakkneskur ma\u00f0ur. \u00dear \u00e1 eftir f\u00f3r annar stj\u00f6rnumeistari \u00ed Berl\u00edn, Galle a\u00f0 leita a\u00f0 pl\u00e1netunni \u00fear sem hinn fyrri tilvitna\u00f0i, e\u00f0a eptir \u00feeim g\u00e1ngreglum sem hann eigna\u00f0i henni; og pl\u00e1netan st\u00f3\u00f0 \u00fear, sem h\u00fan \u00e1tti a\u00f0 standa eptir \u00feeim, \u00feegar Galle fann hana \u00feann 23. sept. 1846. <em>[&#8230;]<\/em>\u00a0 Allt \u00feetta er spunni\u00f0 \u00fataf \u00fe\u00fdngdarl\u00f6gum \u00feeim hinum nafnfr\u00e6gu, er spekingurinn Newton uppg\u00f6tva\u00f0i, hver l\u00f6g ad sta\u00f0festast daglega, og pl\u00e1netan Neptunus er framkomin sem n\u00fdtt vitni upp\u00e1 \u00feeirra sannleika.<\/p><\/blockquote>\n<p>\u00c1ri\u00f0 1878, tveimur \u00e1rum eftir a\u00f0 Bj\u00f6rn Gunnlaugsson l\u00e9st, birtist \u00fe\u00fddd grein \u00ed <em>\u00cdsafold<\/em> undir heitinu <em>Uppg\u00f6tvan Leverriers<\/em> (<a href=\"https:\/\/timarit.is\/page\/3939689\">1. hluti<\/a>; <a href=\"https:\/\/timarit.is\/page\/3939694\">2. hluti<\/a>). \u00de\u00f3tt innihaldi\u00f0 hafi l\u00edti\u00f0 s\u00f6gulegt gildi, gefur greinin sennilega d\u00e1g\u00f3\u00f0a mynd af bla\u00f0aumfj\u00f6llun \u00feess t\u00edma um v\u00edsindaleg efni.<\/p>\n<ul>\n<li>R. W. Smith, 1989: <a href=\"https:\/\/www.jstor.org\/stable\/234933?seq=3#metadata_info_tab_contents\">The Cambridge Network in Action: The Discovery of Neptune<\/a>.<\/li>\n<li>T. Standage, 2000: <a href=\"https:\/\/books.google.is\/books\/about\/The_Neptune_File.html?id=89HaAAAAMAAJ&amp;redir_esc=y\">The Neptune File: Planet Detectives and the Discovery of Worlds Unseen.<\/a><\/li>\n<li>W. Sheean, N. Kollerstron &amp; C. B. Waff, 2004: <a href=\"https:\/\/www.jstor.org\/stable\/26060804?seq=1#metadata_info_tab_contents\">The Case of the Pilfered Planet: Did the British steal Neptune?<\/a><\/li>\n<li>D. Kent, 2011: <a href=\"https:\/\/physicstoday.scitation.org\/doi\/full\/10.1063\/PT.3.1363\">The curious aftermath of Neptune\u2019s discovery<\/a>.<\/li>\n<li>D. Krajnovic, 2016: <a href=\"https:\/\/academic.oup.com\/astrogeo\/article\/57\/5\/5.28\/2738843\">The contrivance of Neptune<\/a>.<\/li>\n<\/ul>\n<p>Eftir fund Nept\u00fanusar og fr\u00e6g\u00f0ina, sem fylgdi \u00ed kj\u00f6lfari\u00f0, lag\u00f0i Le Verrier til atl\u00f6gu vi\u00f0 svipa\u00f0 verkefni, nefnilega \u00fea\u00f0 a\u00f0 \u00fatsk\u00fdra, hvers vegna hreyfing Merk\u00far\u00edusar um s\u00f3lu v\u00e6ri ekki \u00ed fullu samr\u00e6mi vi\u00f0 \u00fatreikninga bygg\u00f0a \u00e1 \u00feyngdarfr\u00e6\u00f0i Newtons. \u00c1ri\u00f0 1859 setti hann fram r\u00f6kstudda kenningu \u00feess efnis, a\u00f0 \u00f3reglan stafa\u00f0i af \u00feyngdartruflunum n\u00fdrrar og \u00e1\u00f0ur \u00f3\u00feekktrar reikistj\u00f6rnu, sem v\u00e6ri n\u00e6r s\u00f3lu en Merk\u00far\u00edus. Hann gaf stj\u00f6rnunni nafni\u00f0 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Vulcan_(hypothetical_planet)\">V\u00falkan<\/a>.<\/p>\n<p>Leitin a\u00f0 n\u00fdju reikistj\u00f6rnunni h\u00f3fst \u00fev\u00ed sem n\u00e6st samstundis eftir tilkynningu Le Verriers og flj\u00f3tlega \u00fe\u00f3ttust \u00fdmsir hafa komi\u00f0 auga \u00e1 V\u00falkan. Fyrsta tilkynningin, sem stj\u00f6rnumeistarinn t\u00f3k alvarlega kom fr\u00e1 franska l\u00e6kninum og stj\u00f6rnu\u00e1hugamanninum <a href=\"https:\/\/en.wikipedia.org\/wiki\/Edmond_Modeste_Lescarbault\">E. M. Lescarbault<\/a> \u00ed \u00e1rslok 1859. Le Verrier tilkynnti <em>Fr\u00f6nsku v\u00edsindaakadem\u00edunni<\/em> um fundinn upp \u00far \u00e1ram\u00f3tunum og fr\u00e9ttin kom n\u00e6r samstundis \u00ed dagbl\u00f6\u00f0um. H\u00e9r \u00e1 landi <a href=\"https:\/\/timarit.is\/page\/2038455\">birstist h\u00fan<\/a> \u00ed <em>\u00cdslendingi<\/em> 20. apr\u00edl 1860 (bls. 15) og 19. ma\u00ed m\u00e1tti sj\u00e1 <a href=\"https:\/\/timarit.is\/page\/2038466\">\u00fe\u00fddda grein<\/a> um efni\u00f0 \u00e1 fors\u00ed\u00f0u sama bla\u00f0s.<\/p>\n<p>Athuganir Lescarbault voru flj\u00f3tlega gagnr\u00fdndar har\u00f0lega og leitin a\u00f0 reikistj\u00f6rnunni h\u00e9lt \u00fev\u00ed \u00e1fram. \u00c1 n\u00e6stu \u00e1ratugum birtust reglulega fr\u00e9ttir um \u00fea\u00f0, a\u00f0 V\u00falkan hef\u00f0i s\u00e9st, en vi\u00f0 n\u00e1nari athugun <a href=\"https:\/\/en.wikipedia.org\/wiki\/Vulcan_(hypothetical_planet)#Search\">reyndust \u00fe\u00e6r allar tilh\u00e6fulausar<\/a>.<\/p>\n<figure id=\"attachment_17074\" aria-describedby=\"caption-attachment-17074\" style=\"width: 335px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-17074\" src=\"https:\/\/uni.hi.is\/einar\/files\/2020\/10\/Vulkan_I\u0301safold-05-09-1878-300x257.jpeg\" alt=\"\" width=\"335\" height=\"287\" \/><figcaption id=\"caption-attachment-17074\" class=\"wp-caption-text\"><span style=\"font-size: 10pt\">\u00datlend fr\u00e9tt \u00ed <em>\u00cdsafold,<\/em> 5. sept 1878 (bls. 88).<\/span><\/figcaption><\/figure>\n<p>R\u00e9tta sk\u00fdringin \u00e1 \u00f3reglunni \u00e1 braut Merk\u00far\u00edusar fannst ekki fyrr en en \u00ed \u00e1rslok 1915, \u00feegar Einstein s\u00fdndi fram \u00e1, a\u00f0 h\u00fan var bein aflei\u00f0ing af <a href=\"https:\/\/en.wikipedia.org\/wiki\/Tests_of_general_relativity#Perihelion_precession_of_Mercury\">afst\u00e6\u00f0ilegum eiginleikum \u00feyngdarinnar<\/a> (sj\u00e1 stutta umfj\u00f6llun um s\u00f6gu almennu afst\u00e6\u00f0iskenningarinnar <a href=\"https:\/\/uni.hi.is\/einar\/2019\/11\/19\/afstaediskenningar-einsteins-og-grein-thorkels-thorkelssonar-um-tilraunir-til-ad-sannreyna-thaer\/\">\u00ed fyrri f\u00e6rslu<\/a>).<\/p>\n<ul>\n<li>O. J. Eggen, 1953: <a href=\"http:\/\/adsabs.harvard.edu\/full\/1953ASPL....6..291E\">Vulcan<\/a>.<\/li>\n<li>N. R. Hanson, 1962: <a href=\"https:\/\/www.jstor.org\/stable\/227787?seq=1#metadata_info_tab_contents\">Leverrier: The Zenith and Nadir of Newtonian Mechanics<\/a>.<\/li>\n<li>R. P. Baum &amp; W. Sheean, 1997: <a href=\"https:\/\/books.google.is\/books?id=jLbzBwAAQBAJ&amp;source=gbs_navlinks_s\">In Search of Planet Vulcan: The Ghost in Newton\u2019s Clockwork Universe.<\/a><\/li>\n<li>T. Levinson, 2015: <a href=\"https:\/\/books.google.is\/books?id=YTW5CgAAQBAJ&amp;source=gbs_navlinks_s\">The Hunt for Vulcan: How Albert Einstein Destroyed a Planet and Deciphered the Universe<\/a>.<\/li>\n<li>W. Sheehan &amp; T. Misch, 2016: <a href=\"https:\/\/societyforthehistoryofastronomy.com\/wp-content\/uploads\/2018\/07\/aa10.pdf\">A special centennial: Mercury, Vulcan, and an early triumph for General Relativity<\/a> (bls. 2-12).<\/li>\n<\/ul>\n<p>Eftir fund Nept\u00fanusar \u00e1ri\u00f0 1846 fengu stj\u00f6rnufr\u00e6\u00f0ingar \u00e1huga \u00e1 \u00fev\u00ed a\u00f0 kanna, hvort fleiri st\u00f3rar reikistj\u00f6rnur kynnu a\u00f0 leynast <a href=\"https:\/\/en.wikipedia.org\/wiki\/Planets_beyond_Neptune\">enn utar \u00ed s\u00f3lkerfinu<\/a>. \u00ddmsar tilraunir til a\u00f0 finna sl\u00edkar stj\u00f6rnur me\u00f0 a\u00f0sto\u00f0 truflanareiknings h\u00f3fust \u00ed kj\u00f6lfari\u00f0 og \u00e1ri\u00f0 1930 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pluto#History\">fannst dvergreikistjarnan Pl\u00fat\u00f3<\/a> \u00ed einnri sl\u00edkri. S\u00ed\u00f0ar kom \u00fe\u00f3 \u00ed lj\u00f3s, a\u00f0 s\u00e1 fundur var tilviljun.<\/p>\n<p>H\u00e9r ver\u00f0ur ekki fjalla\u00f0 n\u00e1nar um \u00feann hluta s\u00f3lkerfisins, sem er <a href=\"https:\/\/en.wikipedia.org\/wiki\/Solar_System#Trans-Neptunian_region\">utan brautar Nept\u00fanusar<\/a>. \u00de\u00f3 get \u00e9g ekki stillt mig um a\u00f0 nefna n\u00fdlega tilg\u00e1tu um <a href=\"https:\/\/en.wikipedia.org\/wiki\/Planet_Nine\">n\u00edundu reikistj\u00f6rnuna<\/a>, sem talsvert hefur veri\u00f0 til umr\u00e6\u00f0u me\u00f0al v\u00edsindamanna. Leitin a\u00f0 henni hefur ekki enn bori\u00f0 \u00e1rangur og \u00ed lj\u00f3si \u00feess hafa sumir l\u00e1ti\u00f0 s\u00e9r detta \u00ed hug, a\u00f0 \u00fearna s\u00e9 ekki um reikistj\u00f6rnu a\u00f0 r\u00e6\u00f0a heldur <a href=\"https:\/\/astronomy.com\/news\/2020\/07\/is-planet-nine-a-black-hole-or-a-planet-harvard-scientists-suggest-a-way-to-find-out\">svartholskr\u00edli<\/a>. Af \u00feessu m\u00e1 sj\u00e1, a\u00f0 enn \u00feann dag \u00ed dag eru settar fram heillandi tilg\u00e1tur um e\u00f0li og eiginleika s\u00f3lkerfisins.<\/p>\n<ul>\n<li>W. G. Hoyt, 1976: <a href=\"https:\/\/www.jstor.org\/stable\/230561?seq=7#metadata_info_tab_contents\">W. H. Pickering&#8217;s Planetary Predictions and the Discovery of Pluto<\/a>.<\/li>\n<li>M. Littmann, 1990: <a href=\"https:\/\/books.google.is\/books?id=RoJMadct4TQC&amp;source=gbs_navlinks_s\">Planets Beyond: Discovering the Outer Solar System<\/a>.<\/li>\n<li>M. Brown, 2019: <a href=\"https:\/\/physicstoday.scitation.org\/doi\/10.1063\/PT.3.4172\">The Planet Nine hypothesis<\/a>.<\/li>\n<\/ul>\n<p>\u00c1 s\u00ednum t\u00edma haf\u00f0i Newton nokkrar \u00e1hyggjur af \u00fev\u00ed, a\u00f0 \u00feyngdartruflanir g\u00e6tu valdi\u00f0 \u00f3st\u00f6\u00f0ugleika, annars vegar \u00ed dreifingu fastastjarnanna \u00ed \u00f3endanlegum stj\u00f6rnuheimi, og hins vegar \u00ed hreyfingum himintungla \u00ed s\u00f3lkerfinu. Fyrra atri\u00f0i\u00f0 ver\u00f0ur teki\u00f0 til umr\u00e6\u00f0u \u00ed n\u00e6stu f\u00e6rslu (<span style=\"color: #00ff00\">2d<\/span>), en h\u00e9r ver\u00f0ur fjalla\u00f0 stuttlega um hi\u00f0 s\u00ed\u00f0arnefnda.<\/p>\n<p>Eins og \u00e1\u00f0ur hefur veri\u00f0 minnst \u00e1, var Newton \u00feeirrar sko\u00f0unar, a\u00f0 vi\u00f0 sk\u00f6pun s\u00f3lkerfisins hef\u00f0i Gu\u00f0 alm\u00e1ttugur komi\u00f0 himintunglunum \u00feannig fyrir, a\u00f0 sem minnst \u00f3regla yr\u00f0i \u00e1 hreyfingum \u00feeirra vegna innbyr\u00f0is \u00feyngdartruflana. Ef \u00ed \u00f3efni stefndi, myndi hann hins vegar gr\u00edpa \u00ed taumana og endurstilla kerfi\u00f0.<\/p>\n<p>Stef\u00e1n Bj\u00f6rnsson var undir verulegum \u00e1hrifum fr\u00e1\u00a0 Newton, eins og sj\u00e1 m\u00e1\u00a0 \u00ed hinni merku disp\u00fatat\u00edu hans, <a href=\"https:\/\/notendur.hi.is\/einar\/SAGA\/SB_cometae_1758.pdf\">Um verkan halastjarna<\/a>, fr\u00e1 1758. Eftir a\u00f0 hafa bent \u00e1, a\u00f0 halastj\u00f6rnur koma \u00far \u00f6llum \u00e1ttum inn \u00ed reikistj\u00f6rnukerfi\u00f0, segir hann me\u00f0al annars (\u00a76, bls. 6-7; H\u00e9r \u00fearf a\u00f0 hafa \u00ed huga, a\u00f0 \u00e1 \u00feessum t\u00edma var massi halastjarna yfirleitt talinn mun meiri en hann er \u00ed raun):<\/p>\n<blockquote><p>Ef halastj\u00f6rnur gengju um <a href=\"https:\/\/en.wikipedia.org\/wiki\/Zodiac\">d\u00fdrahringinn<\/a>, \u00feegar \u00fe\u00e6r koma inn \u00ed reikistj\u00f6rnukerfi okkar, yr\u00f0i minna bil milli \u00feeirra og reikistjarnanna, en ver\u00f0ur \u00ed raun<em> [&#8230;]<\/em> og aflei\u00f0ingin yr\u00f0i s\u00fa a\u00f0 reikistj\u00f6rnurnar myndu rykkjast af miklu meira afli a\u00f0 halastj\u00f6rnunum og halastj\u00f6rnur aftur a\u00f0 reikistj\u00f6rnum. \u00deess vegna myndu brautir reikistjarna og halastjarna bogna \u00far h\u00f3fi fram, <em>[&#8230;]<\/em> s\u00f3lfir\u00f0 og s\u00f3ln\u00e1nd \u00feokast fram e\u00f0a h\u00f6rfa \u00far h\u00f3fi og mi\u00f0skekkjur og fjarl\u00e6g\u00f0ir yr\u00f0u afar \u00f3st\u00f6\u00f0ugar. <em>[&#8230;]<\/em> \u00cd stuttu m\u00e1li sagt yr\u00f0u of miklar truflanir og \u00f3regla \u00e1 hreyfingum allra reikistjarna og halastjarna.\u00a0 Af framans\u00f6g\u00f0u er auglj\u00f3st a\u00f0 g\u00f3\u00f0f\u00fas Gu\u00f0 hefur af \u00f3endanlegri visku sinni r\u00e9ttilega fengi\u00f0 halastj\u00f6rnunum sta\u00f0 utan d\u00fdrahringsins, einmitt \u00ed \u00feeim tilgangi a\u00f0 komist yr\u00f0i hj\u00e1 of miklum truflunum \u00e1 gangi og brautum reglubundinna stjarna, sem annars yr\u00f0u \u00f3hj\u00e1kv\u00e6milega. Svo auglj\u00f3st er gu\u00f0d\u00f3mlegt markmi\u00f0 me\u00f0 \u00fev\u00ed a\u00f0 setja halastj\u00f6rnur utan d\u00fdrahringsins. \u00c9g \u00e1 ekki vi\u00f0 markmi\u00f0 me\u00f0 halastj\u00f6rnum \u00ed sj\u00e1lfum s\u00e9r, en a\u00f0eins a\u00f0 \u00fe\u00e6r skuli vera fjarri d\u00fdrahringnum.<\/p><\/blockquote>\n<p>\u00cd n\u00e6stu setningu vitnar Stef\u00e1n svo \u00ed Newton:<\/p>\n<blockquote><p>\u00d6nnur tilgangsr\u00f6k fyrir \u00fev\u00ed a\u00f0 halastj\u00f6rnur s\u00e9u fjarri d\u00fdrahringnum f\u00e6rir snillingurinn Newton \u00ed <em>[\u00feri\u00f0ju efnisgrein \u00ed <a href=\"https:\/\/isaac-newton.org\/general-scholium\/\">eftirm\u00e1la <\/a>St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lanna]:<\/em> \u201eAf \u00feessu gefur a\u00f0 skilja hvers vegna halastj\u00f6rnurnar eru ekki \u00ed d\u00fdrahringnum eins og reikistj\u00f6rnur, en flakka \u00fea\u00f0an og berast \u00e1 \u00fdmsa vegu um geiminn. Au\u00f0vita\u00f0 \u00ed \u00feeim tilgangi a\u00f0 \u00ed s\u00f3lfir\u00f0 sinni, \u00feegar \u00fe\u00e6r hreyfast h\u00e6gast, s\u00e9u \u00fe\u00e6r sem fj\u00e6rst hver annarri og togi sem minnst gagnkv\u00e6mt hver \u00ed a\u00f0ra.\u201c\u00a0\u00a0 Og \u00feessi tvennu tilgangsr\u00f6k reynist fulln\u00e6gjandi, hlutl\u00e6g, frumspekileg r\u00f6ksemd sem orka\u00f0i \u00e1 Gu\u00f0, svo hann setti halastj\u00f6rnurnar v\u00ed\u00f0sfjarri d\u00fdrahringnum.<\/p><\/blockquote>\n<p>\u00c1 fyrri hluta \u00e1tj\u00e1ndu aldar veltu \u00fdmsir a\u00f0rir fyrir s\u00e9r <a href=\"https:\/\/en.wikipedia.org\/wiki\/Stability_of_the_Solar_System\">st\u00f6\u00f0ugleika s\u00f3lkerfisins<\/a>, \u00fear \u00e1 me\u00f0al Halley og Euler. \u00dea\u00f0 var \u00fe\u00f3 ekki fyrr en \u00feeir <a href=\"https:\/\/en.wikipedia.org\/wiki\/Joseph-Louis_Lagrange\">Lagrange<\/a> og <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pierre-Simon_Laplace\">Laplace<\/a> komu til s\u00f6gunnar upp \u00far mi\u00f0ri \u00f6ldinni, sem ranns\u00f3knir \u00e1 st\u00f6\u00f0ugleikanum h\u00f3fust fyrir alv\u00f6ru. \u00c1 \u00e1runum 1773 til 1784 s\u00fdndu \u00feeir fram \u00e1 me\u00f0 truflanareikningi, a\u00f0 ef utana\u00f0komandi \u00feyngdar\u00e1hrif \u00e1 d\u00e6miger\u00f0a reikistj\u00f6rnu eru ekki meiri en \u00feau, sem n\u00fa r\u00edkja \u00ed s\u00f3lkerfinu, ver\u00f0a breytingar \u00e1 braut hennar sveiflukenndar, en innan vi\u00f0unandi marka. A\u00f0 forsendunum gefnum, \u00e6tti s\u00f3lkerfi\u00f0 \u00fev\u00ed a\u00f0 vera st\u00f6\u00f0ugt (sj\u00e1 einnig <em>vi\u00f0b\u00f3t<\/em> \u00ed f\u00e6rslulok).<\/p>\n<p>Ranns\u00f3knir \u00ed aflfr\u00e6\u00f0i himintungla hafa \u00e1vallt veri\u00f0 vins\u00e6lar me\u00f0al st\u00e6r\u00f0fr\u00e6\u00f0inga, ekki s\u00edst eftir a\u00f0 Frakkinn <a href=\"https:\/\/en.wikipedia.org\/wiki\/Henri_Poincar%C3%A9\">H. Poincar\u00e9<\/a> birti ni\u00f0urst\u00f6\u00f0ur s\u00ednar um<a href=\"https:\/\/en.wikipedia.org\/wiki\/Henri_Poincar%C3%A9#Astronomy_and_celestial_mechanics\"> \u00feriggja hnatta vandam\u00e1li\u00f0<\/a> \u00e1 t\u00edunda \u00e1ratugi n\u00edtj\u00e1ndu aldar. S\u00fa mikilv\u00e6ga umfj\u00f6llun marka\u00f0i upphaf ranns\u00f3kna \u00e1 <a href=\"https:\/\/www.pnas.org\/content\/98\/22\/12342\">ringli (kaos) \u00ed s\u00f3lkerfinu<\/a> og reyndar einnig \u00e1 heilli undirgrein st\u00e6r\u00f0fr\u00e6\u00f0innar, sem gengur undir nafninu <a href=\"https:\/\/en.wikipedia.org\/wiki\/Chaos_theory\">ringlfr\u00e6\u00f0i<\/a>. Um \u00feessa skemmtilegu \u00fer\u00f3un m\u00e1 me\u00f0al annars lesa \u00ed eftirfarandi heimildum:<\/p>\n<ul>\n<li>W. H. Jefferys &amp; V. G. Szebehely, 1978: <a href=\"http:\/\/articles.adsabs.harvard.edu\/\/full\/1978ComAp...8....9J\/0000009.000.html\">Dynamics and stability of the solar system<\/a>.<\/li>\n<li>Robert Magnus, 1991:\u00a0 <a href=\"https:\/\/notendur.hi.is\/~einar\/RobertMagnus1990.pdf\">Er s\u00f3lkerfi\u00f0 st\u00f6\u00f0ugt?<\/a>\u00a0 (Danska \u00fe\u00fd\u00f0ingu Eggerts Briem er a\u00f0 finna \u00ed <em>Normat<\/em> 40, 3, 1992, bls. 100-118).<\/li>\n<li>I. Peterson, 1993: <a href=\"https:\/\/books.google.is\/books?id=Ul2G5jFEejgC&amp;source=gbs_navlinks_s\">Newton&#8217;s Clock: Chaos In The Solar System<\/a>.<\/li>\n<li>F. Diacu &amp; P. Holmes, 1996:<a href=\"https:\/\/books.google.is\/books?id=26UtgDSw_MQC&amp;source=gbs_navlinks_s\"> Celestial Encounters: The Origins of Chaos and Stability<\/a>.<\/li>\n<li>S. D. Snobelen, 2012: <a href=\"https:\/\/isaacnewtonstheology.files.wordpress.com\/2013\/06\/the-myth-of-the-clockwork-universe.pdf\">The Myth of the Clockwork Universe: Newton, Newtonianism, and the Enlightenment<\/a>.<\/li>\n<li>J. Laskar, 2013: <a href=\"https:\/\/arxiv.org\/abs\/1209.5996\">Is the Solar System Stable?<\/a><\/li>\n<li>J. Laskar, 2015: <a href=\"http:\/\/www.scholarpedia.org\/article\/Stability_of_the_solar_system\">Stability of the Solar System<\/a>.<\/li>\n<li>J. K. Zink, K. Batygin &amp; F. C. Adams, 2020: <a title=\"https:\/\/iopscience.iop.org\/article\/10.3847\/1538-3881\/abb8de\" href=\"https:\/\/iopscience.iop.org\/article\/10.3847\/1538-3881\/abb8de\" target=\"_blank\" rel=\"noopener noreferrer\" data-auth=\"NotApplicable\">The Great Inequality and the Dynamical Disintegration of the Outer Solar System<\/a>.<\/li>\n<\/ul>\n<hr \/>\n<p><span style=\"font-size: 10pt\"><strong>Vi\u00f0b\u00f3t<\/strong> (28. okt\u00f3ber 2021). Allt fr\u00e1 \u00fev\u00ed \u00e9g fyrst fr\u00e9tti af \u00fev\u00ed sem ungur n\u00e1msma\u00f0ur, a\u00f0 mig minnir \u00ed kaflanum um Laplace \u00ed hinni fr\u00e1b\u00e6rlega skemmtilegu, en jafnframt sagnfr\u00e6\u00f0ilega \u00f3n\u00e1kv\u00e6mu b\u00f3k, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Men_of_Mathematics\">Men of Mathematics<\/a>, eftir <a href=\"https:\/\/en.wikipedia.org\/wiki\/Eric_Temple_Bell\">E. T. Bell<\/a>, hef \u00e9g haft \u00e1huga \u00e1 vandam\u00e1linu um st\u00f6\u00f0ugleika s\u00f3lkerfisins. Sj\u00e1lfur hef \u00e9g ekkert lagt af m\u00f6rkum \u00e1 \u00fev\u00ed svi\u00f0i, heldur hefur \u00e1huginn \u00e6t\u00ed\u00f0 veri\u00f0 takmarka\u00f0ur vi\u00f0 s\u00f6gu \u00feess og \u00fe\u00e1 einkum \u00ed tengslum vi\u00f0 almenna s\u00f6gu ranns\u00f3kna \u00e1 aflfr\u00e6\u00f0i himintungla. \u00der\u00e1tt fyrir hafa lesi\u00f0 talsvert um \u00feetta efni \u00ed gegnum t\u00ed\u00f0ina, t\u00f3kst m\u00e9r aldrei a\u00f0 skilja til fullnustu sambandi\u00f0 milli framlaga \u00feeirra Laplace og Lagrange til st\u00f6\u00f0ugleikavandam\u00e1lsins. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-size: 10pt\">Fyrir nokkru rakst \u00e9g \u00e1 fr\u00f3\u00f0legar greinar eftir \u00edtalska v\u00edsindafr\u00e6\u00f0inginn <a href=\"https:\/\/www.dsu.univr.it\/?ent=persona&amp;id=49275&amp;lang=en\">Massimiliano Badino<\/a>, \u00fear sem \u00e9g tel mig loksins hafa fengi\u00f0 fulln\u00e6gjandi l\u00fdsingu \u00e1 atbur\u00f0ar\u00e1sinni. Badino bendir jafnframt \u00e1 \u00e1kve\u00f0i\u00f0 vandam\u00e1l va\u00f0andi v\u00edsindas\u00f6guritun, sem margir raunv\u00edsindamenn \u00e6ttu a\u00f0 kannast vi\u00f0. \u00c9g m\u00e6li me\u00f0 \u00feessum greinum hans:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 10pt\">M. Badino, 2017: <a href=\"https:\/\/www.journals.uchicago.edu\/doi\/full\/10.1086\/695606\">Using, Abusing, and Perusing the Past<\/a> (stutt yfirlit).<\/span><\/li>\n<li><span style=\"font-size: 10pt\">M. Badino, 2018: <a href=\"https:\/\/www.academia.edu\/25687069\/And_Yet_It_Stands_The_Stability_of_the_Solar_System_in_Eighteenth_Century_Physical_Astronomy?email_work_card=title\">And Yet It Stands: The Stability of the Solar System in Eighteenth Century Physical Astronomy<\/a> (\u00edtarleg umfj\u00f6llun me\u00f0 tilvitnunum \u00ed frumheimildir).<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<hr \/>\n<p style=\"text-align: center\"><span style=\"font-size: 14pt\">* <a href=\"https:\/\/uni.hi.is\/einar\/2021\/05\/02\/greinaflokkur-um-stjarnedlisfraedi-og-heimsfraedi-a-islandi\/\">Stjarne\u00f0lisfr\u00e6\u00f0i og heimsfr\u00e6\u00f0i \u00e1 \u00cdslandi: Efnisyfirlit<\/a> *<\/span><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Yfirlit um greinaflokkin Enginn raunv\u00edsindama\u00f0ur hefur fengi\u00f0 jafn mikla umfj\u00f6llun \u00ed ritu\u00f0u m\u00e1li og Newton, nema ef vera skyldi Einstein. Fyrir utan s\u00edvaxandi fj\u00f6lda b\u00f3ka og n\u00e6r \u00f3teljandi greinar um \u00feennan fyrsta \u201en\u00fat\u00edma\u201c stjarne\u00f0lisfr\u00e6\u00f0ing, \u00e6vi hans og v\u00edsindaafrek, pers\u00f3nuleika, ranns\u00f3knir \u00ed efnaspeki og bibl\u00edufr\u00e6\u00f0um, sem og opinber emb\u00e6ttisst\u00f6rf, er hans geti\u00f0 \u00ed \u00f6llum almennum alfr\u00e6\u00f0iritum [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4,8,15],"tags":[],"class_list":["post-16233","post","type-post","status-publish","format-standard","hentry","category-atjanda-oldin","category-edlisfraedi","category-nitjanda-old","category-stjornufraedi"],"_links":{"self":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/posts\/16233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16233"}],"version-history":[{"count":0,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/posts\/16233\/revisions"}],"wp:attachment":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}