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• (S. Yu. Yudin, 17:41, 18.9 KBait, otvetov: 17) Ya schitayu, chto v nastoyashee vremya s razlichnymi variaciyami izvestny dve metodiki opredeleniya parametrov orbit planet po nablyudatel'nym dannym. Tipichnymi rezul'tatami primeneniya pervoi metodiki yavlyayutsya teoriya Ptolemeya i zakony Keplera, a vtoroi analiticheskie teorii planet Lever'e i N'yukoma i poluchennye chislennymi metodami efemeridy JPL. Klassifikacii etih metodik ya nigde ne vstrechal, to, vo-pervyh, mne pridetsya dat' im nazvaniya, dopustim, geometricheskaya i fizicheskaya, a, vo-vtoryh, mne zhe pridetsya i ukazat' na ih otlichiya. Do teh por poka v 1665 godu N'yuton i v 1680 godu Guk (ne zavisimo ot N'yutona) prishli k vyvdu, chto sila prityazheniya mezhdu telami obratno proporcional'na kvadratu rasstoyaniya, a v 1687 godu N'yuton v svoih Nachalah svel voedino imeyushiesya na tot moment predstavleniya o zakonah dvizheniya tel, kotorye seichas izvestny kak tri zakona N'yutona, fizicheskih metodik byt' ne moglo.
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I po etomu dazhe Kopernik, opublikovavshii v 1545 godu svoyu geliocentricheskuyu teoriyu stroeniya Solnechnoi sistemy, ispol'zoval geometricheskuyu metodiku s temi zhe deferentami i epiciklami, chto i Ptolemei. I Kepler, otkryvshii v 1609 godu dva svoih pervyh zakona i v tom chisle o dvizhenie planet po ellipsam, tozhe ispol'zoval chisto geometricheskuyu metodiku, approksimiruya razlichnymi geometricheskimi figurami dannye nablyudenii. Tol'ko ne nado putat' geometricheskuyu metodiku opredeleniya parametrov orbit s geometricheskoi, t.e. S pomosh'yu cirkulya i lineiki, metodikoi resheniya matematicheskih zadach, kotoroi N'yuton pol'zovalsya dazhe v svoih Nachalah. I tol'ko posle togo, kak v 1684 godu Leibnic (ne zavisimo ot N'yutona) dal sistematicheskoe izlozhenie differencial'nogo ischisleniya, a v 1686 i integral'nogo ischisleniya, matematicheskie zadachi stalo ne tol'ko namnogo proshe reshat', no i poyavilas' vozmozhnost' reshat' takie slozhnye zadachi, kak opisanie dvizheniya planet s ispol'zovaniem fizicheskih zakonov.
A posle teoreticheskih rabot takih velikih matematikov proshlogo, kak Eiler, Lagranzh, Laplas i Gauss vse eti matematicheskie metody stali dostupny i astronomam. I vot zdes' v metodiku opredeleniya parametrov orbit vklinilos' lishnee zveno fizicheskaya teoriya. Esli Ptolemei, approksimiruya dannye nablyudenii, nahodil neposredstvenno parametry orbit v geocentricheskoi sisteme koordinat (radiusy epiciklov i deferentov), predpolagaya ravnomernoe vrashenie razlichnyh sfer s etimi parametrami, i Kepler opredelyal neposredstvenno parametry orbit v geliocentricheskoi sisteme koordinat (ekscentrisitet, bol'shuyu poluos'), predpolagaya dvizhenie planet po ellipsam so skorostyami v sootvetstvie s naidennym im chisto geometricheskim zakonom ploshadei, to Lever'e s N'yukom i sotrudniki JPL postupali inache. Oni po dannym nablyudenii nahodili optimal'nye parametry ih matematicheskih modelei, postroennyh s ispol'zovaniem fizicheskih teorii, gde ispol'zovalas' ta ili inaya modifikaciya zakona prityazheniya N'yutona. Vot tol'ko kakie metody optimizacii oni pri etom ispol'zovali mne ne izvestno, no v rezul'tate etogo, naprimer, Lever'e v teorii dvizheniya kazhdoi iz vnutrennih planet poluchal pri etom razlichnye optimal'nye znacheniya dlya mass treh drugih planet zemnoi gruppy.
Pri etom Lever'e i N'yukom, pri reshenie differencial'nyh uravnenii, ispol'zovali analiticheskie metody, a sotrudniki JPL chislennye, chto s primeneniem EVM delaet etu zadachu ne slozhnoi. Pri analiticheskom reshenie, t.k.
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Sistemy, sostoyashie iz bolee chem dvuh tel, ne reshayutsya analiticheski (zadacha treh tel), dlya kazhdoi planety reshayut otdel'nuyu zadachu. Pri etom v pravoi chasti differencial'nogo uravneniya, krome sily prityazheniya ot Solnca, zapisyvaetsya eshe tak nazyvaemaya perturbacionnaya funkciya, kotoraya uchityvaet sily prityazheniya ot drugih planet i kotoraya vychislyaetsya zaranee, a posle pervogo shaga resheniya ona utochnyaetsya, chto delaet vychisleniya ochen' trudoemkimi. A pri chislennom reshenie reshayut srazu vsyu sistemu differencial'nyh uravnenii, opisyvayushuyu dvizhenie vseh planet i vozdeistvie vseh planet drug na druga opredelyaetsya neposredstvenno vo vremya resheniya uravnenii, posle kazhdogo shaga resheniya (iteracii).
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