Rambler's Top100Astronet    
  po tekstam   po forumu  vnutri temy 		 

args[0]=message
args[1]=DB::DB::Message=HASH(0x2bba800)
Kinematicheskaya teoriya planet
10.04.2012 10:34 | S. Yu. Yudin

Na obsuzhdenie vynositsya razrabotannaya mnoyu metodika sozdaniya, kak prinyato govorit' u astronomov, teorii planet, kotoraya, kak i mnogie sushestvuyushie teorii planet yavlyaetsya prosto naborom approksimacii, kotorye pozvolyayut vychislit' na proizvol'nyi moment vremeni koordinaty planet. Podrobno s metodikoi mozhno oznakomit'sya v moei stat'e //Kinematicheskaya teoriya planet// http://modsys.narod.ru/ Stat/Stat_Est/Kinematik/Kinematik1.html . Akcentiruyu eshe raz Vashe vnimanie, chto na obsuzhdenie vynositsya imenno metodika, a ne poluchennaya s ee pomosh'yu teoriya planet, hotya sama po sebe interesna i sama teoriya, kotoraya pozvolyaet rasschityvat' koordinaty planet po solnechnomu vremeni UT, a ne po efemeridnomu vremeni ET, kak vse sovremennye teorii, i po etomu dlya moei teorii ne trebuetsya efemeridnaya popravka ET-UT, vliyanie kotoroi na koordinaty planet, rasschitannye po toi ili inoi sovremennoi teorii, stanovitsya tem bol'she, chem dal'she nuzhnaya data ot daty sozdaniya teorii. Naprimer, nizhe ya privozhu tablicu 10 iz svoei stat'i po odnomu iz solnechnyh zatmenii, gde dlya sovremennyh analiticheskih teorii New1 (N'yukom) i JPL1 (NASA), v kotoryh ya uchel tol'ko chast' periodicheskih vozmushenii ot drugih planet, bez efemeridnoi popravki poluchaetsya faza zatmeniya -5% i -60%, t.e. eto ne procent prekrytiya diskom Luny (po diametru) diska Solnca, a naoborot procent v diametrah Solnca, ot rasstoyaniya na kotoroe disk Luny ne doshel do diska Solnca i vremya ukazano dlya momenta, kogda on maksimal'no priblizilsya k Solncu.


Tablica 10. Parametry solnechnogo zatmeniya 15.04.-135 goda nablyudavshegosya v Vavilone (dolgota 44,5 v.d., shirota 32,5 s.sh.) i poluchennye po sovremennym teoriyam i po tablicam Ptolemeya. Dlya sovremennyh teorii efemeridnye popravki rasschitany kak po formule Dalmau, tak i po formule Dzhonsa (v minutah). Vremya dano mestnoe (Vavilon) solnechnoe. Dannye po tablicam Ptolemeya privedeny s ispravlennoi precessiei i vypolneny na 21.07.612 goda po Egipetskomu kalendaryu.

Nazvanie tablic, teorii________faza %__voshod__nachalo__nachalo polnogo__konec__itogo
Nablyudaemye dannye____________100_____05:34___07:10______08:22_______09:30__02:20
JPL1__ET- UT=0__________________-5_____05:33_____-________15:21_________-______-
JPL1__ET- UT=182,5__Dzhons_______70_____05:34___09:33______10:45_______12:01__02:28
JPL1__ET- UT=196,5__Dalmau______75_____05:34___09:14______10:29_______11:43__02:29
New1__ET- UT=0_________________-60____05:33_____-________14:40_________-______-
New1__ET- UT=182,5__Dzhons______40_____05:34____09:38_____10:25_______11:10__01:38
New1__ET- UT=196,5__Dalmau______60____05:34____09:16_____10:06_______10:56__01:40
Ser1+__________E T-UT=0_________100____05:34____07:41_____08:45_______09:57__02:16
Almagest*______ET- UT=0 _________99_____05:31____07:08_____08:14_______09:24__02:16


Podborom efemeridnoi popravki ET-UT mozhno dobit'sya ili togo, chto sovpadet vremya nachala zatmeniya ili my poluchim fazu zatmeniya 100% (dazhe po tablicam Ptolemeya dlya sovremennyh zatmenii), no sovpadeniya i vremeni i 100% fazy udastsya dobit'sya v edinichnyh sluchayah. A vot moya teoriya Ser1+ i tablicy Ptolemeya Almagest* pozvolyayut poluchit' dlya etogo zatmeniya vpolne prilichnyi rezul'tat i bez efemeridnoi popravki. Ob'yasnyaetsya eto i netochnost'yu samih sovremennyh teorii i principial'no ne pravil'nym podhodom dlya opredeleniya efemeridnoi popravki, kotoruyu ya schitayu nuzhnym razdelit' na dve popravki. Podrobno ob efemeridnyh popravkah ya pisal v pervoi stat'e etogo cikla statei //O ravnodenstviyah Gipparha i Ptolemeya// http://modsys.narod.r u/Stat/Stat_Est/Hipp_Ptolo/Hipp_Ptolo2.html i po etomu ostanavlivat'sya na etom ne budu. Povtoryus' tol'ko eshe raz, chto rasschityvat' efemeridnuyu popravku astronomy ne mogut, a starayutsya podobrat' razlichnye approksimacii dlya togo, chtoby bolee menee udachno opisat' zatmeniya, kotorye uzhe nablyudalis'. Seichas naibolee izvestny approksimacii Dzhonsa i Dalmau.


A vozvrashayas' k samoi metodike sozdaniya teorii planet mozhno skazat' sleduyushee. 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 (DE405). A t.k. klassifikacii etih metodik ya nigde ne vstrechal, to, vo-pervyh, mne prishlos' dat' im nazvaniya kinematicheskaya i dinamicheskaya, a, vo-vtoryh, mne zhe prishlos' i ukazat' na ih otlichiya. Do teh por poka v 1665 godu N'yuton i v 1680 godu Guk (ne zavisimo ot N'yutona) ne prishli k vyvdu, chto sila prityazheniya mezhdu telami obratno proporcional'na kvadratu rasstoyaniya, a v 1687 godu N'yuton v svoih Nachalah ne svel voedino imeyushiesya na tot moment predstavleniya o zakonah dvizheniya tel, kotorye seichas izvestny kak tri zakona N'yutona, fizicheskih metodik byt' ne moglo. I po etomu dazhe Kopernik, opublikovavshii v 1545 godu svoyu geliocentricheskuyu teoriyu stroeniya Solnechnoi sistemy, ispol'zoval kinematicheskuyu 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 kinematicheskuyu metodiku, approksimiruya razlichnymi geometricheskimi figurami dannye nablyudenii.


No 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 (naprimer, radiusy epiciklov i deferentov), predpolagaya ravnomernoe vrashenie razlichnyh sfer s etimi parametrami, i Kepler opredelyal neposredstvenno parametry orbit v geliocentricheskoi sisteme koordinat (naprimer, ekscentrisitet i bol'shuyu poluos'), predpolagaya dvizhenie planet po ellipsam so skorostyami v sootvetstvie s naidennym im chisto kinematicheskim 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. 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.


Takim obrazom, s vvedeniem v metodiku obrabotki dannyh nablyudenii razlichnyh fizicheskih teorii, my teper', obrabatyvaya eti dannye, poluchaem ne eksperimental'nye parametry orbit, a eksperimental'no-teoreticheskie, kotorye maksimal'no sootvetstvuyut toi fizicheskoi teorii s pomosh'yu kotoroi byla postroena matematicheskaya model', parametry kotoroi optimizirovalis' po dannym nablyudenii. Prichem, esli by pri etom ne ispol'zovalas' prichinno-sledstvennaya svyaz', ob'edinyayushaya po vremeni otdel'nye oboroty planety vokrug Solnca, to nalichiem etogo promezhutochnogo zvena mozhno bylo by prenebrech', t.k. po lyuboi izvestnoi seichas fizicheskoi teorii vse planety dvizhutsya po ellipticheskim orbitam s nebol'shimi kolebaniyami, vyzvannymi vozdeistviem drugih planet. I, sledovatel'no, prakticheski vse teorii dlya nebol'shogo promezhutka vremeni, naprimer, dlya odnogo oborota planety dadut primerno odinakovye parametry orbity, imeyushei formu ellipsa.

No delo v tom, chto eti ellipsy so vremenem nemnogo smeshayutsya v prostranstve i, sledovatel'no, so vremenem nemnogo izmenyayutsya parametry orbit, naprimer, argument perigeliya ili ugol voshozhdeniya. Takoe smeshenie obespechivaetsya prichinno-sledstvennoi svyaz'yu fizicheskih modelei. Eti neznachitel'nye izmeneniya v parametrah orbit prinyato rasschityvat' na promezhutke v 100 let i po etomu oni nazyvayutsya vekovymi smesheniyami parametrov orbit. I vot imenno po etim vekovym smesheniyam parametrov orbit vse poslednee stoletie opredelyaetsya spravedlivost' toi ili inoi fizicheskoi teorii gravitacii. Vernee ne po samim smesheniyam, a po anomal'nym ostatkam ot etih smeshenii posle vycheta smeshenii, kotorye daet primenenie zakona prityazheniya N'yutona, t.e. klassicheskaya mehanika. A samym izvestnym i samym znachitel'nym seichas schitaetsya anomal'noe smeshenie perigeliya Merkuriya. I nizhe (v tablice 1) ya privozhu znacheniya anomal'nyh ostatkov smesheniya perigeliev chetyreh planet poluchennyh N'yukomom, kotorye ne ob'yasnyayutsya teoriei N'yutona, no ob'yasnyayutsya drugimi teoriyami v dopolnenie k smesheniyu uzhe ob'yasnennomu teoriei N'yutona (v skobkah ukazan istochnik, otkuda vzyaty dannye).

Tablica 1. Anomal'noe smeshenie perigeliya vnutrennih planet.
__________________________Merkurii__Venera___Zemlya____Mars
Nablyudeniya (N'yukom) _________575,06___42,52___1162,92___1602,69
teoriya N'yutona (N'yukom) ______533,82___49,85___1156,95___1594,65
Anomal'nyi ostatok (N'yukom)__41,24____- 7,33_____5,97_____8,04
teoriya Einshteina (Subbotin) ___43,0______8,6______3,8_____1,4
teoriya Gerbera (Haidarov) ______43,0______8,6______3,8_____1,4
teoriya Ritca (Rouzver) _________41,0______8,0_______3,4_____----
teoriya Maha (Zaicev) ___________43,0_____23,0_____17,0____11,0
teoriya Zeelingera (Rouzver) _____41,3______7,3______4,2_____6,3

Tak vot kak raz dlya togo, chtby naiti chisto nablyudaemye smesheniya parametrov orbit, t.e. ochistit' ih ot vliyaniya fizicheskih teorii polozhennyh v osnovu matematicheskih modelei Solnechnoi sistemy v sovremennyh metodikah, ya i razrabotal svoyu metodiku sozdaniya kinematicheskoi teorii planet. Sut' moei metodiki, vernee neskol'ko modificirovannoi metodiki Keplera, sostoit v tom, chto ya kak i on nahozhu parametry ellipticheskoi orbity planety, kogda rashozhdeniya mezhdu nablyudaemymi koordinatami planety i rasschitannymi s zadannymi parametrami ellipsa poluchaetsya minimal'nymi. Pri etom ya sravnivayu ne srazu vse imeyushiesya dannye nablyudenii s raschetnymi, a tol'ko ih chast' za period primerno v 20 let, kogda parametry ellipticheskoi orbity planety hot' i izmenyayutsya no ne znachitel'no, t.e. ya kazhdyi raz nahozhu optimal'nye parametry dlya konkretnogo goda. Naprimer, esli my obrabatyvaem dannye nablyudenii s 1900 po 1920 gody, to nahodim parametry orbity dlya 1910 goda.

Pri etom, nablyudaemye otkloneniya ot raschetnyh koordinat v odnoi i toi zhe tochke ellipsa pri raznyh oborotah planety, kotorye vyzvany, kak prityazheniem ot drugih planet, tak i oshibkami meridiannyh nablyudenii, ya schitayu sluchainymi velichinami, kotorye raspredeleny v sootvetstvie s zakonom normal'nogo raspredeleniya i, sledovatel'no, pri obrabotke dannyh nablyudenii za neskol'ko desyatiletii, sluchainye otkloneniya vzaimno unichtozhat'sya i my poluchim srednee otklonenie koordinat raschetnogo ellipsa ot nablyudaemogo. A vot otkloneniya nablyudaemyh koordinat ot raschetnyh, vyzvannye vekovymi smesheniyami parametrov orbit, yavlyayutsya uzhe ne sluchainymi velichinami. Po etomu, approksimirovav teper' vse poluchennye nami znacheniya optimal'nyh parametrov orbit dlya raznyh let kakoi to zavisimost'yu my poluchim formulu po kotoroi eti parametry izmenyayutsya so vremenem, t.e. naidem i vekovye izmeneniya parametrov orbit.


Principial'nymi otlichiyami moei metodiki ot sovremennoi yavlyayutsya takzhe to, chto ya ne naugad podbirayu massy planet dlya matematicheskih modelei ili parametry ellipticheskoi orbity, kak eto delal Kepler, a ispol'zuyu pri etom metody mnogofaktornogo planirovaniya i to, chto kriteriem optimizacii u menya yavlyaetsya ne otklonenie po dolgote ili shirote (ili ih kombinaciya), a otklonenie po rasstoyaniyu raschetnyh dannyh ot nablyudaemyh v tys.km. Podrobno raspisyvat' metody mnogofaktornogo planirovaniya ili voprosy svyazannye s kriteriyami optimizacii ne budu i komu eto interesno mozhet oznakomitsya s nimi v moei stat'ya, a ya prosto privedu znacheniya vekovyh smeshenii parametrov orbit, kotorye u menya poluchilis' pri sozdanie kinematicheskoi teorii planet Ser0 i po nekotorym uzhe sushestvuyushim teoriyam. V tablice smesheniya ugla perigeliya - dAlfaP, uzla voshozhdeniya - dAlfaU , naklona orbity - dBetta i ekscentrisiteta - dEks, a cifra eto nomer planety.


Tablica 22. Vekovye smesheniya parametrov orbit, poluchennye na programmah Solsys6 i Solsys7 s ispol'zovaniem dannyh poluchennyh po imitatoram (astronomicheskim teoriyam) Solnechnoi sistemy New0, APC2 i JPL2 i dannym matematicheskih modelei Solnechnoi sistemy, a takzhe poluchennyh pri obrabotke neposredstvenno dannyh opticheskih nablyudenii dlya sozdaniya kinematicheskoi astronomicheskoi teorii Ser0. Smesheniya uglov dany v uglovyh sekundah, a smeshenie ekscentrisiteta v bezrazmernyh edinicah i uvelicheno v 10^6 raz. Doveritel'naya veroyatnost' (nadezhnost') dannyh 95%.

_________________________Imitatory_______________________Modeli
Parametr __New0______APC2______Ser0______JPL2________/R^2_______/R^n*
dAlfaP1___+570,73____+574,0 2____+578,0____+572,20_____+529,59_____+573,41
dAlfaU1___-452,18_____-450,34____- 433,2____-449,95______-450,36______-450,40
dBetta1____-21,43______-21,44_____- 19,84_____-21,44_______-21,46______- 21,46
dEks1_____+20,55_____+20,52_____+20,10_____+20,50______+20,42______+20,42

dA lfaP2____+54,41_____+59,12_____+30,3_____+43,64______+45,56______+61,19
dAlfaU2___- 999,86____-1011,65____-996,5____-998,36______-999,08_____-999,06
dBetta2_____- 2,51______-2,42_______-2,83_____-2,52________-2,52_______-2,52
dEks2______-48,01_____- 48,20_____-45,33_____-48,33_______-49,42______- 49,41

dAlfaP3___+1160,37___+1185,68___+1141,6___+1158,55_____+1141,97___+1152,56
d AlfaU3____-869,85____-872,74____-868,0____-861,63______-845,52_____-845,36
dBetta3_____- 47,19_____-47,14_____-47,45_____-47,17_______-47,24______-47,23
dEks3______-41,33_____- 41,62_____-41,57_____-41,93_______-43,29______- 43,29

dAlfaP4___+1601,09___+1599,64___+1582,7___+1600,02_____+1598,09___+1603,70
d AlfaU4___-1054,74___-1058,58____-1028,0____-1050,49_____-1052,79___-1052,77
dBetta4____- 29,11_____-29,16______-29,39______-28,93_______-29,03_____- 29,03
dEks4_____+92,27_____+92,07______+95,53_____+91,63______+96,26_____+96,25

* - pokazatel' stepeni n vo vtoroi modeli v formule N'yutona F=G*m*M/R^n bralsya takim, kakim on byl u N'yukoma, t.e. n=2,0000001612 (u Holla bylo n=2,0000001574).


S nailuchshimi pozhelaniyami Sergei Yudin.




Forumy >> Astronomiya i Internet
Spisok  /  Derevo
Zagolovki  /  Annotacii  /  Tekst
Astronet | Nauchnaya set' | GAISh MGU | Poisk po MGU | O proekte | Avtoram

Kommentarii, voprosy? Pishite: info@astronet.ru ili syuda

Rambler's Top100 Yandeks citirovaniya