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Re[9]: Smeshenie perigeliya Merkuriya i drugih planet
30.07.2008 19:53 | S. Yu. Yudin

A nachalas' vsya putanica s nablyudatel'nymi i raschetnymi (teoreticheskimi) dannymi s N'yukoma (esli ne schitat' Lever'e). I v tablice 12b ya privozhu dannye opublikovannye samim N'yukomom, kotorye vzyaty iz knigi N'yukoma posvyashennoi analizu primenennyh metodov i prinyatyh gipotez pri postroenie ego teorii (Rouzver N.T. Perigelii Merkuriya. Ot Lever'e do Einshteina: Per. s angl. M.: Mir, 1985. 246 s. //sm. tabl. 3.1//). Zdes' N'yukom nablyudatel'nymi dannymi nazval poluteoreticheskie-polunablyudatel'nye dannye, kotorye on poluchil nanizyvaya dannye opticheskih nablyudenii na teoriyu N'yutona s popravkoi Holla, ispol'zuya prichinno- sledstvennuyu svyaz' etoi teorii dlya polucheniya radiusa, a raschetnymi (teoreticheskimi) nazval dannye, kotorye on poluchil s pomosh'yu chistoi teorii N'yutona. Pri etom, N'yukom privodit v svoei tablice dannye, poluchennye im dlya mgnovennoi ekliptiki i po etomu oni otlichayutsya ot privedennyh mnoyu v tablice 11s, poluchennyh mnoyu dlya fiksirovannoi ekliptiki J2000. Bolee togo, on privodit dannye dlya tekushei ekliptiki za vychetom precessii ot nachala nablyudeniya (orientirovochno nachinaya s 1750 g) do tekushego momenta, t.k. v tekushei ekliptike, naprimer, smeshenie perigeliya Merkuriya poluchatsya 5554,43 uglovyh sekundy, chto eshe bol'she zaputyvaet interpretaciyu ego dannyh dlya podtverzhdeniya toi ili inoi fizicheskoi teorii, t.k. vse teorii dayut dannye v fiksirovannoi ekliptike i v chastnosti formula Einshteina (Paulya Gerbera) dlya anomal'nogo (dopolnitel'nogo) smesheniya perigeliya planet podrazumevaet chto massy dvizhutsya v nepodvizhnoi sisteme koordinat. No po bol'shomu schetu vse eto ne imeet nikakogo znacheniya, t.k. ispol'zovannye Einshteinom dlya podtverzhdeniya spravedlivosti ego teorii (OTO) nablyudatel'nye dannye N'yukoma voobshe ne yavlyayutsya imenno nablyudatel'nymi dannymi v obsheprinyatom smysle, t.e. dannymi poluchennymi pryamymi zamerami konkretnyh velichin.

Ne ochen' horosho dlya obosnovaniya toi ili inoi teorii i to, chto N'yukom privel v svoei tablice ne sami vekovye smesheniya perigeliev i uzlov voshozhdeniya, a ih kombinirovannye znacheniya, zavyazannye na drugie parametry, kotorye tozhe izmenyayutsya, i po etomu otsyuda nel'zya poluchit' tochnye znacheniya smesheniev imenno perigeliya i uzla voshozhdeniya. Pravda eti popravki ot nestabil'nosti ekscentrisitetov i uglov naklona budut neznachitel'nye i v principe mozhno bylo by privesti srazu ili ryadom v tablice i dannye imenno po smesheniyam perigeliev i uzlov voshozhdeniya. Po etomu v tablice vo vtoryh strokah ya i privozhu dannye N'yukoma privedennye mnoyu k normal'nomu vidu, t.e. samo smeshenie perigeliya dAlfaP, a ne ego proizvedenie na ekscentrisitet planety Eks*dAlfaP, kak eto bylo u N'yukoma i smeshenie voshodyashego uzla dAlfaU, a ne ego proizvedenie na sinus ugla naklona orbity sin(Betta)*dAlfaU, a smeshenie ekscentrisitetov ya privozhu ne v uglovyh sekundah, kak eto dano u N'yukoma, a v bezrazmernyh velichinah uvelichennyh v 1 000 000 raz. A, dlya perescheta dannyh N'yukoma, postoyannye znacheniya ekscentrisitetov planet i uglov naklona ya vzyal iz teorii N'yukoma, kotorye poluchayutsya dlya 1900 goda. Pri etom, poluchennye mnoyu na programme Solsys6 dannye po vekovym smesheniyam parametrov orbit polucheny po uproshennoi teorii N'yukoma, t.e. bez periodicheskih vozmushenii, kotorye dlya nashih celei i ne nuzhny, t.k. sozdayut tol'ko shum, ot kotorogo potom pri statisticheskoi obrabotke pervichnyh dannyh prihodit'sya ochishat' eti dannye.

Tablica 12b. Vekovye smesheniya parametrov orbit planet, poluchennye N'yukomom kak nablyudatel'nye i raschetnye (teoreticheskie) dannye i poluchennye mnoyu eti zhe dannye na programme Solsys6 pri statisticheskoi obrabotke pervichnyh dannyh za period s 1601 po 1901 gody. Oboznacheniya vekovyh smeshenii parametrov orbit sootvetstvuyut prinyatym v moei programme Solsys6 i v vysheprivedennoi tablice11s (AlfaP perigelii, AlfaU uzel voshozhdeniya, Betta naklon orbity i Eks ekscentrisitet, a poslednyaya cifra sootvetstvuet poryadkovomu nomeru planety).

Parametr____________Nablyudeniya____Teoriya_N'yutona_____Raznost'

Eks1*dAlfaP1______ ___118,24+/-0,40____109,76+/-0,16_____8,48+/-0,43
dAlfaP1______________575,06+/- 1,95____533,82+/-0,78____41,24+/-2,09
dAlfaP1*_____________573,07+/-0,03____532,21+/- 0,12____40,86+/-0,12
dAlfaP1**____________570,75+/-0,02____529,89+/-0,12____40,86+/- 0,12
sin(Betta1)*dAlfaU1____-91,89+/-0,45____-92,50+/-0,16_____0,61+/-0,52
dAlfaU1______________-753,70+/-3,69___-758,70+/-1,31____5,00+/-4,27
dAlfaU1*_____________-758,32+/-0,45___-756,66+/-0,27___-1,66+/-0,45
dAlfaU1**____________-451,92+/-0,29___-450,28+/-0,11___-1,64+/-0,29
dBetta1_______________7,14+/-0,80______6,76+/-0,01_____0,38+/-0,80
dBetta1*______________6,94+/-0,06______6,90+/-0,05_____0,04 +/-0,06
dBetta1**____________-21,43+/-0,00____-21,47+/-0,00_____0,03+/-0,00
dEks1*3600*180/pi_____3,36+/-0,50______4,24+/-0,01_____-0,88+/-0,50
dEks1________________16,29+/-2,42_____20,56+/-0,05_____4,27+/-2,42
dEks1*_______________20,57+/-0,01_____20,52+/-0,11_____0,05+/- 0,11
dEks1**______________20,57+/-0,01_____20,52+/-0,11_____0,05+/- 0,11

Eks2*dAlfaP2___________0,29+/-0,20______0,34+/-0,15______-0,05+/- 0,25
dAlfaP2_______________42,52+/-29,33____49,85+/-21,99____-7,33+/- 36,66
dAlfaP2*______________59,25+/-4,27_____49,08+/-10,22____10,17+/-10,22
dAlfaP2**_____________57,87+/-4,28_____47,69+/-10,22____10,18+/-10,22
sin(Betta2) *dAlfaU2____-105,40+/-0,12____-106,00+/-0,12_____0,60+/-0,17
dAlfaU2_____________- 1780,56+/-2,03___-1790,69+/-2,03____10,14+/-2,87
dAlfaU2*____________-1788,75+/- 0,35___-1786,83+/-0,07____-1,92+/-0,35
dAlfaU2**____________-999,51+/-0,47____- 997,92+/-0,33____-1,59+/-0,47
dBetta2________________3,87+/-0,30______3,49+/- 0,14______0,38+/-0,33
dBetta2*_______________3,63+/-0,00______3,62+/-0,01______0,01+/- 0,01
dBetta2**_____________-2,42+/-0,11______-2,42+/-0,12______0,00+/-0,12
dEks2*3600*180/pi _____-9,46+/-0,20______-9,67+/-0,24______0,21+/- 0,31
dEks2________________-45,86+/-0,97_____-46,88+/-1,16_____1,02+/-1,50
dEks2*_______________-48,08+/-0,08_____-49,17+/-0,33_____1,09+/-0,33
dEks2**______________-48,08+/-0,08_____-49,17+/-0,33_____1,09+/- 0,33

Eks3*dAlfaP3__________19,48+/-0,12_____19,38+/-0,05______0,10+/-0,13
dAlfaP3______________1162,92+/-7,16___1156,95+/-2,98_____5,97+/-7,76
dAlfaP3*_____________1160,36+/-0,43___1146,32+/-2,92____14,04+/-2,92
dAlfaP3**____________1160,36+/-0,41___1144,96+/-2,15____15,40+/-2,15
sin(Betta3) *dAlfaU3_________---_____________---______________---
dAlfaU3___________________--- _____________---______________---
dAlfaU3*__________________---_____________--- ______________---
dAlfaU3**____________-869,84+/-0,17___-905,27+/-7,00____35,43+/- 7,00
dBetta3***____________-47,11+/-0,23____-46,89+/-0,09____-0,22+/-0,27
dBetta3*__________________---_____________---___________---
dBetta3**_____________-47,19+/-0,03____-47,28+/-0,01____0,09+/-0,03
dEks3*3600*180/pi _____-8,55+/-0,09_____-8,57+/-0,04_____0,02+/-0,10
dEks3________________-41,45+/-0,44____-41,55+/-0,19_____0,10+/-0,48
dEks3*_______________-41,33+/-0,11____-42,44+/-0,43_____1,11+/-0,43
dEks3**______________-41,33+/-0,11____-42,54+/-0,44_____1,21+/- 0,44


Eks4*dAlfaP4__________149,55+/-0,35____148,80+/-0,04____0,75+/-0,35
dAlfaP4______________1602,69+/-3,75___1594,65+/-0,43____8,04+/-3,75
dAlfaP4*_____________1602,19+/-0,65___1601,79+/-1,71____0,40 +/- 1,71
dAlfaP4**____________1601,55+/-0,68___1600,80+/-1,15____0,75+/-1,15
sin (Betta4)*dAlfaU4_____-72,60+/-0,20____-72,63+/-0,09____0,03+/-0,22
dAlfaU4_____________-2248,44+/-6,19___-2249,37+/-2,79___0,93+/-6,81
dAlfaU4*____________-2247,27+/-1,06___-2245,68+/-0,31___-1,59+/-1,06
dAlfaU4**___________-1053,12+/-1,97___-1051,60+/-1,00___-1,52+/-1,97
dBetta4_______________-2,26+/-0,20_____-2,25+/-0,04_____-0,01+/-0,20
dBetta4*______________-2,60+/-0,04_____-2,54+/-0,02_____-0,06+/-0,04
dBetta4**_____________-29,05+/-0,08____-29,00+/-0,05____-0,05+/-0,08
dEks4*3600*180/pi _____19,00+/-0,27_____18,71+/-0,01_____0,29+/- 0,27
dEks4_________________92,11+/-1,31_____90,71+/-0,05_____1,40+/-1,31
dEks4*________________92,33+/-0,04_____93,40+/-0,59____-1,07+/-0,59
dEks4**_______________92,33+/-0,04_____93,93+/-0,54____-1,60+/-0,54


*, ** - znacheniya vekovyh smeshenii, poluchennye mnoyu na programme Solsys6 pri obrabotke pervichnyh dannyh za period s 1601 po 1901 gody, gde pervichnye nablyudatel'nye dannye polucheny po teorii planet N'yukoma bez ucheta periodicheskih vozmushenii, a teoreticheskie na matematicheskoi modeli s ispol'zovaniem klassicheskoi teorii N'yutona i s parametrami modeli po dannym N'yukoma (osnovnoi shag resheniya byl 3600 sek, a vblizi perigeliya i uzla voshozhdeniya shag umen'shalsya v 200 raz). V svoei tablice N'yukom ukazyvaet srednie oshibki, no dlya opredeleniya anomal'nosti smesheniya on ispol'zuet veroyatnye oshibki, kotorye poluchayutsya umnozheniem srednih oshibok na 0,67454. U menya zhe v programme Solsys6 poluchayutsya predel'nye otkloneniya s nadezhnost'yu (doveritel'noi veroyatnost'yu) 95%, gde predel'nye otkloneniya opredelyalis' po kriteriyu maksimina, t.e. kak maksimal'nye otkloneniya iz minimal'no vozmozhnyh dlya hotya by chastichnogo perekrytiya vseh dopustimyh otklonenii rasschitannyh pri raznom kolichestve tochek v gruppah dannyh, na kotorye (gruppy) razbivaetsya vsya vyborka.

* - dlya tekushei (mgnovennoi) ekliptiki s vychetom precessii
** - dlya fiksirovannoi ekliptiki J2000
*** - u N'yukoma eto otklonenie ekliptiki ot ekvatora Zemli

Kak vidno iz privedennyh dannyh, raschetnye i nablyudatel'nye dannye privedennye samim N'yukomom malo otlichayutsya ot raschetnyh i nablyudatel'nyh dannyh poluchennyh po ego teorii planet mnoyu, no po nekotorym parametram est' i principial'nye otlichiya. Ya v obshem mogu eto ob'yasnit' tol'ko tem, chto ya primenyal svoyu metodiku (statisticheskuyu) dlya polucheniya vekovyh smeshenii parametrov orbit. A vozmozhno nekotoroe otlichie poluchennyh mnoyu nablyudatel'nyh dannyh ot privedennyh N'yukomom svyazano eshe i s tem, chto ya, kak vyyasnilos' v besede s Hartikovym, ispol'zoval ne original'nuyu teoriyu N'yukoma, a ee sovremennyi variant, kotoryi (lichno dlya menya) ne izvestno chem otlichaetsya ot originala. Hotya rashozhdeniya po nekotorym dannym imeyut vpolne logicheskoe ob'yasnit'. Naprimer, rashozhdeniya po smesheniyu perigeliya Venery svyazano s tem, chto smeshenie perigeliya Venery nosit yavno kvadratichnyi harakter i po etomu o vekovom smeshenie perigeliya Venery govorit' ne korrektno, t.k. v odnom veke ono budet imet' odno znachenie, a v drugom veke drugoe. Naprimer, sam N'yukom v uravnenie regressii (v ego teorii planet) dlya smesheniya perigeliya Venery v tekushei ekliptike daet takie dannye
AlfaP2= Alfa0 + 5068,99*dT 3,515*dT*dT
chto pri prostom vychete precessii 5025,64 uglovyh sekund dast nam
AlfaP2= Alfa0 + 43,35*dT -3,515*dT*dT
Pri etom u nego dT (v yulianskih stoletiyah) otschityvaetsya ot 1900 goda, a ya, obrabotav ego zhe dannye, t.e. dannye kak by nablyudenii poluchennye po ego zhe uravneniyam regressii, s 1601 po 1901 gody poluchayu takuyu zavisimost'
AlfaP2= Alfa0 + 69,73*dT -4,619*dT*dT
gde u menya dT otschityvaetsya ot 1601 goda, i mgnovennoe znachenie vekovogo smesheniya perigeliya Venery v 1900 godu u menya poluchaetsya po etoi zavisimosti 42,11, chto neznachitel'no otlichaetsya ot nachal'nogo znacheniya lineinogo chlena v uravnenie regressii N'yukoma (43,35), kogda za tochku otscheta v ego uravnenie prinyat 1900 god. No, govorya o vekovyh smesheniyah parametrov orbit, my vsegda podrazumevaem, chto oni yavlyayutsya konstantami i, sledovatel'no, kvadratichnye chleny v uravneniyah dlya AlfaP2 dolzhny otsutstvovat'. A vot v nashem sluchae, kogda u nas imeetsya yavnaya nelineinaya zavisimost', a my approksimiruem dannyh za kakoi to period lineinoi zavisimost'yu, u nas v zavisimosti ot prodolzhitel'nosti etogo perioda i ot daty nachala etogo perioda budut poluchat'sya raznye znacheniya vekovogo smesheniya parametra. Naprimer, po moim koefficientam kvadratichnoi approksimacii poluchaetsya, chto pri approksimacii dannyh lineinoi zavisimost'yu za neprodolzhitel'nyi promezhutok vremeni v 1601 godu poluchit'sya znachenie vekovogo smesheniya perigeliya Venery 69,73, a v 1900 godu 42,11. A esli approksimirovat' lineinoi zavisimost'yu ves' interval ot 1601 po 1901 gody, to poluchitsya srednee znachenie, sootvetstvuyushee 1751 godu, t.e. 59,25, chto i otrazheno v tablice 12b. A dlya 1801 goda, t.e. po dannym tablicy 11ss, gde dannye obrabatyvalis' za period s 1601 po 2001 gody poluchaetsya 54,46.

Prodolzhenie sleduet
S nailuchshimi pozhelaniyami Sergei Yudin.




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