planets

ball2_gr.gif (888 bytes)   
ball2_gr.gif (888 bytes)   , J2000 
ball2_gr.gif (888 bytes)   ,  
ball2_gr.gif (888 bytes)  
ball2_gr.gif (888 bytes)   (Standish E.M., JPL/Caltech)

1 a.e. = 149 597 870



(..)

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0.38709830982 0.205631752 7.0049863889    87.96843362     0.00 47.87
0.72332981996 0.006771882 3.3946619444   224.6954354 177.36 35.02
1.00000101778 0.016708617 0.0   365.24218985 23.45 29.79
1.52367934191 0.093400620 1.8497263889   686.92970957 25.19 24.13
5.20260319132 0.048494851 1.3032697222 4330.5957654   3.13 13.06
9.55490959574 0.055508622 2.4888780556 10746.940442 25.33 9.66
19.21844606178 0.046295899 0.77319611 30588.740354 97.86 6.80
30.11038686942 0.008988095 1.7699522 59799.900456 28.31 5.44
39.5181761979 0.2459387823 17.1225991666 90738.995 122.52 4.74

 1/ J2000.

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J2000

, J2000  [1].
J 2000.0 ( JD = 2451545.0 ).
.
t - (TDB) , J2000.0 (JD=2451545.0), ..
t = (JD - 2451545.0)/365250 .

:
a - ,                                      λ - ,  λ = ω +  Ω + M0
e -
,                                                     ω - ,
i -
,                                 Ω - .

, :
k = e cos ω,          h = e sin ω,                q = sin i/2 cos Ω,                 p = sin i/2 sin Ω.

, e, ω, i , Ω k, h, q, p . ,  e, ω, i , Ω k, h, q, p. 
, e, k, h, q, p - .  λ , ω, i Ω , .

                         
                           
                            
                               
   
 a = 0.3870983098
 λ = 252.25090552+5381016286".88982t-1".92789t2+0".00639t3
 e = 0.2056317526+0.0002040653t-2834910-10t2-180510-10t3+2310-10t4-210-10t5
 ω = 77.45611904+5719".11590t-4".83016t2-0".02464t3-0".00016t4 +0".00004t5
 i = 7.00498625-214".25629t+0".28977t2+0".15421t3-0".00169t4-0".00002t5
 Ω = 48.33089304-4515".21727t-31".79892t2-0".71933t3+0".01242t4
 k = 0.0446605976-0.0055211462t-0.0000186057t2+791210-10t3+5910-10t4-210-10t5
 h = 0.2007233137+0.0014375012t-0.0000797412t2+304610-10t3+8110-10t4-10-10t5
 q = 0.0406156338+0.0006543312t-0.0000107122t2+224610-10t3-3810-10t4
 p = 0.0456355046-0.0012763366t-0.0000091335t2+189910-10t3-6410-10t4

 a = 0.7233298200
 λ = 181.97980085+2106641364".33548t+0".59381t2-0".00627t 3
 e = 0.0067719164-0.0004776521t+9812710-10t2+463910-10t3+12310-10t4-310-10t5
 ω = 131.56370300+175".48640t-498".48184t2-20".50042t3-0".72432t4+0".00224t5
 i = 3.39466189-30".84437t-11".67836t2+0".03338t3+0".00269t4+0".00004t5
 Ω = 76.67992019-10008".48154t-51".32614t2-0".58910t3-0".04665t4
 k = -0.0044928213+0.0003125902t+0.0000060406t2-683510-10t3+4910-10t4+610-10t5
 h = 0.0050668473-0.0003612124t+0.0000184676t2+32810-10t3-6110-10t4-210-10t5
 q = 0.0068241014+0.0013813383t-0.0000109094t2-1864210-10t3+6010-10t4+710-10t5
 p = 0.0288228577-0.0004038479t-0.0000623289t2+247310-10t3+42310-10t4-110-10t5.

 a =1.0000010178
 λ =100.46645683+1295977422".83429t-2".04411t2-0".00523t3
 e = 0.0167086342-0.0004203654t-0.0000126734t2+144410-10t3-210-10t4+310-10t5
 ω = 102.93734808+11612".35290t+53".27577t2-0".14095t3+0".11440t4+0".00478t5
 i = 469".97289t-3".35053t2-0".12374t3+0".00027t4-0".00001t5+0".00001t6
 Ω = 174.87317577-8679".27034t+15".34191t2+0".00532t3-0".03734t4-0".00073t5+0".00004t6
 k = -0.0037408165-0.0008226742t+0.0000276246t2+169610-10t3-27010-10t4-710-10t5
 h = 0.0162844766-0.0006202965t-0.0000338263t2+851010-10t3+27710-10t4-510-10t5
 q = -0.0011346887t+0.0000123731t2+1265410-10t3-13710-10t4-310-10t5
 p = 0.0001018038t+0.0000470200t2-541710-10t3-25110-10t4+510-10t5

 a = 1.5236793419+310-10t
 λ = 355.43299958+689050774".93988t+0".94264t2-0".01043t3
 e = 0.0934006477+0.0009048438t-8064110-10t2-251910-10t3+12410-10t4-1010-10t5
 ω = 336.06023395+15980".45908t-62".32800t2+l".86464t3-0".04603t4-0".00164t5
 i = 1.84972648-293".31722t-8".11830t2-0".10326t3-0".00153t4+0".00048t5
 Ω = 49.55809321-10620".90088t-230".57416t2-7".06942t3-0".68920t4-0".05829t5
 k = 0.0853656025+0.0037633015t-0.0002465778t2-3673110-10t3+11110-10t4 +310-10t5
 h = -0.0378997324+0.0062465746t+0.0001552948t2-6348810-10t3-65910-10t4 +710-10t5
 q = 0.0104704257+0.0001713853t-0.0000407749t2-1388310-10t3+9210-10t4 +1810-10t5
 p = 0.0122844931-0.0010802008t-0.0000192222t2+871910-10t3+30910-10t4 .

 a = 5.2026032092+1913210-10t-3910-10t2-6010-10t3-1010-10t4+110-10t5
 λ = 34.35151874+109256603".77991t-30".60378t2+0".05706t3+0".04667t4-0".00591t5-0".00034t6
 e = 0.0484979255+0.0016322542t-0.0000471366t2-2006310-10t3+101810-10t4-2110-10t5+110-10t6
 ω = 14.33120687+7758".75163t+259".95938t2-16".14731t3+0".74704t4-0".02087t5-0".00016t6
 i = 1.30326698-71".55890t+11".95297t2+0".34909t3-0".02710t4-0".00124t5 +0".00003t6
 Ω = 100.46440702+6362".03561t+326".52178t2-26".18091t3-2".10322t4+0".04459t5 +0".01154t6
 k = 0.0469857457+0.0011300656t-0.0001092396t2-4308910-10t3+196310-10t4+2110-10t5-210-10t6
 h = 0.0120038766+0.0021714660t+0.0000985396t2-5163510-10t3-99010-10t4 +6910-10t5
 q = -0.0020656001-0.0003134485t-0.0000167052t2+797510-10t3+36510-10t4-210-10t5-110-10t6
 p = 0.0111837479-0.0002342791t+0.0000208686t2+527210-10t3-34210-10t4 +510-10t5

 a = 9.5549091915-0.0000213896t+44410-10t2+67010-10t3+11010-10t4-710-10t5-110-10t6
 λ = 50.07744430+43996098".55732t+75".61614t2-0".16618t3-0"11484t4-0".01452t5+0".00083t6
 e = 0.0555481426-0.0034664062t-0.0000643639t2+3395610-10t3-21910-10t4-310-10t5 +610-10t6
 ω = 93.05723748+20395".49439t+190".25952t2+17".68303t3+1".23148t4+0".10310t5 +0".00702t6
 i = 2.48887878+91".85195t-17".66225t2+0".06105t3+0".02638t4-0".00152t5 -0".00012t6
 Ω =113.66550252-9240".19942t-66".23743t2 +1".72778t3+0".26990t4 +0".03610t5-0".00248t6
 k = -0.0029599926-0.0052959042t+0.0003092222t2+0.0000129279t3-634710-10t4-5410-10t5 +810-10t6
 h = 0.0554296096-0.0037559081t-0.000319842t2+0.0000159875t3+302210-10t4-23110-10t5 +210-10t6
 q = -0.0087174677+0.0008017413t+0.0000414442t2-1999710-10t3-89610-10t4 +610-10t5 +210-10t6
 p = 0.0198914760+0.0005944060t-0.0000523589t2-1299310-10t3+85610-10t4 -1610-10t5-110-10t6

  a = 19.2184460618-371610-10t+97910-10t2
  λ = 314.05500511+15424811".93933t-1".75083t2+0".02156t3
  e = 0.0463812221-0.0002729293t+0.0000078913t2+244710-10t3-17110-10t4
 ω = 173.00529106+3215".56238t-34".09288t2+1".48909t3+0".06600t4
  i = 0.77319689-60".72723t+1".25759t2+0".05808t3+0".00031t4
 Ω = 74.00595701+2669".15033t+145".93964t2 +0".42917t3-0".09120t4
 k = -0.0459513238+0.0001834412t-0.0000008085t2-454010-10t3+21810-10t4
 h = 0.0056379131-0.0007496435t+0.0000121020t2-420910-10t3-17110-10t4
 q = 0.0018591507-0.0001244938t-0.0000020737t2+76210-10t3
 p = 0.0064861701-0.0001174473t+0.0000031780t2+73210-10t3

 a = 30.1103868694-1663510-10t+68610-10t2
 λ = 304.34866548+7865503".20744t+0".21103t2-0".00895t3
 e = 0.0094557470+0.0000603263t+0t2-48310-10t3
 ω = 48.12027554+1050".71912t+27".39717t2
 i = 1.76995259+8".12333t+0".08135t2-0".00046t3
 Ω = 131.78405702-221".94322t-0".78728t2 -0".28070t3+0".00049t4
 k = 0.0059997757+0.0000087130t-0.0000011990t2-40310-10t3
 h = 0.0066924241+0.0000782434t+0.0000008080t2-39510-10t3
 q = -0.0102914782-0.0000007273t-0.000000657t2+16710-10t3
 p = 0.0115168398+0.0000257554t+0.0000001938t2+13310-10t3

,

,   [1].
J 2000.0 ( JD = 2451545.0 ).
.
t - (TDB) , J2000.0 (JD=2451545.0), ..
t = (JD - 2451545.0)/365250 .
, e, k, h, q, p - .  λ , ω, i Ω ( λ = ω +  Ω + M0),   .
k = e cos ω,          h = e sin ω,                q = sin i/2 cos Ω,                 p = sin i/2 sin Ω

                 
                       
                         
                          
 

 a = 0.3870983098
 λ = 252.25090552+5381066598".20037t+109".25943t2+0".06522t3-0".23500t4-0".00179t5+0".00020t6
 e = 0.2056317526+0.0002040653t-2834910-10t2-180510-10t3+2310-10t4-210-10t5
 ω = 77.45611904+56030".42645t+106".35716t2+0".03418t3-0".23516t4-0".00176t5 +0".00020t6
 i = 7.00498625+65".57301t-6".51516t2+0".20113t3+0".00019t4-0".00019t5
 Ω = 48.33089304+42700".01444t+63".14994t2+0".77259t3-0".20893t4-0".00219t5 +0".00016t6
 k = 0.0446605976-0.0544807963t-0.0018059782t2+0.0006632523t3+0.0000149034t4-2366810-10t5-59710-10t6
 h = 0.2007233137+0.0123309371t-0.0073733874t2-0.0001849726t3+0.000044500t4+1007510-10t5-102810-10t6
 q = 0.0406156338-0.0093417782t-0.0009192871t2+0.0000651977t3-3741610-10t4-128410-10t5-6710-10t6
 p = 0.0456355046+0.0085265821t-0.0009553697t2-0.0000671085t3-3300510-10t4 +171110-10t5-3710-10t6 

 a = 0.7233298200
 λ = 181.97980085+2106691666".31989t+111".65021t2+0".05368t3-0".23516t4-0".00179t5+0".00020t6
 e = 0.0067719164-0.0004776521t+9812710-10t2+463910-10t3+12310-10t4-310-10t5
 ω = 131.56370300+50477".47081t-387".42545t2-20".44048t3-0".95948t4+0".00044t5 +0".00020t6
 i = 3.39466189+36".13261t-0".31523t2-0".02525t3+0".00085t4-0".00008t5
 Ω = 76.67992019+32437".57636t+146".22586t2-0".33446t3-0".23007t4-0".00088t5 +0".00009t6
 k = -0.0044928213-0.0009230666t+0.0002250026t2-0.0000014513t3-1681010-10t4 +62710-10t5 +5010-10t6
 h = 0.0050668473-0.0014568806t-0.0000583901t2+0.0000226090t3-604110-10t4 -99810-10t5 +4310-10t6
 q = 0.0068241014-0.0045125642t-0.0001183914t2+0.0000177623t3+524410-10t4 -17310-10t5-1110-10t6
 p = 0.0288228577+0.0011583648t-0.0003491466t2-0.0000087743t3+653510-10t4+26410-10t5-210-10t6

 a = 1.0000010178
 λ = 100.46645683+1296027711".03429t+109".15809t2+0".07207t3-0".23530t4-0".00180t5+0".00020t6
 e = 0.0167086342-0.0004203654t-0.0000126734t2+144410-10t3-210-10t4+310-10t5
 ω = 102.93734808+61900".55290t+164".47797t2-0".06365t3-0".12090t4+0".00298t5+0".00020t6
 k = -0.0037408165-0.0047928949t+0.0002812540t2+0.0000740171t3-2697410-10t4-381010-10t5+8610-10t6
 h = 0.0162844766-0.0015323228t-0.0007203925t2+0.0000324712t3+5858910-10t4-171910-10t5-21310-10t6

 a = 1.5236793419+310-10t
 λ = 355.43299958+689101069".33069t+111".78674t2+0".05624t3-0".23516t4-0".00180t5+0".00020t6
 e = 0.0934006477+0.0009048438t-8064110-10t2-251910-10t3+12410-10t4-1010-10t5
 ω = 336.06023395+66274".84990t+48".51610t2+l".93131t3-0".28118t4-0".00344t5+0".00020t6
 i = 1.84972648-21".63885t+4".59350t2-0".02376t3-0".01708t4+0".00065t5+0".00005t6
 Ω = 49.55809321+27792".68736t+5".60611t2+8".16222t3-0".45709t4-0".04722t5+0".00435t6
 k =0.0853656025+0.0130045425t-0.0042870473t2-0.0002595083t3+0.0000354092t4+1598810-10t5-110410-10t6
 h = -0.0378997324+0.0270616164t+0.0022454557t2-0.0004514091t3-0.0000226552t4+2192110-10t5+95910-10t6
 q = 0.0104704257-0.0016892678t-0.0000827820t2+0.0000036153t3+16910-10t4 +14210-10t5+310-10t6
 p = 0.0122844931+0.0013708983t-0.0001073425t2-0.0000026091t3-23110-10t4-3410-10t5+1410-10t6

 a = 5.2026032092+1913210-10t-3910-10t2-6010-10t3-1010-10t4+110-10t5
 λ = 34.35151874+109306899".89453t+80".38700t2+0".13327t3-0".18850t4+0".00411t5-0".00014t6
 e = 0.0484979255+0.0016322542t-0.0000471366t2-2006310-10t3+101810-10t4-2110-10t5+110-10t6
 ω = 14.33120687+58054".86625t+370".95016t2-16".07110t3+0".51186t4-0".02268t5+0".00004t6
 i = 1.30326698-197".87442t+1".67744t2-0".00838t3-0".00737t4+0".00085t5 +0".00004t6
 Ω = 100.46440702+36755".18747t+145".13295t2+1".45556t3-0".59609t4-0".04324t5 +0".00175t6
 k = 0.0469857457-0.0017969926t-0.0020420604t2-0.0000402595t3+0.0000168641t4+600010-10t5-62310-10t6
 h = 0.0120038766+0.0136285825t+0.0000425103t2-0.0002108419t3-0.0000061928t4+1109710-10t5+44410-10t6
 q = -0.0020656001-0.0019057660t+0.0001082507t2+0.0000089680t3-363810-10t4-11710-10t5-710-10t6
 p = 0.0111837479-0.0008397312t-0.0001594973t2+0.0000079342t3+379010-10t4 -6710-10t5-110-10t6

  a =9.5549091915-0.0000213896t+44410-10t2+67010-10t3+11010-10t4-710-10t5-110-10t6
  λ =50.07744430+44046398".47038t+186".86817t2-0".10748t3-0"35004t4-0".01630t5+0".00103t6
  e =0.0555481426-0.0034664062t-0.0000643639t2+3395610-10t3-21910-10t4-310-10t5+610-10t6
 ω =93.05723748+70695".40745t+301".51155t2+17".74174t3+0".99628t4+0".10132t5 +0".00722t6
  i =2.48887878-134".50388t-5".46800t2+0".31168t3+0".03207t4-0".00237t5 -0".00023t6
 Ω =113.66550252+31575".16875t-43".83321t2 -8".09520t3+0".18433t4 +0".06867t5 -0".00276t6
 k=-0.0029599926-0.0188130068t+0.0012832568t2+0.0003847521t3-0.0000214188t4-2525010-10t5+114910-10t6
 h= 0.0554296096-0.0044777281t-0.0032610492t2+0.0002000704t3+0.0000346305t4-1743610-10t5-155810-10t6
 q = -0.0087174677-0.0029141582t+0.0001573853t2+0.0000123470t3-706810-10t4 -34710-10t5+3810-10t6
 p = 0.0198914760-0.0016330327t-0.0002233181t2+0.0000111755t3+617410-10t4-48210-10t5-2410-10t6

 a = 19.2184460618-371610-10t+97910-10t2
 λ = 314.05500511+15475106".01961t+109".40272t2+0".09474t3-0".23521t4-0".00180t5+0".00020t6
 e = 0.0463812221-0.0002729293t+0.0000078913t2+244710-10t3-17110-10t4
 ω = 173.00529106+53509".64266t+77".06068t2+1".56227t3-0".16921t4 0".00180t5+0".00020t6
 i = 0.77319689+27".87845t+13".49529t2-0".33095t3-0".03444t4+0".00171t5+0".00012t6
 Ω =74.00595701+18760".59902t+482".21068t2 +66".54269t3-3".52490t4-0".32819t5+0".03056t6
 k = -0.0459513238-0.0011912655t+0.0015449434t2+0.0000112035t3-8353610-10t4-51310-10t5+16510-10t6
 h = 0.0056379131-0.0119540733t-0.0001355308t2+0.0001320336t3+784910-10t4-414010-10t5-3310-10t6
 q = 0.0018591508-0.0005713216t-0.0000197484t2-4984610-10t3+39110-10t4+26710-10t5+310-10t6
 p = 0.0064861701+0.0002340588t+0.0000106579t2-1189210-10t3-458910-10t4-1410-10t5+1210-10t6

 a = 30.1103868694-1663510-10t+68610-10t2
 λ = 304.34866548+7915799".13277t+111".17536t2+0".06468t3-0".23514t4-0".00180t5+0".00020t6
 e = 0.0094557470+0.0000603263t+0t2-48310-10t3
 ω = 48.12027554+51346".64445t+138".36149t2+0".07363t3-0".23514t4-0".00180t5+0".00020t6
 i = 1.76995259-335".09412t-2".54991t2+0".09845t3+0".00101t4-0".00005t5-0".00001t6
 Ω = 131.78405702+39679".34159t+93".42773t2-2".29323t3-0".33948t4-0".00479t5-0".00006t6
 k = 0.0059997757-0.0016231779t-0.0002022477t2+0.0000148438t3+1229810-10t4-32310-10t5-3310-10t6
 h = 0.0066924241+0.0015412377t-0.0001928011t2-0.0000180270t3+815710-10t4+68610-10t5-810-10t6
 q = -0.0102914782-0.0016743192t+0.0003058350t2+5678210-10t3-1375210-10t4-13310-10t5+2510-10t6
 p = 0.0115168399-0.0025854022t-0.0001182648t2+23743610-10t3+246910-10t4-63910-10t5-910-10t6

 

[2]
289.27991666
113.34214416
. 109.60685333
17.122599167
0.2459387823
39.5181761979  ..
6.9244599.10-5 / = 3.9674232.10-3/

:

  1. J.L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touzé, G. Francon, J.Laskar (1994). Numerical expressions for precession formulae and mean elements for the Moon and the planets.
    Astron. Astrophys., v. 282, p. 663-683.
  2. Bretagnon P. (1982). Theorie du mouvement de l'ensemble des planetes. Solution VSOP82.
    Astron. Astrophys., V. 114, p. 278 - 288.

: ..
ural@sai.msu.ru