Eléments perturbés

P (ans)

a

e

i

L2000.0

Ω

ϖ

Masse

R. equat.

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Soleil

01/01

02/01

03/01

04/01

05/01

06/01

07/01

08/01

09/01

10/01

11/01

12/01

13/01

14/01

15/01

16/01

17/01

18/01

19/01

20/01

21/01

22/01

23/01

24/01

25/01

26/01

27/01

28/01

29/01

30/01

31/01

01/02

02/02

03/02

04/02

05/02

06/02

07/02

08/02

09/02

10/02

11/02

12/02

13/02

14/02

15/02

16/02

17/02

18/02

19/02

20/02

21/02

22/02

23/02

24/02

25/02

26/02

27/02

28/02

01/03

02/03

03/03

04/03

05/03

06/03

07/03

08/03

09/03

10/03

11/03

12/03

13/03

14/03

15/03

16/03

17/03

18/03

19/03

20/03

21/03

22/03

23/03

24/03

25/03

26/03

27/03

28/03

29/03

30/03

31/03

01/04

02/04

03/04

04/04

05/04

06/04

07/04

08/04

09/04

10/04

11/04

12/04

13/04

14/04

15/04

16/04

17/04

18/04

19/04

20/04

21/04

22/04

23/04

24/04

25/04

26/04

27/04

28/04

29/04

30/04

01/05

02/05

03/05

04/05

05/05

06/05

07/05

08/05

09/05

10/05

11/05

12/05

13/05

14/05

15/05

16/05

17/05

18/05

19/05

20/05

21/05

22/05

23/05

24/05

25/05

26/05

27/05

28/05

29/05

30/05

31/05

01/06

02/06

03/06

04/06

05/06

06/06

07/06

08/06

09/06

10/06

11/06

12/06

13/06

14/06

15/06

16/06

17/06

18/06

19/06

20/06

21/06

22/06

23/06

24/06

25/06

26/06

27/06

28/06

29/06

30/06

01/07

02/07

03/07

04/07

05/07

06/07

07/07

08/07

09/07

10/07

11/07

12/07

13/07

14/07

15/07

16/07

17/07

18/07

19/07

20/07

21/07

22/07

23/07

24/07

25/07

26/07

27/07

28/07

29/07

30/07

31/07

01/08

02/08

03/08

04/08

05/08

06/08

07/08

08/08

09/08

10/08

11/08

12/08

13/08

14/08

15/08

16/08

17/08

18/08

19/08

20/08

21/08

22/08

23/08

24/08

25/08

26/08

27/08

28/08

29/08

30/08

31/08

01/09

02/09

03/09

04/09

05/09

06/09

07/09

08/09

09/09

10/09

11/09

12/09

13/09

14/09

15/09

16/09

17/09

18/09

19/09

20/09

21/09

22/09

23/09

24/09

25/09

26/09

27/09

28/09

29/09

30/09

01/10

02/10

03/10

04/10

05/10

06/10

07/10

08/10

09/10

10/10

11/10

12/10

13/10

14/10

15/10

16/10

17/10

18/10

19/10

20/10

21/10

22/10

23/10

24/10

25/10

26/10

27/10

28/10

29/10

30/10

31/10

01/11

02/11

03/11

04/11

05/11

06/11

07/11

08/11

09/11

10/11

11/11

12/11

13/11

14/11

15/11

16/11

17/11

18/11

19/11

20/11

21/11

22/11

23/11

24/11

25/11

26/11

27/11

28/11

29/11

30/11

01/12

02/12

03/12

04/12

05/12

06/12

07/12

08/12

09/12

10/12

11/12

12/12

13/12

14/12

15/12

16/12

17/12

18/12

19/12

20/12

21/12

22/12

23/12

24/12

25/12

26/12

27/12

28/12

29/12

30/12

31/12

01/01

Saturne - plan équatorial

Direction Terre-Saturne

Plan eclp.

Plan orb.

Plan equ.

Visibilité des plans (3D)

Saturne, axe, anneaux (3D)

Δt/10

Système Saturne

EM Bary

Saturn 

a

e

i

L

lon. peri.

long. node

tps = 0 (slider from 0 to 25283, step If[fdtps, 0.001, 0.1])
tscl: (tps + 365.5) / 36525
fevol = false
G27: 0.3232736
G26: 102.9376819
ω_T: G26 + If[fevol, (tscl * G27), 0]
F26: 100.46457166
F27: 35999.37244981
LL_T = Mod(F26 + (F27 * (tps + 365.49431) / 36525), 360)
M_T = Mod(((LL_T - ω_T) * π / 180), (2 * π))
jjh: round((((tps - floor(tps)) * 24) * 10000), 0) / 10000
F29: 1222.49362201
F28: 49.9542442300001
H29: -0.28867794
H28: 113.66242448
G28: 92.5988783000001
G29: -0.4189721
LL_S = Mod(F28 + (F29 * (tps + 369.4207) / 36530), 360)
Ω_S: H28 + If[fevol, (tscl * H29), 0]
ω_S = Mod(G28 + If[fevol, (tscl * G29), 0] - Ω_S, 360)
ωb_S = Mod(ω_S + Ω_S, 360)
E29: 0.00193609
E28: 2.48599187
D27: -4.392E-5
D26: 0.01671123
D29: -5.09910000000001E-4
D28: 0.0538617900000001
C27: 5.62000000000001E-6
C26: 1.00000261
C29: -0.0012506
C28: 9.53667594000001
E20: 83.5400000000004
D20: 40.59
B7: 29.447498
P_S: (B7 * 365.25)
M_S: ((LL_S - ωb_S) * π / 180)
f1_S(x) = x - M_S
v1z = UnitVector(zAxis)
ε: 23.43928
Mrotε: {{1, 0, 0}, {0, cos(ε°), sin(ε°)}, {0, (-sin(ε°)), cos(ε°)}}
i_S: E28 + If[fevol, (tscl * E29), 0]
v1rot = Vector((Mrotε * Vector[(1; D20°; E20°)]))
H = (0, 0, 0)
v1orb = Rotate(Vector[Rotate[v1z, i_S°, xAxis]], Ω_S°, zAxis)
e_S: D28 + If[fevol, (tscl * D29), 0]
f2_S(x) = (e_S * sin(x))
I_S = Intersect(f1_S, f2_S, (-0.5569902150575718, -0.028473159443928475))
u'_S: (x(I_S) * 180 / π)
v_S: (2 * atand((sqrt((1 + e_S) / (1 - e_S)) * tan((u'_S * ° / 2)))))
a_S: C28 + If[fevol, (C29 * tscl), 0]
r_S: (a_S * (1 - e_S^(2)) / (1 + (e_S * cos(v_S))))
S = Rotate(Rotate[Rotate[(r_S; v_S), i_S°, xAxis], Ω_S°, zAxis], ω_S°, Line[H, v1orb])
c_S: (a_S * e_S)
b_S: sqrt(a_S^(2) - c_S^(2))
B2: 0.2408467
C2: 0.38709927
D2: 0.20563593
E2: 7.00497902000003
F2: 252.250324
G2: 48.3307659000007
H2: 77.4577963000005
I2: 3.3E23
J2: 2439700
B3: 0.615197260000004
C3: 0.723335660000003
D3: 0.00677672000000002
E3: 3.39467605
F3: 181.9791
G3: 76.6798426000007
H3: 131.602467
I3: 4.87E24
J3: 6051800
B4: 1.0000174
C4: 1.00000261
D4: 0.01671123
E4: -1.531E-5
F4: 100.464572
G4: 0
H4: 102.937682
I4: 5.97E24
J4: 6371000
B5: 1.8808476
C5: 1.52371034
D5: 0.0933941000000002
E5: 1.84969142
F5: -4.55343205
G5: 49.5595389000006
H5: -23.9436296
I5: 6.42E23
J5: 3389500
B6: 11.862615
C6: 5.20288700000003
D6: 0.04838624
E6: 1.30439695
F6: 34.3964405
G6: 100.473909
H6: 14.7284798
I6: 1.9E27
J6: 69911000
C7: 9.53667594000003
D7: 0.0538617900000002
E7: 2.48599187
F7: 49.9542442000003
G7: 113.662424
H7: 92.5988783000005
I7: 5.68E26
J7: 58232000
B8: 84.0168460000005
C8: 19.1891646
D8: 0.04725744
E8: 0.772637830000003
F8: 313.238105
G8: 74.0169250000007
H8: 170.954276
I8: 8.68E25
J8: 25362000
B9: 164.79132
C9: 30.0699228
D9: 0.00859048000000002
E9: 1.77004347
F9: -55.1200297000003
G9: 131.784226
H9: 44.9647623
I9: 1.02E26
J9: 25362000
B10: 247.92065
C10: 39.4821168
D10: 0.2488273
E10: 17.1400121
F10: 238.929038
G10: 110.303937
H10: 224.068916
I10: 1.3100000000000001E22
J10: 1151000
B11: 11.862615
C11: 0.00465247263709884
D11: 0
E11: 7.25000000000001
G11: 75.7600000000001
H11: 0
I11: 2.0E30
J11: 696000000
B15: 58.6462000000005
B16: -243.018
B17: 0.997269680000005
B18: 1.02595676
B19: 0.41354
B20: 0.44401
B21: -0.718330000000005
B22: 0.671250000000005
B23: -6.38720000000005
B24: 27.28
Pl_{ecl} = OrthogonalPlane((0, 0, 0), v1z)
Pl_{equ} = OrthogonalPlane(S, Line[(0, 0, 0), v1rot])
Pl_{orb} = OrthogonalPlane((0, 0, 0), v1orb)
corb2 = Rotate(Ellipse[H, ((-2 * c_S), 0), a_S, xOyPlane], i_S°, xAxis)
corb_S = Rotate(Rotate[corb2, Ω_S°, zAxis], ω_S°, Line[H, v1orb])
lgequ = IntersectPath(Pl_{ecl}, Pl_{equ})
lgnds = IntersectPath(Pl_{ecl}, Pl_{orb})
P_T: (B4 * 365.25)
u_S: x(I_S)
v'_S = Mod(((2 * atand((sqrt((1 + e_S) / (1 - e_S)) * tan((u'_S * ° / 2))))) * 180 / π), 360)
l0_T: 100 + 34 / 60 + 34.9367 / 3600
l_T = Mod(l0_T + (360 / P_T * tps), 360)
l0_S: 165 + 56 / 60 + 8.3875 / 3600
S': (x(S), y(S))
an0: 2001
jours: {M1, M2, M3, M4, M5, M6, M7, M8, M9, M10, M11, M12, M13, M14, M15, M16, M17, M18, M19, M20, M21, M22, M23, M24, M25, M26, M27, M28, M29, M30, M31, M32, M33, M34, M35, M36, M37, M38, M39, M40, M41, M42, M43, M44, M45, M46, M47, M48, M49, M50, M51, M52, M53, M54, M55, M56, M57, M58, M59, M60, M61, M62, M63, M64, M65, M66, M67, M68, M69, M70, M71, M72, M73, M74, M75, M76, M77, M78, M79, M80, M81, M82, M83, M84, M85, M86, M87, M88, M89, M90, M91, M92, M93, M94, M95, M96, M97, M98, M99, M100, M101, M102, M103, M104, M105, M106, M107, M108, M109, M110, M111, M112, M113, M114, M115, M116, M117, M118, M119, M120, M121, M122, M123, M124, M125, M126, M127, M128, M129, M130, M131, M132, M133, M134, M135, M136, M137, M138, M139, M140, M141, M142, M143, M144, M145, M146, M147, M148, M149, M150, M151, M152, M153, M154, M155, M156, M157, M158, M159, M160, M161, M162, M163, M164, M165, M166, M167, M168, M169, M170, M171, M172, M173, M174, M175, M176, M177, M178, M179, M180, M181, M182, M183, M184, M185, M186, M187, M188, M189, M190, M191, M192, M193, M194, M195, M196, M197, M198, M199, M200, M201, M202, M203, M204, M205, M206, M207, M208, M209, M210, M211, M212, M213, M214, M215, M216, M217, M218, M219, M220, M221, M222, M223, M224, M225, M226, M227, M228, M229, M230, M231, M232, M233, M234, M235, M236, M237, M238, M239, M240, M241, M242, M243, M244, M245, M246, M247, M248, M249, M250, M251, M252, M253, M254, M255, M256, M257, M258, M259, M260, M261, M262, M263, M264, M265, M266, M267, M268, M269, M270, M271, M272, M273, M274, M275, M276, M277, M278, M279, M280, M281, M282, M283, M284, M285, M286, M287, M288, M289, M290, M291, M292, M293, M294, M295, M296, M297, M298, M299, M300, M301, M302, M303, M304, M305, M306, M307, M308, M309, M310, M311, M312, M313, M314, M315, M316, M317, M318, M319, M320, M321, M322, M323, M324, M325, M326, M327, M328, M329, M330, M331, M332, M333, M334, M335, M336, M337, M338, M339, M340, M341, M342, M343, M344, M345, M346, M347, M348, M349, M350, M351, M352, M353, M354, M355, M356, M357, M358, M359, M360, M361, M362, M363, M364, M365, M366}
jj: floor(tps) + 1
jlast = If(Mod[floor(jj), 1461] ≟ 0, 1, 0)
jan4: Mod[jj, 1461] + (jlast * 1461)
j31dec = If(jan4 ≟ 0 ∧ tps > 0 ∨ jan4 ≟ 365 ∨ jan4 ≟ 730 ∨ jan4 ≟ 1095 ∨ jan4 ≟ 1460 ∨ jan4 ≟ 1461, 1, 0)
jan: jan4 - (365 * floor(jan4 / (365 + j31dec)))
mm = Mod((jjh * 60), 60)
nban1: floor(abs(jan4 - 1 + jlast) / 365)
nban4: (floor((jj - 1) / 1461) * 4) - jlast
nbans: nban1 + nban4
hh: floor(jjh)
ua: 149597870700
a_T: C26 + If[fevol, (tscl * C27), 0]
T_c: (a_T; l_T°)
corb_T = Circle((0, 0), a_T)
e_T: D26 + If[fevol, (tscl * D27), 0]
f2_T(x) = (e_T * sin(x))
f1_T(x) = x - M_T
I_T = Intersect(f1_T, f2_T, (6.243450673576878, -6.638398859690753E-4))
u_T: x(I_T)
u'_T: (x(I_T) * 180 / π)
v_T: (2 * atand((sqrt((1 + e_T) / (1 - e_T)) * tan((u'_T * ° / 2)))))
v'_T = Mod(((2 * atand((sqrt((1 + e_T) / (1 - e_T)) * tan((u'_T * ° / 2))))) * 180 / π), 360)
r_T: (a_T * (1 - e_T^(2)) / (1 + (e_T * cos(v_T))))
T = Rotate((r_T; v_T), ω_T°, zAxis)
c_T: (a_T * e_T)
corb2_T = Rotate(Ellipse[H, ((-2 * c_T), 0), a_T, xOyPlane], ω_T°, zAxis)
Pellipse1: {(a_S - c_S, 0), ((-c_S), b_S), ((-c_S) - a_S, 0), ((-c_S), (-b_S))}
Pellipse = Rotate(Rotate[Rotate[Pellipse1, i_S°, xAxis], Ω_S°, zAxis], ω_S°, Line[H, v1orb])
A = Element(Pellipse, 1)
A': (x(A), y(A))
B = Element(Pellipse, 2)
B': (x(B), y(B))
C = Element(Pellipse, 3)
C': (x(C), y(C))
D = Element(Pellipse, 4)
D': (x(D), y(D))
v'axe = UnitVector(Line[C', A'])
F'_2: ((-2 * c_S) * v'axe)
F_2: ((-2 * c_S), 0)
a'_S: Distance[A', C'] / 2
cproj = Ellipse(H, F'_2, a'_S, xOyPlane)
lgTS' = Ray(T, S')
faxeTS = false
fplaneclp = true
fplanequat = false
fplanorb = true
lgTS = Ray(T, S)
fsat = false
v1axeT = Vector((1; 90°; (90 - 23.45)°))
fdtps = false
inct = If(fdtps, 0.01, 0.1)
fbis = If(jan4 > 1095, true, false)
ljours = If(fbis, Insert["29/02", jours, 60], jours)
axeP_T = Segment(T + v1axeT / 3, T - v1axeT / 3)
axeP_S = Segment(S + (v1rot * 0.75), S - (v1rot * 0.75))
fsyssat = false
N, N' = Intersect(lgnds, cproj)
E26: -1.531E-5
H26: 0
E27: -0.01294668
H27: 0
texte2: "Date : " + (Element[ljours, jan]) + "/" + (nbans + an0) + "   " + (If[hh < 10, "0", ""]) + "" + hh + ":" + (If[mm < 10, "0", ""]) + "" + mm + "
No jours : " + (floor(jj)) + ""
texte6 = Text("γ point vernal", (12, 0, 0.2))
texte4: "                                                                           
   - Terre Soleil              :  " + (Distance[T, H]) + " ua
   - Saturne Soleil          :  " + (Distance[H, S]) + " ua
                                                                         "
texte3: "Distances                                                          
   - Terre plan anneaux : " + ((Distance[T, Pl_{equ}] * ua / 1000)) + " km
   - Soleil plan anneaux : " + ((Distance[H, Pl_{equ}] * ua / 1000)) + " km"
texte1: "Saturne                                                              
   - long. hélioc. :  " + (Mod[(atan2(y(S),x(S)) * 180 / π), 360]) + "°
   - lat. hélioc.     : " + ((atan(z(S) / sqrt(x(S)^(2) + y(S)^(2))) * 180 / π)) + "°
                              " + (If[z(S) ≥ 0, "au-dessus", "au-dessous"]) + " de l'écliptique
Terre
   - long; hélioc. : " + (Mod[(atan2(y(T),x(T)) * 180 / π), 360]) + "°"
canneau = Sequence(Circle[S, i, v1rot], i, 0.6, 1.1, 0.12)
lgHS = Ray(H, S)
v1sol = Vector((1; 345.76° + (1.397° * tscl); 82.75°))
axeP_H = Segment(H + v1sol, H - v1sol)