orbite_lune
Author: PhM

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

P (ans)

a

e

i

L2000.0

Mercury

Venus

Terre+Lune

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

P (ans)

a

e

i

L2000.0

Ω

ω

Ω

ω

année

Terre+Lune

Mercury

Venus

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

P (ans)

P (ans)

a

e

i

L2000.0

Ω

ω

Mouvements et libration de la Lune

PhM - janvier 2018

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P(jours)

Construction

Lune

a

e

i

i equat

rév. synodique

rév. sidérale

rév. tropique

rév. anomalistique

rév. draconitique

rot. périgée

rot. noeuds

km

j

j

j

j

j

ans

ans

rot périgée

directe

rétrograde

Diam.

km

Masse

Volume

km3

Dens. moy.

Albédo  géométrique

Libration

Vitesses

Options de visualisation

Orbite circulaire

Caractéristiques de l'ellipse

 Vitesses des curseurs                    
 - Touche SHIFT appuyée :  0.1 x
 - Touche CTRL appuyée :   10 x
 - Touche Alt appuyée      : 100 x

________________________________________________________________________















________________________________________________________________________
 

Rter: 6378.137
M_T = 5.967479674796748E24 (slider from -5 to 9.999999999999999E24, step 1)
G: (6.67428 * 10^(-11))
B46: 0.0549
D4: 0.01671123
c1: ((100 * B46) - 1) / 90
c2: B46 - c1
g_e = 0 (slider from 0 to 9.9, step 0.1)
e: (c1 * g_e) + (c2 * g_e^(2))
f2(x) = (e * sin(x))
tps = 0 (slider from 0 to 365, step 0.1)
P_L: 27.3216609
t_{peri}: (21 + 55 / 60) / 24
M: (360 / P_L * (tps - t_{peri}))
f1(x) = x - Mod[M, 360]°
I = Intersect(f1, f2, (6.073177213713667, 0))
u: (x(I) * 180 / π)
v: ((2 * atan((sqrt((1 + e) / (1 - e)) * tan((u / 2)°)))) * 180 / π)
a: 60.2666
r: (a * (1 - e^(2)) / (1 + (e * cos(v°))))
R_T: 1
ua: 149597870700
c: (a * e)
F': ((-2 * c), 0)
L: (r; v°)
M_S: (2 * 10^(30))
T = (0, 0)
ell_T = Ellipse(T, F', a)
dtan, g = Tangent(L, ell_T)
vit_L: sqrt(((G * M_T) * (2 / (((r * Rter) * 1000)) - 1 / (((a * Rter) * 1000))))) / 1000
V1tan = UnitVector(dtan)
L_V = Translate(L, Vector[((-50 * vit_L) * V1tan)])
y_L: (r * sin(v°))
grd: 15
R_L: (0.2725 * R_T)
C4: 1.00000261
tpera: 4 + (14 + 17 / 60 + 49 / 3600) / 24
B36: 365.2563631
l_{2018}: 84.7996187
C2: 0.38709927
D2: 0.20563593
E2: 7.00497902
F2: 252.250324
G2: 77.4577963
H2: 48.3307659
C3: 0.72333566
D3: 0.00677672
E3: 3.39467605
F3: 181.9791
G3: 131.602467
H3: 76.6798426
E4: -1.531E-5
F4: 100.464572
G4: 102.937682
H4: 0
C5: 1.52371034
D5: 0.0933941
E5: 1.84969142
F5: -4.55343205
G5: -23.9436296
H5: 49.5595389
C6: 5.202887
D6: 0.04838624
E6: 1.30439695
F6: 34.3964405
G6: 14.7284798
H6: 100.473909
C7: 9.53667594
D7: 0.05386179
E7: 2.48599187
F7: 49.9542442
G7: 92.5988783
H7: 113.662424
C8: 19.1891646
D8: 0.04725744
E8: 0.77263783
F8: 313.238105
G8: 170.954276
H8: 74.016925
C9: 30.0699228
D9: 0.00859048
E9: 1.77004347
F9: -55.1200297
G9: 44.9647623
H9: 131.784226
C10: 39.4821168
D10: 0.2488273
E10: 17.1400121
F10: 238.929038
G10: 224.068916
H10: 110.303937
B2: 0.2408467
B3: 0.615197260000001
B4: 1.0000174
B5: 1.8808476
B6: 11.862615
B7: 29.447498
B8: 84.0168460000002
B9: 164.79132
B10: 247.92065
B13: 87.969256
B15: 224.6997056
B17: 365.2563631
B19: 686.979852
B21: 4332.589
B23: 10759.23
B25: 30685.4
B27: 60266
B29: 90588
C13: 0.240842501
D13: 0.38709843
E13: 0.20563661
F13: 7.00559432
G13: 252.25166724
H13: 77.45771895
I13: 48.33961819
D14: 0
E14: 2.123E-5
F14: -0.00590158
G14: 149472.67486623
H14: 0.15940013
I14: -0.12214182
C15: 0.6151835487
D15: 0.72332102
E15: 0.00676399
F15: 3.39777545
G15: 181.9797085
H15: 131.76755713
I15: 76.67261496
D16: -2.6E-7
E16: -5.107E-5
F16: 4.3494E-4
G16: 58517.8156026
H16: 0.05679648
I16: -0.27274174
C17: 1
D17: 1.00000018
E17: 0.01673163
F17: -5.4346E-4
G17: 100.46691572
H17: 102.93005885
I17: -5.11260389
D18: -3.0E-8
E18: -3.661E-5
F18: -0.01337178
G18: 35999.37306329
H18: 0.3179526
I18: -0.24123856
C19: 1.8808155627
D19: 1.52371243
E19: 0.09336511
F19: 1.85181869
G19: -4.56813164
H19: -23.91744784
I19: 49.71320984
D20: 9.7E-7
E20: 9.149E-5
F20: -0.00724757
G20: 19140.29934243
H20: 0.45223625
I20: -0.26852431
C21: 11.861775559
D21: 5.20248019
E21: 0.0485359
F21: 1.29861416
G21: 34.33479152
H21: 14.27495244
I21: 100.29282654
D22: -2.864E-5
E22: 1.8026E-4
F22: -0.00322699
G22: 3034.90371757
H22: 0.18199196
I22: 0.13024619
C23: 29.4566531576
D23: 9.54149883
E23: 0.05550825
F23: 2.49424102
G23: 50.07571329
H23: 92.86136063
I23: 113.63998702
D24: -3.065E-5
E24: -3.2044E-4
F24: 0.00451969
G24: 1222.11494724
H24: 0.54179478
I24: -0.25015002
C25: 84.010582988
D25: 19.18797948
E25: 0.0468574
F25: 0.77298127
G25: 314.20276625
H25: 172.43404441
I25: 73.96250215
D26: -2.0455E-4
E26: -1.55E-5
F26: -0.00180155
G26: 428.49512595
H26: 0.09266985
I26: 0.05739699
C27: 164.9964411204
D27: 30.06952752
E27: 0.00895439
F27: 1.7700552
G27: 304.22289287
H27: 46.68158724
I27: 131.78635853
D28: 6.447E-5
E28: 8.18E-6
F28: 2.24E-4
G28: 218.46515314
H28: 0.01009938
I28: -0.00606302
D29: 39.48686035
E29: 0.24885238
F29: 17.1410426
G29: 238.96535011
H29: 224.09702598
I29: 110.30167986
D30: 0.00449751
E30: 6.016E-5
F30: 5.01E-6
G30: 145.18042903
H30: -0.00968827
I30: -0.00809981
B32: 2017
C36: 1
D36: D17 + (($B$32 - 2000) / 100 * D18)
E36: E17 + (($B$32 - 2000) / 100 * E18)
D37: D19 + (($B$32 - 2000) / 100 * D20)
E37: E19 + (($B$32 - 2000) / 100 * E20)
D34: D13 + (($B$32 - 2000) / 100 * D14)
E34: E13 + (($B$32 - 2000) / 100 * E14)
D35: D15 + (($B$32 - 2000) / 100 * D16)
E35: E15 + (($B$32 - 2000) / 100 * E16)
D38: D21 + (($B$32 - 2000) / 100 * D22)
E38: E21 + (($B$32 - 2000) / 100 * E22)
D39: D23 + (($B$32 - 2000) / 100 * D24)
E39: E23 + (($B$32 - 2000) / 100 * E24)
D40: D25 + (($B$32 - 2000) / 100 * D26)
E40: E25 + (($B$32 - 2000) / 100 * E26)
D41: D27 + (($B$32 - 2000) / 100 * D28)
E41: E27 + (($B$32 - 2000) / 100 * E28)
D42: D29 + (($B$32 - 2000) / 100 * D30)
E42: E29 + (($B$32 - 2000) / 100 * E30)
B34: 87.9692560000002
C34: 0.240842501
B35: 224.6997056
C35: 0.615183548700002
C37: 1.8808155627
B38: 4332.589
C38: 11.861775559
B39: 10759.23
C39: 29.4566531576
B40: 30685.4
C40: 84.0105829880005
B41: 60266
C41: 164.9964411204
B42: 90588
F34: F13 + (($B$32 - 2000) / 100 * F14)
G34: G13 + (($B$32 - 2000) / 100 * G14)
H34: H13 + (($B$32 - 2000) / 100 * H14)
I34: I13 + (($B$32 - 2000) / 100 * I14)
F36: F17 + (($B$32 - 2000) / 100 * F18)
F37: F19 + (($B$32 - 2000) / 100 * F20)
F35: F15 + (($B$32 - 2000) / 100 * F16)
F38: F21 + (($B$32 - 2000) / 100 * F22)
F39: F23 + (($B$32 - 2000) / 100 * F24)
F40: F25 + (($B$32 - 2000) / 100 * F26)
F41: F27 + (($B$32 - 2000) / 100 * F28)
F42: F29 + (($B$32 - 2000) / 100 * F30)
G36: G17 + (($B$32 - 2000) / 100 * G18)
G37: G19 + (($B$32 - 2000) / 100 * G20)
G35: G15 + (($B$32 - 2000) / 100 * G16)
G38: G21 + (($B$32 - 2000) / 100 * G22)
G39: G23 + (($B$32 - 2000) / 100 * G24)
G40: G25 + (($B$32 - 2000) / 100 * G26)
G41: G27 + (($B$32 - 2000) / 100 * G28)
G42: G29 + (($B$32 - 2000) / 100 * G30)
H36: H17 + (($B$32 - 2000) / 100 * H18)
H37: H19 + (($B$32 - 2000) / 100 * H20)
H35: H15 + (($B$32 - 2000) / 100 * H16)
H38: H21 + (($B$32 - 2000) / 100 * H22)
H39: H23 + (($B$32 - 2000) / 100 * H24)
H40: H25 + (($B$32 - 2000) / 100 * H26)
H41: H27 + (($B$32 - 2000) / 100 * H28)
H42: H29 + (($B$32 - 2000) / 100 * H30)
I36: I17 + (($B$32 - 2000) / 100 * I18)
I37: I19 + (($B$32 - 2000) / 100 * I20)
I35: I15 + (($B$32 - 2000) / 100 * I16)
I38: I21 + (($B$32 - 2000) / 100 * I22)
I39: I23 + (($B$32 - 2000) / 100 * I24)
I40: I25 + (($B$32 - 2000) / 100 * I26)
I41: I27 + (($B$32 - 2000) / 100 * I28)
I42: I29 + (($B$32 - 2000) / 100 * I30)
C29: B29 / B17
B30 = NaN
C42: B42 / B36
C1_1: 0.983289358
C2_1: 0.983284449
C3_1: 0.983286218
hms: (Mod[tps, 1] * 24)
C1_2: 0.983289358
C2_2: 0.983284449
C3_2: 0.983286218
lperi: 104 + 11 / 60 + 27.6 / 3600
calend: {Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, Z11, Z12, Z13, Z14, Z15, Z16, Z17, Z18, Z19, Z20, Z21, Z22, Z23, Z24, Z25, Z26, Z27, Z28, Z29, Z30, Z31, Z32, Z33, Z34, Z35, Z36, Z37, Z38, Z39, Z40, Z41, Z42, Z43, Z44, Z45, Z46, Z47, Z48, Z49, Z50, Z51, Z52, Z53, Z54, Z55, Z56, Z57, Z58, Z59, Z60, Z61, Z62, Z63, Z64, Z65, Z66, Z67, Z68, Z69, Z70, Z71, Z72, Z73, Z74, Z75, Z76, Z77, Z78, Z79, Z80, Z81, Z82, Z83, Z84, Z85, Z86, Z87, Z88, Z89, Z90, Z91, Z92, Z93, Z94, Z95, Z96, Z97, Z98, Z99, Z100, Z101, Z102, Z103, Z104, Z105, Z106, Z107, Z108, Z109, Z110, Z111, Z112, Z113, Z114, Z115, Z116, Z117, Z118, Z119, Z120, Z121, Z122, Z123, Z124, Z125, Z126, Z127, Z128, Z129, Z130, Z131, Z132, Z133, Z134, Z135, Z136, Z137, Z138, Z139, Z140, Z141, Z142, Z143, Z144, Z145, Z146, Z147, Z148, Z149, Z150, Z151, Z152, Z153, Z154, Z155, Z156, Z157, Z158, Z159, Z160, Z161, Z162, Z163, Z164, Z165, Z166, Z167, Z168, Z169, Z170, Z171, Z172, Z173, Z174, Z175, Z176, Z177, Z178, Z179, Z180, Z181, Z182, Z183, Z184, Z185, Z186, Z187, Z188, Z189, Z190, Z191, Z192, Z193, Z194, Z195, Z196, Z197, Z198, Z199, Z200, Z201, Z202, Z203, Z204, Z205, Z206, Z207, Z208, Z209, Z210, Z211, Z212, Z213, Z214, Z215, Z216, Z217, Z218, Z219, Z220, Z221, Z222, Z223, Z224, Z225, Z226, Z227, Z228, Z229, Z230, Z231, Z232, Z233, Z234, Z235, Z236, Z237, Z238, Z239, Z240, Z241, Z242, Z243, Z244, Z245, Z246, Z247, Z248, Z249, Z250, Z251, Z252, Z253, Z254, Z255, Z256, Z257, Z258, Z259, Z260, Z261, Z262, Z263, Z264, Z265, Z266, Z267, Z268, Z269, Z270, Z271, Z272, Z273, Z274, Z275, Z276, Z277, Z278, Z279, Z280, Z281, Z282, Z283, Z284, Z285, Z286, Z287, Z288, Z289, Z290, Z291, Z292, Z293, Z294, Z295, Z296, Z297, Z298, Z299, Z300, Z301, Z302, Z303, Z304, Z305, Z306, Z307, Z308, Z309, Z310, Z311, Z312, Z313, Z314, Z315, Z316, Z317, Z318, Z319, Z320, Z321, Z322, Z323, Z324, Z325, Z326, Z327, Z328, Z329, Z330, Z331, Z332, Z333, Z334, Z335, Z336, Z337, Z338, Z339, Z340, Z341, Z342, Z343, Z344, Z345, Z346, Z347, Z348, Z349, Z350, Z351, Z352, Z353, Z354, Z355, Z356, Z357, Z358, Z359, Z360, Z361, Z362, Z363, Z364, Z365, Z366}
fconstruct = false
sgT = Segment(T, L)
A: (a - c, 0)
p: ((a * (1 - e^(2))) * 6382)
x_L: (r * cos(v°)) + c
V_L = Vector(L, L_V)
O: ((-c), 0)
vmax: sqrt(((G * M_S) * (1 + e) / (1 - e) / a / ua)) / 1000
vit: (sqrt(((G * M_S) * p)) / p * (1 + e) / 1000)
L' = Intersect(Line[T, L], OrthogonalLine[L_V, sgT])
Vr = Vector(L, L')
Vamp_r: (Length[Vr] * 100)
L_u: (a; u°) + ((-c), 0)
sSTu = Segment(L_u, T)
sTu = Segment(L_u, (x(L_u), 0))
l_{peri}: 98.7687944
long_L: v + l_{peri}
M_L: (73.4 * 10^(21))
V_M = Translate(Vector[(15 * (cos((M + 180)°), sin((M + 180)°)))], L)
ang = Angle(V_M, Vector[L, T])
dp = OrthogonalLine(L, V_M, xOyPlane)
cc_L = Circle(L, (grd * R_L))
N_1, N_2 = Intersect(dp, cc_L)
sddiam_L = Segment(N_1, N_2)
J = Intersect(cc_L, Ray[L, Vector[T, L]])
f = CircumcircleSector(N_1, J, N_2)
B45: 384400
B47: 5.1453
B48: 1.5424
B49: 29.5305881
B50: 27.3216609
B51: 27.3215816
B52: 27.5545502
B53: 27.2122178
C47: °
C48: °
B55: 18.61
B54: 8.85
B56: 3476
B59: 3.341
B60: 0.12
B57: (73.4 * 10^(21))
B58: (22 * 10^(9))
vang_N: -360 / ((B55 * 365.25))
pos0_N: 154.4028
lg_N = Line(T, (1; (((tps - 1) * vang_N) + pos0_N)°))
texte6: " Excentricité " + e + " (Lune g_e= 1)"
c_M = Circle(O, a)
cc_T = Circle(T, (grd * R_T / 2))
tvis = OrthogonalLine(L, Line[T, L])
texte9: "" + (Element[calend, floor(tps + 1)]) + "/2018"
hmin = Mod(floor((hms * 60)), 60)
hsec: floor(Mod[floor((hms * 3600)), 60] + 0.5)
flibration = false
fvitesses = false
dpT = OrthogonalLine(L, sgT)
fcirc = false
texte5: "angle : " + (If[y_L > 0, (ang * 180 / π), (((2 * π) - ang) * 180 / π)]) + "°"
felements = true
texte10: "a = " + ((a * Rter)) + " km
b = " + ((sqrt(a^(2) - c^(2)) * Rter)) + " km
c = " + ((c * Rter)) + " km"
texte11: "e = " + e + ""
L_C: (a; ((360 / P_L * (tps - t_{peri})))°) + O
texte12: "v tang : " + vit_L + " km/s   v rad. : " + (((vit_L * V1tan) * UnitVector[Line[T, L]])) + " km/s"
A': ((-a) - c, 0)
texte3: " Position de la Lune :                               
 - distance : " + r + " R_T (" + ((6363 * r)) + " km)
 - long.       : " + (Mod[v, 360]) + "°"
texte1: " " + (floor(hms)) + "h" + (If[hmin < 10, "0", ""]) + "" + (floor(hmin)) + "min"
texte13: "Excentricité : " + e + "  (Lune : g_e = 1)"