variables orbites
Author: aaa

Géocentrique

Date origine

Date

Année

Mois

Jour

Heures

Minutes

1 ua

P

lg périh

Terre

a

e

long. 0

année périh

mois péri

jour péri

heure péri

min péri

Orbites - construction

Configuration

γ

Trace

Vénus

Carte du ciel

B8 = 1.796589572125403 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Lper_T: B8
B24 = 20
B23 = 15
B22 = 4
B21 = 1
B20 = 2009
jjp_T: 367.0 * B20 - floor(7.0 * (B20 + floor((B21 + 9.0) / 12.0)) / 4.0) - floor(3.0 * floor(floor(B20 + floor((B21 - 9.0) / 7.0)) / 100.0 + 1.0) / 4.0) + floor(275.0 * B21 / 9.0) + B22 + 1721029.0 - 0.5 + B23 / 24.0 + B24 / 24.0 / 60.0
B5 = 0.017
e_T: B5
B4 = 1.49598034E8
B14 = 1
B15 = 1
B16 = 0
B17 = 0
B13 = 2010
jj0: 367.0 * B13 - floor(7.0 * (B13 + floor((B14 + 9.0) / 12.0)) / 4.0) - floor(3.0 * floor(floor(B13 + floor((B14 - 9.0) / 7.0)) / 100.0 + 1.0) / 4.0) + floor(275.0 * B14 / 9.0) + B15 + 1721029.0 - 0.5 + B16 / 24.0 + B17 / 24.0 / 60.0
tps = 0 (slider from 0 to 4000, step 0.01)
jj: jj0 + tps
B1 = 1.4959787E8
a_T: B4 / B1
fgeo = true
B7 = 365.256
per_T: B7
AM_T: (jj - jjp_T) * 360.0 / per_T
u0_T = Mod(3.141592653589793 / 180.0 * AM_T, 6.283185307179586)
u1_T: u0_T + (u0_T + e_T * sin(u0_T) - u0_T) / (1.0 - e_T * cos(u0_T))
u2_T: u1_T + (u0_T + e_T * sin(u1_T) - u1_T) / (1.0 - e_T * cos(u1_T))
u3_T: u2_T + (u0_T + e_T * sin(u2_T) - u2_T) / (1.0 - e_T * cos(u2_T))
u4_T: u3_T + (u0_T + e_T * sin(u3_T) - u3_T) / (1.0 - e_T * cos(u3_T))
u_T: u4_T + (u0_T + e_T * sin(u4_T) - u4_T) / (1.0 - e_T * cos(u4_T))
v_T: 2.0 * atan(tan(u_T / 2.0) * sqrt((1.0 + e_T) / (1.0 - e_T))) * 180.0 * ° / 3.14159
θ_T: v_T + Lper_T
ρ_T: a_T * (1.0 - e_T^(2.0)) / (1.0 + e_T * cos(v_T))
y_T: ρ_T * sin(θ_T)
x_T: ρ_T * cos(θ_T)
y_G = If(fgeo, ρ_T * sin(θ_T), 0.0)
x_G = If(fgeo, ρ_T * cos(θ_T), 0.0)
H: (-1.0 * x_G, -1.0 * y_G)
T: (x_T - x_G, y_T - y_G)
C5 = 0.00677
e_V: C5
C4 = 1.082086E8
a_V: C4 / B1
C8 = 2.2938146773968158 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Lper_V: C8
C7 = 224.701
per_V: C7
C20 = 2009
C22 = 4
C21 = 10
C23 = 4
C24 = 28
jjp_V: 367.0 * C20 - floor(7.0 * (C20 + floor((C21 + 9.0) / 12.0)) / 4.0) - floor(3.0 * floor(floor(C20 + floor((C21 - 9.0) / 7.0)) / 100.0 + 1.0) / 4.0) + floor(275.0 * C21 / 9.0) + C22 + 1721029.0 - 0.5 + C23 / 24.0 + C24 / 24.0 / 60.0
AM_V = Mod((jj - jjp_V) * 360.0 / per_V, 360.0)
u0_V: 3.141592653589793 / 180.0 * AM_V
u1_V: u0_V + (u0_V + e_V * sin(u0_V) - u0_V) / (1.0 - e_V * cos(u0_V))
u2_V: u1_V + (u0_V + e_V * sin(u1_V) - u1_V) / (1.0 - e_V * cos(u1_V))
u3_V: u2_V + (u0_V + e_V * sin(u2_V) - u2_V) / (1.0 - e_V * cos(u2_V))
u4_V: u3_V + (u0_V + e_V * sin(u3_V) - u3_V) / (1.0 - e_V * cos(u3_V))
u_V: u4_V + (u0_V + e_V * sin(u4_V) - u4_V) / (1.0 - e_V * cos(u4_V))
v_V: 2.0 * atan(tan(u_V / 2.0) * sqrt((1.0 + e_V) / (1.0 - e_V))) * 180.0 * ° / 3.14159
θ_V: v_V + Lper_V
ρ_V: a_V * (1.0 - e_V^(2.0)) / (1.0 + e_V * cos(v_V))
y_V: ρ_V * sin(θ_V)
x_V: ρ_V * cos(θ_V)
V: (x_V - x_G, y_V - y_G)
L_{Vhelio} = Angle(Vector[Vector[H, V]])
L_{Vgeo} = Angle(Vector[Vector[T, V]])
L_{Vcal} = If(fgeo, L_{Vgeo}, L_{Vhelio})
ε = 0.4092797095926703 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
δ: asin(sin(ε) * sin(L_{Vcal}))
rh = 3.819718634205488
cosα: cos(L_{Vcal}) / cos(δ)
sinα: cos(ε) * sin(L_{Vcal}) / cos(δ)
α: Mod[Angle[(1.0, 0.0), (0.0, 0.0), (cosα, sinα)], 6.28319] * rh
B19 = 5.388704065532492 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
lg_T: v_T + B8
F2_V = Rotate((-1.0 * 2.0 * a_V * e_V, 0.0), Lper_V, H)
C19 = 4.7858324353086115 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
C_V = Rotate((-1.0 * a_V * e_V, 0.0), Lper_V, H)
lg_V: v_V + C8
pv: C7
alp: floor((floor(jj + 0.5) - 1867216.25) / 36524.25)
a: floor(jj + 0.5) + 1.0 + alp - floor(alp / 4.0)
b: a + 1524.0
c: floor((b - 122.1) / 365.25)
d: floor(365.25 * c)
hr: (jj + 0.5 - floor(jj + 0.5)) * 24.0
ht: floor(hr)
mt: floor((hr - ht) * 60.0)
jjs = Mod(floor(jj - 0.5) + 0.5 + 1.5, 7.0)
texte3: "" + (If[jjs ≟ 0.0, "Dimanche", If[jjs ≟ 1.0, "Lundi", If[jjs ≟ 2.0, "Mardi", If[jjs ≟ 3.0, "Mercredi", If[jjs ≟ 4.0, "Jeudi", If[jjs ≟ 5.0, "Vendredi", "Samedi"]]]]]])
C16: ht
C17: mt
el_V = Ellipse(F2_V, H, a_V)
e: floor((b - d) / 30.6001)
jr: b - d - floor(30.6001 * e) + Mod[jj + 0.5, 1.0]
mr: e - If[e < 13.5, 1.0, 13.0]
yr: c - If[mr > 2.5, 4716.0, 4715.0]
texte1: "Date : " + (floor(jr)) + "/" + mr + "/" + yr + "    " + C16 + "h" + C17 + "min"
C15: floor(jr)
C14: mr
C13: yr
L_{0T}: B19
L_{0V}: C19
F2_T = Rotate((-1.0 * 2.0 * a_T * e_T, 0.0), Lper_T, H)
el_T = Ellipse(F2_T, H, a_T)
IT_1, IT_2 = Intersect(el_T, Line[F2_T, H])
aps_T = Segment(IT_1, IT_2)
IV_1, IV_2 = Intersect(el_V, Line[F2_V, H])
aps_V = Segment(IV_1, IV_2)
bv: a_V * sqrt(1.0 - e_V * e_V)
ca_V = Circle(C_V, a_V)
elong = Angle(Vector[Vector[T, H]], Vector[Vector[T, V]])
forb = false
fconfig = true
tconf, t, h, m = Polygon(H, V, T)
aconf = Angle(H, T, V)
f_{conj} = If(aconf < 0.5 * ° ∨ aconf > 359.5 * °, true, false)
f_{opp} = If(aconf > 179.5 * ° ∧ aconf < 180.5 * °, true, false)
ftrace = true
V': V
H': H
T': T
f_{quade} = If(aconf > 89.5 * ° ∧ aconf < 90.5 * °, true, false)
f_{quado} = If(aconf > 269.5 * ° ∧ aconf < 270.5 * °, true, false)
vtv = Vector(T, V)
vtv2: vtv / Length[vtv] / 2.0
lr_V: L_{Vgeo}
ycarte: 1.5 + 1.146 * tan(δ / 2.0)
texte6: "[" + (If[f_{conj}, "Conjonction", ""]) + (If[f_{opp}, "Opposition", ""]) + (If[f_{quado}, "Quadrature Ouest", ""]) + (If[f_{quade}, "Quadrature Est", "-------------------"]) + "]"
ff(x) = u0_T + e_T * sin(x)
rr = Iteration(ff(x), u0_T, 2.0)
rrd: rr * 180.0 / 3.141592653589793
rrr: rr - 2.0 * 3.141592653589793
m0_T = Mod(AM_T * 3.141592653589793 / 180.0, 6.283185307179586)
xcarte: -(If[α < 12.0, α, α - 24.0]) * 0.15
V_C: (xcarte, ycarte)
C9 = 1.2510506115661337 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
C10 = 0.05924799398575071 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
C11 = 6052
L_{Sgeo} = Angle(Vector[Vector[T, H]])
δ_S: asin(sin(ε) * sin(L_{Sgeo})) * 180.0 * ° / 3.141592653589793
sinsα: cos(ε) * sin(L_{Sgeo}) / cos(δ_S)
cossα: cos(L_{Sgeo}) / cos(δ_S)
α_S: Mod[Angle[(1.0, 0.0), (0.0, 0.0), (cossα, sinsα)], 6.28319] * rh
xscarte: -(If[α_S < 12.0, α_S, α_S - 24.0]) * 0.15
yscarte: 1.5 + 1.146 * tan(δ_S / 2.0)
S_C: (xscarte, yscarte)
d_{TV} = Distance(T, V)
texte7: "Dist T-V : " + d_{TV}
diam_V: 0.1 / d_{TV}
texte2: "Elongation Vénus : " + elong
texte4: "longitude Vénus : " + L_{Vgeo}
β: 90.0 * ° - L_{Vgeo} + lg_V + If[elong < 180.0 * °, 90.0°, 270.0°]
α_T: Mod[Angle[(1.0, 0.0), (0.0, 0.0), (-(cossα), -(sinsα))], 6.28319] * 180.0 / 3.141592653589793 / 15.0
xtcarte: -(If[α_T < 12.0, α_T, α_T - 24.0]) * 0.15
ytcarte: 1.5 + 1.146 * tan(-(δ_S) / 2.0)
T_C: (xtcarte, ytcarte)
v1_{Vgeo} = Vector((0.0, 0.0), (cos(L_{Vgeo}), sin(L_{Vgeo})))
v1_{Sgeo} = Vector((0.0, 0.0), (cos(L_{Sgeo}), sin(L_{Sgeo})))
v1_{Thelio}: -(v1_{Sgeo})
texte8: "Vénus : α=" + α + "  δ=" + (δ * 180.0 / 3.141592653589793)
fcarte = true

Tool: ekep
Input: C5, um0, um1, um2, um3, um4
Output: um

um1: um0 + (um0 + C5 * sin(um0) - um0) / (1.0 - C5 * cos(um0))
um2: um0 + (um1 + C5 * sin(um1) - um1) / (1.0 - C5 * cos(um1))
um3: um0 + (um2 + C5 * sin(um2) - um2) / (1.0 - C5 * cos(um2))
um: um0 + (um4 + C5 * sin(um4) - um4) / (1.0 - C5 * cos(um4))