Erbites des exoplanètes
Author: phm

Excentricité

Masse planète (en masses Terre)

Période (en jours)

Masse étoile (en masses solaires)

Excentricité

G = 6.672E-11
m_S = 2.0E30
tps = 856.7 (slider from 0 to 5000, step 0.1)
M_E = 6.1 (slider from 0.1 to 20, step 0.1)
e = 0.24 (slider from 0 to 1, step 0.0050)
P_{SYS} = 401 (slider from 1 to 5000, step 1)
M = Mod(tps * 360 / P_{SYS}, 360)
u_0: 3.141592653589793 / 180 * M
u_1: u_0 + (u_0 + e * sin(u_0) - u_0) / (1 - e * cos(u_0))
u_2: u_1 + (u_0 + e * sin(u_1) - u_1) / (1 - e * cos(u_1))
u_3: u_2 + (u_0 + e * sin(u_2) - u_2) / (1 - e * cos(u_2))
u_4: u_3 + (u_0 + e * sin(u_3) - u_3) / (1 - e * cos(u_3))
u: u_4 + (u_0 + e * sin(u_4) - u_4) / (1 - e * cos(u_4))
v: 2 * atan(tan(u / 2) * sqrt((1 + e) / (1 - e))) * 180 * ° / 3.14159
a: cbrt((P_{SYS} / 365.25)^(2)) * 150
p: a * (1 - e * e) * 1000000000
C: sqrt(G * m_S * M_E * p)
M_P = 301 (slider from 1 to 6000, step 1)
a_E: a * M_P / (M_E * 330000)
a_P: a - a_E
F2_P: -2 * a_P * e
F2_E: 2 * a_E * e
el_P = Ellipse((0, 0), (F2_P, 0), a_P)
el_E = Ellipse((0, 0), (F2_E, 0), a_E)
ρ: a_P * (1 - e^(2)) / (1 + e * cos(v))
P: (ρ; v)
d1 = Line(P, (0, 0))
E_1, E_2 = Intersect(el_E, d1)
E: E_2
sp = Segment(E, P)
tgp, b = Tangent(P, el_P)
vit: C / p * sqrt(1 + 2 * e * cos(v) + e * e) / 1000
α = Angle(xAxis, tgp)
P' = Intersect(Line[E, P], OrthogonalLine[(x(P) + vit * cos(α + π), y(P) + vit * sin(α + π)), Line[E, P]])
vit2: C / p * sqrt(1 + 2 * e * cos(v) + e * e)
Vr = Vector(P, P')
Vvit = Vector(P, Translate[P, (vit; α + π)])
texte5: "V = " + vit + " km/s    Vrad = " + (Length[Vr]) + " km/s"
P_V: ((tps - floor(tps / P_{SYS}) * P_{SYS}) / P_{SYS} * 150, vit)
P_{VR}: ((tps - floor(tps / P_{SYS}) * P_{SYS}) / P_{SYS} * 150, Length[Vr] * If[Length[P] > Length[P'], -1, 1])