Orbites des exoplanètes
Author: phm

Excentricité

Masse planète (en masses Terre)

Période (en jours)

Masse étoile (en masses solaires)

Excentricité

Trace

tps = 47.4 (slider from 0 to 500, step 0.1)
M_P = 10890.1 (slider from 0.1 to 33000, step 0.1)
M_E = 1.1 (slider from 0.1 to 20, step 0.1)
e = 0.27 (slider from 0 to 1, step 0.0050)
P = 60.9 (slider from 1 to 400, step 0.1)
M = Mod(tps * 360.0 / P, 360.0)
u_0: 3.141592653589793 / 180.0 * M
u_1: u_0 + (u_0 + e * sin(u_0) - u_0) / (1.0 - e * cos(u_0))
u_2: u_1 + (u_0 + e * sin(u_1) - u_1) / (1.0 - e * cos(u_1))
u_3: u_2 + (u_0 + e * sin(u_2) - u_2) / (1.0 - e * cos(u_2))
u_4: u_3 + (u_0 + e * sin(u_3) - u_3) / (1.0 - e * cos(u_3))
u: u_4 + (u_0 + e * sin(u_4) - u_4) / (1.0 - e * cos(u_4))
v: 2.0 * atan(tan(u / 2.0) * sqrt((1.0 + e) / (1.0 - e))) * 180.0 * ° / 3.14159
a: cbrt((P / 365.25)^(2.0))
a_S: a * M_P / (M_E * 330000.0)
a_P: a - a_S
r(x) = (1.0 - e * e) / (1.0 + e * cos(x)) * a_P
yp(x) = r(x) * sin(x)
xp(x) = r(x) * cos(x)
lvt: sqrt(xp(v)^(2.0) + yp(v)^(2.0))
ρ: a_P * (1.0 - e^(2.0)) / (1.0 + e * cos(v))
v2: e * e / (1.0 - e * e)^(2.0) * sin(v)^(2.0) + 1.0 / ρ^(2.0)
vit: sqrt(v2)
E: (ρ; v)
F2_P: -2.0 * a_P * e
F2_S: 2.0 * a_S * e
el_P = Ellipse((0.0, 0.0), (F2_P, 0.0), a_P)
el_S = Ellipse((0.0, 0.0), (F2_S, 0.0), a_S)
d1 = Line(E, (0.0, 0.0))
S_1, S_2 = Intersect(el_S, d1)
S: S_2
se = Segment(S, E)
el_P2: (1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 x + e * a_P)^(2.0) / a_P^(2.0) + 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 y^(2.0) / (a_P * a_P * (1.0 - e * e)) = 1.0
G = (0, 0)
vp = Vector(E, (x(E) + xp'(v) / lvt * vit / 50.0, y(E) + yp'(v) / lvt * vit / 50.0))
ph: (tps + P / 4.0) / P - floor((tps + P / 4.0) / P)
vx: x(vp)
vy: y(vp)
xpp(x) = xp'(x)
ypp(x) = yp'(x)
PVR: (ph * 0.2 + 0.2, 4.0 * vy)
ρ_E: ρ * M_P / (M_E * 330000.0)
PVR': PVR
b = true
vex: -1.0 * vx * M_P / M_E / 330000.0
vey: -1.0 * vy * M_P / M_E / 330000.0
ve = Vector(S, (x(S) + vex, y(S) + vey))
PVE: (ph * 0.2 + 0.2, 4.0 * vey)
PVE': PVE