c9_kepler.py

Created by anaali
Created on February 10, 2024
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T**2/a**3=4pi**2/G.M=constante
FA/B= (G*mA*mB)/d**2
v=2pir/T
1ere loi: repere heliocentrique
orbite ellpse, soleil foyer
2eme loi: segemnt reliant soleil
à la planete balaie des aires égale
pendant des aires égales


F=(G*mT*ms)/r**2 * n
2nd loi newton:
ms*a=F
ms*a=(G*mT*ms)/r**2 *n
a==(G*mT)/r**2 *n
repere de frenet (constant, aps de t) 
aT=dv/dt=0
an=V**2/r 
mais an=(G*mT)/r**2 *n
d'ou 
V**2/r = G*mT)/r**2
V**2=(G*mT)/r
v= sqrt( (G*mT)/r)
donc T=2pir / V
= 2pir/ sqrt( (G*mT)/r)
= 2 pir * sqrt(r/ G*mT)
= 2 pi * sqrt(r**3/ G*mT)

T**2 = 4pi**2*r**3 / G*mT
T**2/r**3 =4pi**2 / G*mT

r**3/T**2= G*mT/ 4pi**2