ph13.py

Created on December 15, 2024

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Démontre V=racine GxM /r

Nous allons utiliser la deuxième loi de newton et la loi de gravitation
universelle 



F=GxMxm/r2



Ensuite comme F=ma et 



a=v2/r car d’après le repère de frenet 



a=dv/dt UT + v2/r UN

Et dv/dt =0 alors a= v2/r



Donc F=mxv2/r 



Par identification   G x  M x m / r2=m x v2 /r



V2=GxM/r

V=racine de GxM/r



Démontrer la 3 eme loi de kepler :

T2/r3=4pi2/GxM



On sait que T=2pi x r/v et V=racine de GxM/r



Donc T= 2pi x r/racine de GxM/r



T=2pi x racine r3/GxM



T2=4 pi 2 x r3/GxM



Donc

T2/r3=4 pi 2/GxM 

V=2 pi x r et T=2 pi x r / V



T2/r3= K 



K= coefficient directeur d’une droite

 yb-ya/xb-xa

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ph13.py