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Satellite - Terre
Loi universelle de la gravitation
Satellite - Terre
1) Voir figure:
2) La loi de gravitation permet d'ecrire:
ms x go = (poids) = (force d'attraction) = G x ms x MT/RT2
D'où :
go = G x MT/RT2
3)
FT/S = G x mS x mT / h2
= G x mS x mT / (RT + 2RT)2
= G x mS x mT / 9 RT2
= (mS/9) x G x mT / RT2
= (mS/9) x go = Po/9
FT/S mS go/9 = Po/9
= 1000 N/9 = 111.11 N
4)Po/2 = G x mS x mT / (h' + RT)2
mS x go/2 = G x mS x mT / (h' + RT)2
go/2 = G x mT / (h' + RT)2
D'où :
(h' + RT)2 = 2 x G x mT / go
(h' + RT)2 = 2 x G x mT x RT2/ G x MT
(h' + RT)2 = 2 x RT2
D'où :
h' + RT = √2 x RT
h' = (√2 - 1 ) x RT = 2643 km,
(arrondi à l'unité)
5)
D'après la loi de la gravitation:
G mS x mA/(dA + RA)2 = G mS x mB/[D - (dA + RA) + RB]2
D'où:
mA/(dA + RA)2 = mB/[D - (dA + RA) + RB]2
mA x [D - (dA + RA) + RB]2 = mB x (dA + RA)2
D - (dA + RA) + RB = (mB/mA)1/2 x (dA + RA)
On applique:
RB = 500 km,
MA = 4 MB ,
RA = 2 RB,
dA = 3 RB,
D - (3 RB + 2 RB) + RB = (1/4)1/2 x (3RB + 2RB)
D - 4 RB = 5RB/2
D = 4 RB + 5 RB/2 = 13 RB/2 = 6.5 RB
6)
D = 6.5 x 500 km
D = 3250 km
-- Abdurrazzak Ajaja
octobre 2022
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