An areosynchronous satellite orbits Mars (mass = 6.42 x 1023 kg) once every Martian day, 88640 s. At what radius does it orbit?

Answer 1

Let

M = Mass of Mars

m = Mass of Satellite

G = Gravitational Constant

r = distance between center of Mars and Satellite

So

Gravitational force = F = G Mm/r²

this provides centripetal force to satellite

F= mv²/r

Equating

GM/r² = v² /r

v² = GM/r

v = √(GM/r)

Velocity = Distance / Time = 2pi r/T

2pi r/T = √(GM/r)

T = 2 pi (r³ /GM) ^1/2

Plug in

Given values to get r