Question

two satellite X and Y are moving in a circular orbit of radii r and 2r respectively around the same planet what is the ratio of critical velocities

Answer 1

let mass of planet is M , mass of satellite x is Mx and mass of satellite y is My

now, for satellite X
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Fg = GMMx/r² = MxVx²/r
GM/r = Vx² ---------(1)

for satellite Y
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Fg = GMMy/(2r)² = MyVy²/(2r)
GM/2r = Vy ² ----------(2)

divide equation (1) and (2)

2/1 = Vx²/Vy²

take square root both sides

√2/1 = Vx/Vy

Vx/Vy =√2 /1

Answer 2

Answer will b Vx/Vy =√2 /1

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