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

The ratio of their critical velocities are √2 : 1

Hope it helps....................

Answer 2

let mass of planet is M , mass of satellite x is Mx and mass of satalite y is My
for satellite x .
here gravitational force is balanced by centrifugal force .
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Fg = GMMx/r² =MxVx²/r

Vx² = GM/r -------(1)

for satellite y
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Fg =GMMy² /(4r)² =MVy²/(2r)

Vy² = GM/2r ---------(2)

divide equation (1) and (2)

Vx²/Vy² = 2/1

Vx /Vy = √2/1