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A satellite of mass m is orbiting the earth in a circular orbit at a height 2 R above earth surface where R is the radius of the earth. If it starts losing energy at a constant rate β , then it will fall on the earth surface after the time t = GMm nβR . Assuming that the satellite is approximately in a circular orbit at all times, find the value of n .

Correct answer

3

Step-by-step solution

E i = - GMm 2 3 R , E f = - GMm 2 R ∴   βt = GMm R 1 2 – 1 6 βt = GMm 3 R   ⇒   t = GMm 3 βR

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