Gravitation Question 351
Question: A satellite of mass m is orbiting the earth in a circular orbit of radius R. It starts losing energy due to small air resistance at the rate of C J/s. Find the time taken for the satellite to reach the earth.
Options:
A) $ [\frac{GMm}{C}\left[ \frac{1}{R}-\frac{1}{r} \right]] $
B) $ [\frac{GMm}{2C}\left[ \frac{1}{R}+\frac{1}{r} \right]] $
C) $ [\frac{GMm}{2C}\left[ \frac{1}{R}-\frac{1}{r} \right]] $
D) $ [\frac{2GMm}{C}\left[ \frac{1}{R}+\frac{1}{r} \right]] $
Show Answer
Answer:
Correct Answer: C
Solution:
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$ [E=-\frac{GMm}{2r}] $ $ [-\frac{dE}{dt}=\frac{GMm}{2r}\frac{1}{r^{2}}\frac{dr}{dt}] $
$ [\int\limits_{0}^{t}{dt=-\frac{GMm}{2C}\int\limits_{r}^{R}{\frac{dr}{r^{2}};t=\frac{GMm}{2C}\left[ \frac{1}{R}-\frac{1}{r} \right]}}] $
