Rankers Physics
Topic: Gravitation
Subtopic: Planet and Satellite

Two satellites are in the parking orbits around the earth. Mass of one is 10 times that of the other. The ratio of their periods of revolution is :
1
√10
10
100

Solution:

The orbital period of a satellite depends only on the radius of its orbit and the mass of the Earth, not on the mass of the satellite itself. The period \( T \) is given by:

\[
T = 2\pi \sqrt{\frac{r^3}{GM}}
\]

Since the masses of the satellites do not appear in this formula, the periods of the two satellites will be the same if they are in the same orbit, regardless of their masses.

Therefore, the ratio of their periods of revolution is:

\[
\frac{T_1}{T_2} = 1
\]

So, the ratio is 1:1.

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