The time period of the satellite of the earth is 5 hr. If the separation between earth and satellite is increased to 3 times the previous value, then what will be the new time period of satellite.

Explanation

To solve the problem, we will use Kepler's Third Law of planetary motion, which relates the time period of a satellite to its distance from the center of the Earth. The law states that the square of the time period (T) of a satellite is directly proportional to the cube of the semi-major axis (R) of its orbit:

\[ T^2 \propto R^3 \]

This can be expressed as:

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