Question

The time period of a satellite revolving in a circular orbit of radius $R$ is $T.$ Time period of another satellite revolving in the circular orbit of radius $4R$ is

• A. $4T$
• B. $\frac{T}{4}$
• C. $8T$
• D. $\frac{T}{8}$

Answer 1

Answer: (C)

$8T$

Answer is C.

According to Kepler's third law, the square of the time period of revolution of a planet around the Sun, is directly proportional to the cube of the semi major axis of the orbit. (radius of the orbit when the orbit can be assumed to be circular.) Thus, $T^2\propto R^3$.
where T = time period of revolution of the planet and R = radius of its orbit.
In this case, the new radius is 4R. So the new time period is 8T.
Hence, the time period of the satellite with the orbit of radius 4R is 8T.