Question

Two satellites of mass $m$ and $9\,m$ are orbiting a planet in orbits of radius $R$. Their periods of revolution will be in the ratio of

• A. 9:01
• B. 3:01
• C. 1:01
• D. 1:03

Answer 1

The Correct Option is C

The Correct Option is (C): 1:1

Answer 2

Kepler’s third law states that the square of the period of revolution is proportional to the cube of the semi-major axis of the orbit.

From Kepler’s third law  T²=R³,

where, T = period of revolution for an object around a planet and

R = Radius of the orbit which is the same as the semi-major axis for a circular orbit.

Let the time period for satellite of mass m  = T₁, and for satellite of mass 9m = T₂, Let the radius of a satellite of mass m orbiting the planet = R₁ and satellite of mass 9m orbiting the same planet be R₂

So, for two satellites orbiting the same planet, the ratio of their periods of revolution  (T₁ and T₂) will be:

\(=>\frac{T^2_1}{T_2^2}=\frac{R^2_1}{T_2^3}\)

Given that both planet are orbiting the same planet, therefore R₁=R₂=R  and substituting the value in the above equation we get:

\(=>\frac{T^2_1}{T_2^2}=\frac{R^3}{R^3}=1\)

\(=>\frac{T_1}{T_2}=1\)

So, the ratio of their periods of revolution is 1. This means that the periods of revolution for the two satellites are the same, regardless of their masses.