Question

Two satellites of mass $M_A$ and $M_B$ are revolving around a planet of mass $M$ in radius $R_A$ and $R_B$ respectively. Then

• A. $T_A>T_B$ if $R_A>R_B$
• B. $T_A>T_B$ if $M_A>M_B$
• C. $T_A=T_B$ if $M_A>M_B$
• D. $T_A>T_B$ if $R_A<R_B$

Answer 1

The correct option is A

$T_A>T_B$ if $R_A>R_B$

Correct Option:

Option A

1. Kepler's third law of Planetary motion: According to this law, “The square of the orbital time period of a planet is directly proportional to the cube of the semi-minor axis of the orbit.” Mathematically it can be expressed as, $T^2\propto R^3$.
2. So, from this law the relation between time periods and radii of the satellite is ${\left(\frac{T_A}{T_B}\right)}^2={\left(\frac{R_A}{R_B}\right)}^3$. Thus, if $R_A>R_B$ then $T_A>T_B$. So, this option is correct.

Kepler's third law of Planetary motion

Incorrect Option:

Option B

The time period of the orbit of a satellite does not depend upon its mass. So, this option is incorrect.

Option C

The time period of the orbit of a satellite does not depend upon its mass. So, this option is incorrect.

Option D

The time period of the orbit of a satellite increases with the increase in radius. So, this option is incorrect.

Hence, option A is correct.