Question

EARTH SATELLITE
The time period T of the moon of planet mars (mass $M_m$) is related to its orbital radius R as (G= Gravitational constant)

• A. $T^2=\frac{4{\pi }^2{R}^3}{G{M}_m}$
• B. $T^2=\frac{4{\pi }^{2}G{R}^3}{M_m}$
• C. $T^2=\frac{2\pi R^{3}G}{M_m}$
• D. $T^2=4\pi M_{m}G{R}^3$

Answer 1

The correct option is A $T^2=\frac{4{\pi }^2{R}^3}{G{M}_m}$

Time period $T=\frac{2\pi }{V_0}$

$T=\frac{2\pi R}{\sqrt{{GM}_m}}(=V_0=\sqrt{\frac{GM}{R}})$

$T^2=\frac{4{\pi }^2{R}^3}{{GM}_m}$