Question

A planet of mass M has a satellite of mass m, revolving around the planet in a circular orbit of radius r and time period T. The mass (M) of the planet is

• A. $\frac{4\pi^{2}r^{3}}{GT^{2}}$
• B. $\frac{4\pi^{2}r^{2}}{GT^{3}}$
• C. $\frac{GT^{2}}{4\pi r^{3}}$
• D. $\frac{r^{3}G}{4\pi T^{2}}$

Answer 1

Answer: (A)

$\frac{4\pi^{2}r^{3}}{GT^{2}}$

Answer 2

$F = \frac{GMm}{r^{2}} = mr\omega^{2} = mr\left( \frac{2\pi}{T} \right)^{2}M = \frac{mr^{3}4\pi^{2}}{GmT^{2}} = \frac{4\pi^{2}r^{3}}{GT^{2}}$