Question

What is the mass of the planet that has a satellite whose time period is $T$ and orbital radius is $r$?

• A. $\frac{4{\pi }^2{r}^3}{G{T}^2}$
• B. $\frac{4{\pi }^2{r}^3}{G{T}^1}$
• C. $\frac{4{\pi }^2{r}^3}{G{T}^3}$
• D. $\frac{4{\pi }^{2}T}{G{T}^2}$

Answer 1

The correct option is A $\frac{4{\pi }^2{r}^3}{G{T}^2}$

we know $T=2\pi \sqrt{\frac{r^3}{GM}}$
squaring both side $T^2=4{\pi }^2\frac{r^3}{GM}$
$\therefore M=\frac{4{\pi }^2{r}^3}{T^{2}G}$