Question

The planet Mars has two moons, if one of them has a period $7$ hours, $30$ minutes and an orbital radius of $9.0 \times 10^{3} \,km$. Find the mass of Mars.
$\left\{\text { Given } \frac{4 \pi^{2}}{G}=6 \times 10^{11} \,N^{-1} \,m^{-2} \, kg ^{2}\right\}$

• A. $5.96 \times 10^{19} \, kg$
• B. $3.25 \times 10^{21} \,kg$
• C. $7.02 \times 10^{25} \, kg$
• D. $6.00 \times 10^{23} \,kg$

Answer 1

Answer: (D)

$T^{2}=\frac{4 \pi^{2}}{G M} \cdot r^{3}$
$M=\frac{4 \pi^{2}}{G} \cdot \frac{r^{3}}{T^{2}}$
by putting values
$M=6 \times 10^{23}$