Question

The planet Mars has two moons, phobos and delmos. Phobos has a period of $7$ hours, $39$ minutes and an orbital radius of $9.4 \times 10^{3} km .$ The mass of Mars is

• A. $6.48 \times 10^{19} kg$
• B. $6.48 \times 10^{23} kg$
• C. $6.48 \times 10^{27} kg$
• D. $6.48 \times 10^{31} kg$

Answer 1

Answer: (B)

$T^{2}=\frac{4 \pi^{2}}{G M_{m}} R^{3} \Rightarrow M_{m}=\frac{4 \pi^{2}}{G T^{2}} R^{3}$
$=\frac{4 \times(3.14)^{2} \times(9.4)^{3} \times\left(10^{6}\right)^{3}}{\left(6.67 \times 10^{-11}\right) \times(459 \times 60)^{2}}=6.48 \times 10^{23} kg$