Question

A Mars satellite moving in an orbit of radius 9.4 × 103 km takes 27540 s to complete one revolution. Calculate the mass of Mars.

Answer 1

Answer:

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Explanation:

Answer 2

The mass of Mars is $6.5 \times 10^{23} \mathrm{kg}$.

Explanation:

In the orbit, the mars satellite moves with the radius $9.4 \times 10^3 \mathrm{km}$. To complete one revolution, it will take 27540 s.

The calculations are below:

$T=2 \pi \sqrt{\frac{r^{3}}{G M} }$

$\Rightarrow(27540)^{2}=\frac{(6.28)^{2}\left(9.4 \times 10^{6}\right)^{2}}{6.67} \times 10^{-11} \times M$

$M=\frac{(6.28)^{2} \times(9.4)^{3} \times 10^{18}}{6.67 \times 10^{-11} \times(27540)^{2}}$

$=6.5 \times 10^{23} \mathrm{kg}$.

So, the mass of the mars is $=6.5 \times 10^{23} \mathrm{kg}$.