Solve the following :
Question:

A Mars satellite moving in an orbit of radius $9.4 \times 103 \mathrm{k} \mathrm{m}$ takes $27540 \mathrm{~s}$ to complete one evolution. Calculate the mass of Mars.

Solution:

Time period of revolution of satellite around the mars is given by

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

$M=$ Mars mass

$r=$ Distance of the satellite from center of the planet

$27540=2 \times 3.14 \sqrt{\frac{\left(9.4 \times 10^{\mathrm{s}} \times 10^{\mathrm{s}}\right)^{\mathrm{s}}}{6.67 \times 10^{-11} \times M}}$

$\mathrm{M}=6.5 \times 10^{23} \mathrm{kgs}$

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