Question

A mars satellite moving in an orbit of radius $9.4\times {10}^3$ km takes 27540 s to complete one revoluton. calculate the mass of mars.

Answer 1

$T=2\pi \sqrt{\frac{r^3}{GM}}\Rightarrow 27540=2\times 3.14\sqrt{\frac{(9.4\times {10}^3\times {10}^3{)}^3}{6.67\times {10}^{-11}\times M}}or(27540{)}^2=(6.28{)}^2\times \frac{(9.4\times {10}^5{)}^3}{6.67\times {10}^{-11}\times M}orM=\frac{(6.28{)}^2\times (9.4{)}^3\times {10}^{18}}{6.67\times {10}^{-11}\times (27540{)}^2}=6.5\times {10}^{23}kg$