A Mars satellite moving in an orbit of radius $9.4\times {10}^3 \mathrm{km}$ takes $27540 \mathrm{s}$ to complete one revolution. Calculate the mass of Mars.

A satellite of mass $1000 \mathrm{kg}$ is supposed to orbit the earth at a height of $2000 \mathrm{km}$ above the Earth's surface. Find,

$\left(a\right)$ Its speed in the orbit,

$\left(b\right)$ Its kinetic energy,

$\left(c\right)$ The potential energy of the earth-satellite system and

$\left(d\right)$ Its time period. Mass of the Earth$=6\times {10}^{24 }\mathrm{kg}$.

$\left(a\right)$ Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of the Earth's rotation?

$\left(b\right)$ If the satellite is directly above the north pole at some instant, find the time it takes to come over the equatorial plane. Mass of the Earth $=6\times {10}^{24} \mathrm{kg}$.