If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth,the height of the satellite above the surface of the earth is

The planet Mars has two moons. If one of them has a period of $7\, \text{hours}, 30\, \text{minutes}$ and an orbital radius of $9.0 \times 10^{3}\, \text{km}$, find the mass of Mars. $\left\{\text{Given}: \frac{4 \pi^{2}}{G} = 6 \times 10^{11}\, \text{N}^{-1} \text{m}^{-2} \text{kg}^{2}\right\}$

$A$ satellite is placed in a circular orbit around the Earth at an altitude of $1000 \,km$. The time period of the satellite in minutes is approximately (mass of the Earth $= 6 \times 10^{24} \,kg$, radius of the Earth $= 6.4 \times 10^6 \,m$, $G = 6.67 \times 10^{-11} \,Nm^2 \,kg^{-2}$).

If $r$ represents the radius of the orbit of a satellite of mass $m$ moving around a planet of mass $M$,the velocity of the satellite is given by

$A$ planet of mass $m$ moves in an ellipse around the sun of mass $M_S$ such that its maximum and minimum distances are $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the center of the sun is

$A$ satellite of mass $m$ is revolving around the Earth of mass $M$ in an orbit of radius $r$ with constant angular velocity $\omega$. The angular momentum of the satellite is ($G$ = gravitational constant).