$A$ particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r}$,where $k$ is a constant. The periodic time of this motion is proportional to:

What is the orbital velocity of a satellite? Derive its equation.

$A$ satellite is in an elliptical orbit around a planet $P.$ It is observed that the velocity of the satellite when it is farthest from the planet is $6$ times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is $......$

The distance between the centre of the Earth and the Moon is $384000 \, km$. If the mass of the Earth is $6 \times 10^{24} \, kg$ and $G = 6.67 \times 10^{-11} \, N m^2/kg^2$,the orbital speed of the Moon is nearly ......... $km/s$.

If $L$ is the angular momentum of a satellite revolving around the Earth in a circular orbit of radius $r$ with speed $v$,then .........

$A$ satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_e$. By firing rockets attached to it,its speed is instantaneously increased in the direction of its motion so that it becomes $\sqrt{\frac{3}{2}}$ times larger. Due to this,the farthest distance from the centre of the earth that the satellite reaches is $R$. The value of $R$ is $....R_e$.