If $g \propto \frac{1}{R^3}$ (instead of $\frac{1}{R^2}$),then the relation between the time period $T$ of a satellite near the Earth's surface and the radius $R$ will be:

$A$ body moves in a circular orbit of radius $R$ under the action of a central force. The potential due to the central force is given by $V(r) = kr$ ($k$ is a positive constant). The period of revolution of the body is proportional to:

$A$ satellite revolves around the earth in an elliptical orbit. Its speed

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

The gravitational potential energy required to raise a satellite of mass $m$ to a height $h$ above the Earth's surface is $E_1$. Let the energy required to put this satellite into orbit at the same height be $E_2$. If $M$ and $R$ are the mass and radius of the Earth respectively,then the ratio $E_1: E_2$ is:

Two satellites of mass $50\,kg$ and $100\,kg$ revolve around the earth in circular orbits of radius $9\,R$ and $16\,R$ respectively,where $R$ is the radius of the earth. The ratio of the speeds of the two satellites will be: