$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $d_1$ and its velocity is $v_1$. When it is farthest from the Sun,its distance from the Sun is $d_2$. What is its velocity at that point?

What is a geostationary satellite? What is the orbital period of a geostationary satellite?

The radii of circular orbits of two satellites $A$ and $B$ of the earth are $4R$ and $R$ respectively,where $R$ is the radius of the earth. If the speed of satellite $B$ is $6V$,then the speed of satellite $A$ will be:

If the gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$) where $R$ is the separation between them,then a particle in a circular orbit under such a force would have its orbital speed $v$ proportional to

$A$ planet is moving in a circular orbit. It completes $2$ revolutions in $360$ days. What is its angular frequency?

Consider a star of mass $m_2 \ kg$ revolving in a circular orbit around another star of mass $m_1 \ kg$ with $m_1 \gg m_2$. The heavier star slowly acquires mass from the lighter star at a constant rate of $\gamma \ kg/s$. In this transfer process,there is no other loss of mass. If the separation between the centers of the stars is $r$,then its relative rate of change $\frac{1}{r} \frac{dr}{dt} \ (\text{in } s^{-1})$ is given by: