$A$ geostationary satellite is orbiting the earth at a height of $6R$ above the surface of the earth,where $R$ is the radius of the earth. The time period of another satellite at a height of $2.5R$ from the surface of the earth is

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

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:

Select the correct statement from the following:

$A$ satellite moves in a stable circular orbit around the Earth if (where $V_{H}$,$V_{c}$,and $V_{e}$ are the horizontal velocity,critical velocity,and escape velocity respectively):

$A$ planet is revolving around the sun in a circular orbit with a radius $r$. The time period is $T$. If the force between the planet and the star is proportional to $r^{-3/2}$,then the square of the time period is proportional to