The kinetic energy of a revolving satellite of mass $m$ at a height equal to thrice the radius of the Earth $R$ is:

$A$ satellite of the earth is revolving in a circular orbit with a uniform velocity $V$. If the gravitational force suddenly disappears,the satellite will

The period of moon's rotation around the earth is nearly $29$ days. If moon's mass were $2$ fold, its present value and all other things remained unchanged, the period of moon's rotation would be nearly ......... $days$.

$A$ planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1$ and $v_2$ are the linear velocities at these points respectively,then the ratio $\frac{v_1}{v_2}$ is

If the gravitational constant $G$ is decreasing with time,what will remain unchanged for a satellite orbiting around the Earth?

The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance $r$ from its centre. In that region,a small star is in a circular orbit of radius $R$. Then the period of revolution,$T$ depends on $R$ as