An artificial satellite revolves around a planet for which gravitational force $(F)$ varies with distance $r$ from its centre as $F \propto r^2$. If $v_0$ is its orbital speed,then

$A$ spaceship approaches the moon (mass $= M$,radius $= R$) along a parabolic path which is almost tangential to its surface. At the moment of maximum approach,the brake rocket is fired to convert the spaceship into a satellite of the moon. Find the change in speed.

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is

Two satellites are launched simultaneously into orbits of radius $R$ and $4R$. At an instant,the two satellites are on the same radial line. The time after which they have maximum separation is (mass of Earth = $M_e$). Assume the same sense of rotation.

The period of a satellite,in a circular orbit near an equatorial plane,will not depend on

Two satellites $A$ and $B$ go round the planet $P$ in circular orbits having radii $4 R$ and $R$ respectively. If the speed of the satellite $A$ is $3 v$,the speed of satellite $B$ will be ...........