The period of revolution increases in the order of:

$A$ planet $(P_1)$ is moving around a star of mass $2M$ in an orbit of radius $R$. Another planet $(P_2)$ is moving around another star of mass $4M$ in an orbit of radius $2R$. The ratio of the time periods of revolution of $P_2$ and $P_1$ is . . . . . . .

$A$ satellite moves around the Earth in a circular orbit of radius $R$ making one revolution per day. $A$ second satellite moving in a circular orbit moves around the Earth once in $8$ days. The radius of the orbit of the second satellite is

$A$ planet orbits in an elliptical path of eccentricity $e$ around a massive star considered fixed at one of the foci. The point in space,where it is closest to the star is denoted by $P$ and the point,where it is farthest is denoted by $A$. Let $v_P$ and $v_A$ be the respective speeds at $P$ and $A$,then

If $r_p, v_p, L_p$ and $r_a, v_a, L_a$ are radii,velocities and angular momenta of a planet at perihelion and aphelion of its elliptical orbit around the Sun respectively,then

When a satellite moves around the earth in a certain orbit,the quantity which remains constant is: