The fig. shows the motion of a planet around the un in an elliptical orbit with sun at the  focus. The shaded areas can be assumed to be equal. If $t_1$ and $t_2$ represent the  time taken for the planet to move from $A$ to $B$ and $C$ to $D$ respectively, then

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. $F \propto {1\over r^3}$, but still remaining a central force. Then

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

A planet revolves around sun whose mean distance is $1.588$ times the mean distance between earth and sun. The revolution time of planet will be ........... $ years$

The satellite of mass $m$ revolving in a circular orbit of radius $r$ around the earth has kinetic energy $E$. Then its angular momentum will be

The time period of a geostationary satellite is $24\; \mathrm{h}$, at a helght $6 \mathrm{R}_{\mathrm{E}}( \mathrm{R}_{\mathrm{E}}$ is radius of earth) from surface of earth. The time period of another satellite whose helght is $2.5 \mathrm{R}_{\mathrm{E}}$ from surface will be