$A$ satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in the figure. The ratio of the speed of the satellite at point $a$ to that at point $b$ is:

The radius of the orbit of a geostationary satellite is (mean radius of earth is $R$,angular velocity about own axis is $\omega$,and acceleration due to gravity on earth's surface is $g$).

The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of radius $\frac{3r}{2}$ is

What are the directions of rotation of a polar satellite and the Earth?

Earth revolves around the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to

The distance between two stars of masses $3 M_S$ and $6 M_S$ is $9 R$. Here $R$ is the mean distance between the centers of the Earth and the Sun,and $M_S$ is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period $n T$,where $T$ is the period of Earth's revolution around the Sun. The value of $n$ is. . . . .