The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

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. . . . .

$A$ satellite of mass $m$ revolves around the Earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the Earth,the orbital speed of the satellite is:

Why can the entire surface of the Earth be viewed with the help of a polar satellite?

Earth is moving around the sun in an elliptical orbit as shown. The ratio of $OB$ and $OA$ is $R$. Then the ratio of Earth's velocities at $A$ and $B$ is

The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively, such that $r_B = 100 r_A$. The ratio of the orbital speed of planet $A$ to that of planet $B$ is (both planets are revolving around the sun in circular orbits).