The Earth moves around the Sun in an elliptical orbit as shown in the figure. The ratio $OA/OB = x$. The ratio of the speed of the Earth at $B$ to that at $A$ is nearly

$A$ satellite is revolving around a planet in a circular orbit close to its surface. Let $\rho$ be the mean density and $R$ be the radius of the planet. Then the period of the satellite is ($G=$ universal constant of gravitation).

Given the radius of Earth $R$ and the length of a day $T$,the height of a geostationary satellite is: [$G$ = Gravitational Constant,$M$ = Mass of Earth]

$A$ geostationary satellite is orbiting the earth at a height of $6R$ from the earth's surface ($R$ is the earth's radius). What is the period of rotation of another satellite at a height of $2.5R$ from the earth's surface?

If the escape velocity of a body from the surface of the earth is $11.2 \,km \,s^{-1}$, then the orbital velocity of a satellite in an orbit which is at a height equal to the radius of the earth is

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in a circular orbit of radius $R$ around the sun will be proportional to