Two satellites $S_{1}$ and $S_{2}$ are revolving in circular orbits around a planet with radii $R_{1} = 3200 \, km$ and $R_{2} = 800 \, km$ respectively. The ratio of the speed of satellite $S_{1}$ to the speed of satellite $S_{2}$ in their respective orbits is $\frac{1}{x}$,where $x =$

$A$ satellite is moving around the earth with speed $v$ in a circular orbit of radius $r$. If the orbit radius is decreased by $1\%$,its speed will

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

The radius of a planet is $R$. $A$ satellite revolves around it in a circle of radius $r$ with angular velocity $\omega_0$. The acceleration due to gravity on the planet's surface is

$A$ satellite is revolving around the Earth in a circular orbit at a uniform speed $v$. If the gravitational force suddenly disappears,the speed of the satellite will be ..............

The gravitational potential energy required to raise a satellite of mass $m$ to a height $h$ above the Earth's surface is $E_1$. Let the energy required to put this satellite into orbit at the same height be $E_2$. If $M$ and $R$ are the mass and radius of the Earth respectively,then the ratio $E_1: E_2$ is: