The minimum and maximum distances of a planet revolving around the Sun are $x_{1}$ and $x_{2}$. If the minimum speed of the planet on its trajectory is $v_{0}$,then its maximum speed will be:

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication.
$(a)$ Calculate the height of such a satellite.
$(b)$ Find out the minimum number of satellites that are needed to cover the entire Earth,so that at least one satellite is visible from any point on the equator.
Given: $M = 6 \times 10^{24} \ kg$,$R = 6400 \ km$,$T = 24 \ h$,$G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$.

If the gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$) where $R$ is the separation between them,then a particle in a circular orbit under such a force would have its orbital speed $v$ proportional to

The mean radius of Earth is $R$,and its angular speed on its axis is $\omega$. What will be the radius of orbit of a geostationary satellite?

Two satellites of earth,$S_{1}$ and $S_{2}$,are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?

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