The earth (mass $M = 6 \times 10^{24} \ kg$) revolves around the sun with an angular velocity $\omega = 2 \times 10^{-7} \ rad/s$ in a circular orbit of radius $R = 1.5 \times 10^8 \ km$. The force exerted by the sun on the earth in newtons is:

$A$ satellite of mass $m$ is revolving close to the surface of a planet of density $d$ with time period $T$. The value of the universal gravitational constant $G$ in terms of $d$ and $T$ is given by:

Two point masses of mass $m_1 = fM$ and $m_2 = (1 - f)M$ $(f < 1)$ are in outer space (far from the gravitational influence of other objects) at a distance $R$ from each other. They move in circular orbits about their centre of mass with angular velocities $\omega_1$ for $m_1$ and $\omega_2$ for $m_2$. In that case:

$A$ planet revolves around the sun in an elliptical orbit. When it is closest to the sun,its distance from the sun is $d_1$ and its velocity is $v_1$. When it is farthest from the sun,its distance from the sun is $d_2$ and its velocity is $v_2$. Find the value of $v_2$.

The time period of a geostationary satellite is

The periodic time of a communication satellite is ......... $hours$.