Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively,measured from the centre of mass of the system. The magnitude of the gravitational force that $m_1$ exerts on $m_2$ is

$Assertion$ : An astronaut experiences weightlessness in a space satellite.
$Reason$ : When a body falls freely,it does not experience gravity.

Weightlessness experienced while orbiting the earth in a spaceship is the result of:

If a satellite has to orbit the earth in a circular path every $6 \text{ hrs}$, at what distance from the surface of the earth should the satellite be placed (in $\text{ km}$)? (Radius of earth $R_e = 6400 \text{ km}$)
(Assume $\frac{GM}{4\pi^2} = 8 \times 10^{12} \text{ m}^3\text{s}^{-2}$, where $G$ and $M$ are the gravitational constant and mass of earth, and $10^{1/3} = 2.1$)

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:

$A$ satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation,the quantity $\frac{3 \pi}{G d}$ represents :