$A$ 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 :

$A$ planet is moving around the sun in an elliptical orbit at different positions $A, B, C, D$. The maximum kinetic energy of the planet is at position:

The periodic time of a satellite revolving above Earth's surface at a height equal to $R$ (where $R$ is the radius of the Earth) is given by (where $g$ is the acceleration due to gravity at Earth's surface):

$A$ ball is dropped from a spacecraft revolving around the earth at a height of $120 \, km$. What will happen to the ball?

Consider a binary star system consisting of two stars of masses $M_1$ and $M_2$ separated by a distance of $30 \text{ AU}$ with a period of revolution equal to $30 \text{ years}$. If one of the two stars is $5$ times farther from the centre of mass than the other, find the masses of the two stars in terms of solar masses.

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?