Two stars of equal masses $M$ are orbiting in a circle of radius $R$. Their orbital time period is proportional to

$A$ 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 :

$A$ particle is moving in an elliptical orbit as shown in the figure. If $\vec{p}$, $\vec{L}$, and $\vec{r}$ denote the linear momentum, angular momentum, and position vector of the particle (from focus $O$) respectively at point $A$, then the direction of $\vec{\alpha} = \vec{p} \times \vec{L}$ is along

Two stars of masses $M$ and $2M$ are at a distance $d$ apart and are revolving around their common center of mass. The angular velocity of the system of the two stars is ($G$ is the universal gravitational constant).

$A$ satellite of the earth is revolving in a circular orbit with a uniform velocity $V$. If the gravitational force suddenly disappears,the satellite will

The motion of planets in the solar system is governed by which of the following conservation laws?