$A$ 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

The time period $T$ of a satellite is related to the density $(\rho)$ of the planet around which it is orbiting close to the surface as:

$A$ satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in the figure. The ratio of the speed of the satellite at point $a$ to that at point $b$ is:

Two satellites $A$ and $B$ of same mass are moving around a planet at an altitude of $3R$ and $5R$ respectively. Select the correct statement.

$A$ satellite of mass $m$ is moving in a circular orbit of radius $r$ around the earth. The angular momentum of the satellite about the center of orbit is ($M=$ mass of earth,$G=$ gravitational constant).

Two satellites revolve around a planet in coplanar circular orbits in an anticlockwise direction. Their periods of revolution are $1\, h$ and $8\, h$ respectively. The radius of the orbit of the nearer satellite is $2 \times 10^{3}\, km$. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi}{x}\, rad\, h^{-1}$ where $x$ is ..... .