The minimum and maximum distances of a planet revolving around the Sun are $x_{1}$ and $x_{2}$. If the minimum speed of the planet on its trajectory is $v_{0}$,then its maximum speed will be:

Two satellites of equal mass are revolving around Earth in elliptical orbits of different semi-major axes. If their angular momenta about the Earth's center are in the ratio $3:4$,then the ratio of their areal velocities is ........

Which of the following graphs represents the relationship between the orbital velocity $(v_o)$ of a satellite and its distance $(r)$ from the center of the Earth?

The distance of a geostationary satellite from the surface of the Earth (radius $R_e = 6400 \ km$) in terms of $R_e$ is ....... (in $R_e$)

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 ..... .

$A$ $10\; kg$ satellite circles Earth once every $2\; hours$ in an orbit having a radius of $8000\; km$. Assuming that Bohr's angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom, find the quantum number of the orbit of the satellite.