Two satellites $A$ and $B$ revolve round the same planet in coplanar circular orbits lying in the same plane. Their periods of revolutions are $1 \mathrm{~h}$ and $8 \mathrm{~h}$, respectively. The radius of the orbit of $A$ is $10^4 \mathrm{~km}$. The speed of $B$ is relative to $A$. When they are closed in $\mathrm{km} / \mathrm{h}$ is

A planet is revolving around the sun in a circular orbit with a radius $r$. The time period is $T$. If the force between the planet and star is proportional to $r^{-3 / 2}$, then the square of time period is proportional to

The weight of a body on the surface of the earth is 63 N. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

A space ship is launched into a circular orbit close to earth’s surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull?

(Radius of earth = 6400 km, g = 9.8 m/s$^2$)

What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth $=R$ )

Two satellites $S_1$ and $S_2$ are revolving round a planet in coplanar circular orbits of radii $r_1$ and $r_2$ in the same direction, respectively. Their respective periods of revolution are $1 \mathrm{~h}$ and $8 \mathrm{~h}$. The radius of orbit of satellite $S_1$ is equal to $10^4 \mathrm{~km}$. What will be their relative speed (in $\mathrm{km} / \mathrm{h}$) when they are closest?