$A$ 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:

Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is

Spaceman Fred's spaceship (which has negligible mass) is in an elliptical orbit about Planet Bob. The minimum distance between the spaceship and the planet is $R$; the maximum distance between the spaceship and the planet is $2R$. At the point of maximum distance,Spaceman Fred is traveling at speed $v_0$. He then fires his thrusters so that he enters a circular orbit of radius $2R$. What is his new speed?

The correct formula for the height $h$ of a satellite from the Earth's surface is:

Which of the following statements is correct in respect of a geostationary satellite?

$A$ test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho(r) = \frac{K}{r^2}$. Identify the correct relation between the radius $R$ of the particle's orbit and its period $T$.