Weightlessness experienced while orbiting the earth in a spaceship is the result of:

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $d_1$ and its velocity is $v_1$. When it is farthest from the Sun,its distance from the Sun is $d_2$. What is its velocity at that point?

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$ respectively. What is its distance from the sun when it is at a position perpendicular to the major axis of the orbit drawn from the sun?

Two particles of equal mass $m$ go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is