Two satellites of Earth, \(S_1\)_, and \(S_2\), are moving in the same orbit. The mass of \(S_1\) is four times the mass of \(S_2\). Which one of the following statements is true?

Two astronauts are floating in a gravity free space after having lost contact with their spaceship. The two will:

The centripetal force acting on a satellite orbiting around the earth and the gravitational force of the earth acting on the satellite, both are equal to \(F\). The net force on the satellite is:
1. zero
2. \(F\)
3. \(F\sqrt{2}\)
4. \(2F\)

A planet is revolving around a massive star in a circular orbit of radius \(R\). If the gravitational force of attraction between the planet and the star is inversely proportional to \(R^3,\) then the time period of revolution \(T\) is proportional to:
1. \(R^5\)
2. \(R^3\)
3. \(R^2\)
4. \(R\)

Magnitude of potential energy (\(U\)) and time period \((T)\) of a satellite are related to each other as:
1. \(T^2\propto \frac{1}{U^{3}}\)
2. \(T\propto \frac{1}{U^{3}}\)
3. \(T^2\propto U^3\)
4. \(T^2\propto \frac{1}{U^{2}}\)

A satellite of mass \(m\) revolving around the earth in a circular orbit of radius \(r\) has its angular momentum equal to \(L\) about the centre of the earth. The potential energy of the satellite is: 
1. \(- \frac{L^{2}}{2 mr}\)
2. \(- \frac{2L^{2}}{mr^2}\)
3. \(- \frac{3L^{2}}{m^2r^2}\)
4. \(- \frac{L^{2}}{mr^2}\)