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?

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 planet is orbiting the sun in an elliptical orbit. Let \(U\) denote the potential energy and \(K\) denote the kinetic energy of the planet at an arbitrary point in the orbit.
Choose the correct statement from the given ones:

A satellite of mass \(M\) is revolving around the Earth in a stationary orbit with a time period \(T.\) If \(10\%\) of the satellite's mass is detached, what will happen to its time period?
1. remain the same
2.  increase by \(10\%\)
3.  decrease by \(10\%\)
4. decrease by \(20\%\)