1) Two stars of equal mass M move with constant speed v in a circular orbit of radius R about their common centre of mass as shown in the figure below.

What is the net force on each star?

2) Which statement about a geostationary satellite is true?

3) A rock is thrown vertically upward near the surface of Planet X with a velocity of 45 m s^–1 and it comes to an instantaneous rest 5.2 s later. If the same rock is now thrown up near the surface of Planet Y with the same initial velocity as that on Planet X, at 5.2 s later it is still moving upwards at a speed of 25 m s^–1. If both planets do not have atmosphere, what is the ratio of the gravitational field strength near the surface of Planet Y to that of Planet X?

4) An experimental satellite is found to have a weight W when assembled before launching from a rocket site. It is placed in a circular orbit at a height h = 6R above the surface of the Earth (of radius R). What is the gravitational force acting on the satellite whilst in orbit?

5) Outside a uniform sphere of mass M, the gravitational field strength is the same as that of a point mass M at the centre of the sphere. The Earth may be taken to be a uniform sphere of radius r. The gravitational field strength at its surface is g. What is the gravitational field strength at a height h above the ground?