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Question :
11) Four identical bodies of mass M, at the vertices : 2040058

11) Four identical bodies of mass *M*, at the vertices of a square with a diagonal 2*R*, orbit their common center of mass in a circular motion with a radius *R*. How much energy is required to separate the four stars so they are an infinite distance apart?

12) The Schwarzchild radius is defined for a given mass *M* as the radius for which the escape velocity would be exactly equal to the speed of light, *c*. What is the expression for this radius in terms of *G*, *M*, and *c*?

13) Triton, the largest of Neptune's moons has a retrograde rotation. This means that it revolves about Neptune in the opposite direction to Neptune's direction of rotation about its own axis. The gravitational attraction of Triton causes tides on Neptune, which gradually slow down its rotation about its own axis. What consequences does this have for Triton?

14) Our Moon revolves about Earth in the same direction as Earth's direction of rotation about its own axis. The gravitational attraction of the Moon causes tides on Earth, which gradually slow down its rotation about its own axis. What consequences does this have for the Moon?

15) Tidal locking is what makes the Moon rotate about its own axis at the same rate that it revolves around Earth. Using as a model of a moon two identical masses of mass *m* connected by a light rod, explain how the forces on the masses would tend to keep this satellite in a fixed orientation.