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## Challenging Physics Problems for Practice: Gravitation

 1. A satellite of mass Ms is orbiting the Earth in a circular orbit of radius Rs. Due to a critical failure in its solar panels, it starts losing power at a constant rate C. If Me and Re denote the mass and radius of the Earth, then find the time it takes the satellite to fall to the surface of the Earth. 2. Assume the Earth to be a uniform sphere of mass M and radius R. Find the pressure P inside the sphere caused by the gravitational compression as a function of r, the distance from the center. 3. A comet moves towards the sun with a velocity u (when far from the sun) and aiming parameter l. The aiming parameter l is the arm of the vector u relative to the center of the sun (labeled C in the diagram). Find the minimum distance r' of this body from the sun. The mass of the sun can be taken as Ms.
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