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## Challenging Physics Problems for Practice: Gravitation

 1. A small asteroid starts falling onto the sun from a distance equal to the radius of the Earth's orbit. Initially the body starts off with zero velocity. Using Kepler's law, find in terms of the Earth's orbital time period T how long the rock will take to fall into the sun. 2. 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. 3. A planet is moving around the sun (mass Ms) in an elliptical orbit. When it is at a distance ro from the sun, its velocity is vo and the angle between the radius vecor ro and the velocity vector vo is equal to ø. Find the maximum and the minimum distance that will separate this planet from the sun.
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