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Challenging Physics Problems for Practice: Gravitation

1.

An artificial satellite (mass m) of a planet (mass M) revolves in a circular orbit whose radius is n times the radius R of the planet. The satellite experiences a slight resistance due to cosmic dust. The resistance force is dependent on the satellite velocity as F = a v2, where a is a constant. Calculate how long the satellite will remain in orbit before it falls on to the planet's surface.

2.

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.

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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