| 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. |
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| 2. |
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. |
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| 3. |
A rocket is fired vertically with a velocity vo. Derive an expression for its velocity v at a height h, given that the radius of earth is R. |
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