UVa CM:Space station orbit

Problem
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A space station orbits Earth on a circular trajectory. At some moment the captain 	decides to change the trajectory by turning on the rocket engine for a very short period of time. During the time the engine was on, it accelerated the station in its direction of motion. As a result, the station speed increased by a factor of \alpha. Provide the conditions, in terms of \alpha, that the new trajectory is elliptic, parabolic or hyperbolic. Justify your answers.
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Solution
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Category:Problems