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Problem


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.



Solution