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- Derivation of Kepler's laws 4 answers
How does one prove that an orbit of a satellite around a planet of significantly greater mass than the satellite is a conic section (i.e. an ellipse, circle, hyperbola, or parabola)?
Also, there is also the case of a degenerate orbit, which we have for example when the satellite starts at rest with respect to the planet, and the satellite moves along a straight line towards the center of the planet.
By the way, I realize this may be an extremely tough question, because I have seen once before the derivation with vector calculus that bounded orbits are ellipses, and it is definitely quite involved. As such, you may wish to provide an outline of how might this be done (does one have to consider bounded and open orbits separately, for example?) and omit the math.
Also note that I assume the satellite is small compared to the planet because I don't want to add the complexity of a two body-system orbiting around the center of mass just yet!