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I've been looking at the Kepler's problem, and it looks like your orbit (elliptic, parabolic or hyperbolic) are given in terms of energy and angular momentum. I was wondering: if I have a central attractive potential (such as the Sun) and a projectile starting from an infinite distance at a given velocity and impact parameter, would it be possible to obtain the orbit equation for such an object? I mean: I would like to solve Kepler's problem for a projectile after a given velocity and impact parameter.