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I have read that using Newtonian physics, the gravitation interaction between two bodies traces the path of a conic, if one is orbiting the other it is an ellipse, if it is a fly by it forms part of a hyperbola, somewhere in-between is a porabola.

 

It seems that a simple condition for two bodies to be orbiting is that one body needs to make a 180 degree turn, if that is so then it could only possibly be an ellipse and therefore be in orbit.

 

Taking relativity into account, is it possible for two bodies to come near each other and one make a 180 degree turn but still end up being ejected from the field?

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