Orbital energy is the mechanical energy associated with relative motion and mutual attraction. In the isolated Newtonian two-body problem, let be the reduced mass, the separation and the relative speed. ThenDividing by gives specific orbital energy. With zero potential energy at infinity, negative gives a bound Kepler orbit, zero gives the parabolic limit and positive gives an unbound encounter.
For an elliptic orbit, with semi-major axis . Energy loss can therefore shrink a bound orbit, whereas a sufficiently large gain can unbind it. External forces or interactions with additional bodies invalidate conservation of the isolated pair's orbital energy.
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