= Orbital energy
{title2=$E$}
<Orbital energy> is the mechanical <energy> associated with relative motion and mutual attraction. In the isolated Newtonian <two-body problem>, let $\mu=m_1m_2/(m_1+m_2)$ be the <reduced mass>, $r$ the separation and $v$ the relative <speed>. Then
$$
E=\frac12\mu v^2-\frac{Gm_1m_2}{r}.
$$
Dividing by $\mu$ gives <specific orbital energy>. With zero potential energy at infinity, negative $E$ gives a bound <Kepler orbit>, zero gives the parabolic limit and positive $E$ gives an unbound encounter.
For an <elliptic orbit>, $E=-Gm_1m_2/(2a)$ with <semi-major axis> $a$. 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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