= Parabolic dry-merger energy accounting
{title2=$E_F=E_I+E_A$}
In a <dry galaxy merger>, zero orbital energy at infinite separation and retention of all mass and energy give $E_F=E_I+E_A$. If the progenitors and remnant satisfy the <virial theorem>, their <gravitational radii> obey $R_F/R_I=(1+\eta)^2/(1+\epsilon\eta)$, where $\eta=M_A/M_I$ and $\epsilon=\langle v_A^2\rangle/\langle v_I^2\rangle$. The latter average is weighted by satellite mass. Nonzero orbital energy, escaping stars, or dissipative losses change the energy accounting.
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