= Gas-driven contraction of a planetesimal binary
For a weakly perturbed circular <binary planetesimal>, the constant differential headwind does zero work averaged over the unperturbed orbit. <Orbit-averaged drag work> gives
$$
\langle\dot a\rangle=-2\kappa a,\qquad
\tau=\frac1{2\kappa}=\frac{m_1+m_2}{2(m_1/t_2+m_2/t_1)}.
$$
With constant <aerodynamic stopping times>, $a(t)=a_0e^{-t/\tau}$. This averaging assumes drag is slow compared with the <orbital period> and does not appreciably distort the circular orbit within one period.
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