= Stellar relaxation time
{title2=$t_{\rm rel}$}
The <stellar relaxation time> is the <time> on which random gravitational encounters change a <star>'s <velocity> by an amount comparable to its characteristic random <velocity>. A weak straight-line encounter at relative <speed> $u$ and <impact parameter> $b$ gives a kick $2Gm/(bu)$. Three-dimensional encounter counting gives $d\langle|\Delta\mathbf v|^2\rangle/dt=8\pi G^2m^2n\log(b_{\max}/b_{\min})/u$. Definitions of relaxation, <velocity> averaging and system structure alter order-one coefficients; the robust spherical scaling is $t_{\rm rel}\sim v^3/(G^2m^2n\log\Lambda)\sim(N/\log N)t_{\rm dyn}$. Collisionless simulation requirements depend on the duration and permitted fractional relaxation, not a universal minimum particle number.
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