Rotational Brownian motion (astronomy)

In astronomy, rotational Brownian motion is the random walk in orientation of a binary star's orbital plane, induced by gravitational perturbations from passing stars.

Consider a binary that consists of two massive objects (stars, black holes etc.) and that is embedded in a stellar system containing a large number of stars. Let ${\displaystyle M_{1}}$ and ${\displaystyle M_{2}}$ be the masses of the two components of the binary whose total mass is ${\displaystyle M_{12}=M_{1}+M_{2}}$. A field star that approaches the binary with impact parameter ${\displaystyle p}$ and velocity ${\displaystyle V}$ passes a distance ${\displaystyle r_{p}}$ from the binary, where

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