Rotational Brownian motion (astronomy) 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 formula_1 and formula_2 be the masses of the two components of the binary whose total mass is formula_3. A field star that approaches the binary with impact parameter formula_4 and velocity formula_5 passes a distance formula_6 from the binary, where formula_7 the latter expression
Brownian motion moment of probability of displacement formula_2, is interpreted as mass diffusivity "D": Then the density of Brownian particles "ρ" at point "x" at time "t" satisfies the diffusion equation: Assuming that "N" particles start from the origin at the initial time "t"=0, the diffusion equation has the solution This expression (which is a normal distribution with the mean formula_12 and variance formula_13 usually called Brownian motion formula_14) allowed Einstein to calculate the moments directly. The first moment is seen to vanish, meaning that the Brownian particle is equally likely to move to the left as it is to move to