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 bridge Brownian bridge A Brownian bridge is a continuous-time stochastic process "B"("t") whose probability distribution is the conditional probability distribution of a Wiener process "W"("t") (a mathematical model of Brownian motion) subject to the condition (when standardized) that "W"(T) = 0, so that the process is pinned at the origin at both "t=0" and "t=T". More precisely: The expected value of the bridge is zero, with variance formula_2, implying that the most uncertainty is in the middle of the bridge, with zero uncertainty at the nodes. The covariance of "B"("s") and "B"("t") is "s"(T − "t")/T if "s" < "t". The