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
Reflected Brownian motion "roughly speaking, "Z" is pushed in direction "R" whenever the boundary surface formula_5 is hit, where "R" is the "j"th column of the matrix "R"." Stability conditions are known for RBMs in 1, 2, and 3 dimensions. "The problem of recurrence classification for SRBMs in four and higher dimensions remains open." In the special case where "R" is an M-matrix then necessary and sufficient conditions for stability are The marginal distribution (transient distribution) of a one-dimensional Brownian motion starting at 0 restricted to positive values (a single reflecting barrier at 0) with drift "μ " and variance "σ" is for