Rotational Brownian motion (astronomy) that the rotation axis of the binary is oriented at angle θ at time "t". The evolution equation for "F" is formula_17 If <Δξ>, "a", ρ and σ are constant in time, this becomes formula_18 where μ = cos θ and τ is the time in units of the relaxation time "t", where formula_19 The solution to this equation states that the expectation value of μ decays with time as formula_20 Hence, "t" is the time constant for the binary's orientation to be randomized by torques from field stars. Rotational Brownian motion was first discussed in the context of binary
Brownian motion square root of the total population. Suppose that a Brownian particle of mass "M" is surrounded by lighter particles of mass "m" which are traveling at a speed "u". Then, reasons Smoluchowski, in any collision between a surrounding and Brownian particles, the velocity transmitted to the latter will be "mu"/"M". This ratio is of the order of 10 cm/s. But we also have to take into consideration that in a gas there will be more than 10 collisions in a second, and even greater in a liquid where we expect that there will be 10 collision in one second. Some