# Maxwell-Boltzman speed distribution

For a class assignment, I have to do a Barnes-Hut Galaxy simulation.

The assignment includes:

The dots' velocities following the Maxwell distribution with typical velocity of $$v={\left<v\right>}^{\frac{1}{2}}$$ and that mean that each of the velocity vector components vave normal distribution with mean zero and $$\sigma = \frac{v}{\sqrt{3}}$$

The "dots" it mentions represent stars in the simulated galaxy.

Someone can explain to me the meaning of that? How the mean of all the components can be zero if, for example, $V=85\,\mathrm{kmh}$?

• Are you sure that this is copied correctly? I mean I'd have expected for it to say$${v}_{\text{RMS}} ~ \equiv ~ \sqrt{{\left<v^{2}\right>}}\,,$$where ${v}_{\text{RMS}}"$ is the "root-mean square" of the velocities. It's basically just like taking a normal average, except you square all of the numbers first, then take the square-root at the end. – Nat Jul 19 '18 at 6:11
• Hmm, are you sure it is $\langle v\rangle=0$ and not $\langle v_z\rangle=\langle v_\phi\rangle=0$ (cf this answer of mine). – Kyle Kanos Jul 19 '18 at 11:01
• This question was cross-posted and answered on computational science SE. I believe that SE discourages cross-posting to avoid duplication of effort, so maybe the OP could consider deleting this version of the question? – user197851 Jul 20 '18 at 7:19