Distribution of radial velocities in a gas

[Arnoldas]

The lecturer did not explain this for some reason.

Assuming that we have a gass where all the particles have a certain absolute velocity v. Directions of v vector are random though, giving velocity vector a uniform direction distribution. That means that a velocity vector of any random particle has equal probability to point in any direction. But what if we observe this gas from a very far distance ( like atmosphere of a star): we can then only observe the radial velocities of particles. That means that we would observe all velocities in the interval [-v,v]. But the question is what would be the distribution that we would observe (particles per velocity curve)? for example which velocity would be most prominent? Would it also be a uniform curve?-thats what lecturer claimed in haste.

 

[mfb]

All have the same velocity v? Then their velocity vectors form a sphere, and "seen from far away" you can pick one coordinate as your "observed direction". Then you just have to find the surface area as function of this coordinate, which is a formula you can look up (or derive yourself).