Reduced mass μ
Reduced mass μ is used throughout physics and engineering as a correction ‘factor’ for interacting particles whose interaction affects the centre of mass. It is given by
where m is the mass of the particle and M is the mass of the particle it interacts with. For example, the reduced mass μe of an orbital electron is given by
where me is the mass of the orbiting electron and mp is the mass of the proton. This is due to their mutual interaction given by Newton’s Third Law of Motion, which causes the two to rotate about a mutual origin of orbit, instead of at the centre of mass of either one of the particles.
The reduced mass mN of N mutually interacting bodies is given by
where mn is the mass of the nth body.
The reduced mass often sees an additional relativistic
correction, given for N bodies by
since mrel = γm for a rest mass m. Note that γn is the Lorentz factor for the nth body travelling at velocity vn ≈ c, defined such that
For only two bodies, this simply becomes