Deriving reduced Mass

How to derive the reduced mass

What is reduced mass?

When two bodies are in a rotational motion, expressing them as  single body would help simplify the calculations  for the system by expressing it as a with a singular mass.It is called reduced mass because the result is always lesser than both the masses. The result is the product of both masses, derived by the sum of the two masses. The derivation of which is explained below

Explanation of derivation ( This part is written on my own)

1. Given that the electron and the nucleus are on opposing sides of the rotational centre, one of the coordinates is negative and the other is positive. Since the centre of rotation is at the origin, the mass of the particle is inversely proportional to the the distance from the centre.
2. Given that it is a rotating body, the nucleus and the electron can be described as point masses as they are miniscule objects circular in shape rotating the centre. The quantity that correlates the mass and radius of the rotation is the Moment of Inertia 
3. The momentum of the mass and the nucleus is the same to create a zero net momentum to keep its motion rotational and not translatory. 

Citations 

Arthur Beiser, Concepts of Physics, 2nd edition, units 4.7 and 8.6