Effective Potential Energy from Central Force Motion

[KT KIM]

Hi, I'm studying undergrad mechanics, Central force motion, Marion's book in specific,
Here, the Potential Energy is defined weird way (in my opinion though)

(μ is reduced mass)

So potential Energy becomes

Called "Effective Potential Energy"

But, I can't agree with calling it potential just because it has dimensions of energy.
Mathematically it is right. But intuitively, I have no idea where it came from. little help please.

 

[Simon Bridge]

But, I can't agree with calling it potential just because it has dimensions of energy.

... well you don;'t have to agree, just make sure you understand that this is the term commonly used so that you will understand it in future.

It's called an effective potential energy (as opposed to a potential energy) because it plays the same role as potential energy so it is potential energy like in it's effect. Can you think of a better term for it?

You can also tackle it this way - keeping the central coordinate system - how much work would you need to do to assemble the system described by the model?