Does Gravitational Potential Energy Apply to Dual Massive Particles?

[chuy]

Hi,

We know that the gravitational potential energy of a mass m over the Earth is:

$$-G\frac{mM_E}{r}$$

But the Earth is very heavy, ¿if $$m\approx M$$ the gravitational potential energy of a system of two particles also is:

$$U(r)=-G\frac{mM}{r}$$ ?

Bye!

 

[Astronuc]

If m = M_E = M, then the potential energy of a binary Earth system would be $$U(r)=-G\frac{M^2}{r}$$.