Potential energy of a system

[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 $$U(r)=-G\frac{M^2}{r}$$.

 

[kyle8921]

Hello,

Yes, the gravitational potential energy of a system of two particles can be calculated using the same formula as the potential energy of a single mass over the Earth. This is because the gravitational potential energy is dependent on the mass of the objects and their distance apart, not just the mass of the Earth. So, if the masses of the two particles are similar to the mass of the Earth, the potential energy of the system will also be similar to the potential energy of a single mass over the Earth. However, it is important to note that this formula assumes a point mass and does not take into account any other factors such as the shape or distribution of the masses.