What Determines Gravitational Potential Energy?

[Harry17]

Homework Statement

When considering 2 masses in space, both of mass M and radius r separated by a large distance, is their kinetic energy (ie loss of gravitational potential energy) =(GM^2)/(2r) or is it twice that value?

When you calculate the gravitational potential energy, is that the GPE of the whole system or of the individual object, and the total gravitational potential energy is 2 times that value?

Relevant Equations

GMm/r

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[PeroK]

Good question! How much of this can you work out yourself?

 

[Harry17]

Intuition tells me that that’s the gravitational potential energy of the system- but I’m unsure. As a little exercise I considered a free and a stationary mass and reasoned that the free mass finishes with all the energy, which is equal to the loss of GPA. This led me to think that the total kinetic energy of the system with 2 free masses is equal to the gravitational potential, but my teacher argues the contrary. Any light you could shed on this would be appreciated, thanks

 

[PeroK]

Intuition tells me that that’s the gravitational potential energy of the system- but I’m unsure. As a little exercise I considered a free and a stationary mass and reasoned that the free mass finishes with all the energy, which is equal to the loss of GPA. This led me to think that the total kinetic energy of the system with 2 free masses is equal to the gravitational potential, but my teacher argues the contrary. Any light you could shed on this would be appreciated, thanks

Yes, that's a valid argument. If you hold one mass in place, then that restraining force does no work, so all the GPE goes into the KE of the second mass. You can calculate the work done more easily (as only one mass is moving) by integrating the force. This does indeed equal the usual formula for potential energy.

To be clear:

$-\frac{Gm_1m_2}{r}$

Represents the total GPE of a two body system. Not only in cases where $m_1 >> m_2$.

 

[Harry17]

Much appreciated, thank you