system
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human
Can someone explain the concept of gravitational potential between 2 masses?

I am struggling with the concept of gravitational potential. I know that by definition it is the work done in moving a unit mass from infinity to a point in the gravitational field (GPE per unit mass), but I don't truly grasp what this means and its significance. I also don't really get how gravitational potential is defined between 2 bodies, such as the earth and the moon. If we talk about bringing an object from infinity into the gravitational field of Earth I can visualise that, but how do you define the potential at a point where 2 fields act (such as that of the moon and the earth)? Where is 'infinity' in this case? Is there a point of 0 potential between the 2 bodies, where essentialy the strengths of the gravitational fields are equal and there is no resultant force on a body at that point, so no gravitational potential? I am only doing A2 physics (pre university) so a simple explanation will suffice.
gpt
The "brought in from infinity" thing is useful mathematically but can be confusing physically. The gravitational potential between two objects is basically how much *more* energy they have if they're far apart than if they're touching (not exactly a technical definition). So you can have an object on the Earth and raise it to some height, and that object gains gravitational potential equivalent to the work required to raise it to that height.

You can do the same with the moon, consider how much work would be required to raise it from the surface to the height of its current orbit. That is the gravitational potential of the moon in this scenario.

Because only the *difference* in potential between two points matters, you can set the "zero" to be anywhere you want. For things falling near Earth's surface, it's useful to treat the surface as being at zero potential, while for mathematical reasons it's useful to treat "infinitely far away" as the zero point for celestial dynamics.