What is the potential energy of a ball in a state of gravitational equilibrium?

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In a state of gravitational equilibrium, a ball experiences zero net force due to equal gravitational pulls from the Earth and the Moon. The potential energy of the ball can be calculated by considering the individual contributions from both celestial bodies. These potential energies are scalar quantities and therefore add together, rather than canceling each other out. Thus, the total potential energy of the ball is the sum of the potential energies from the Earth and the Moon. Understanding this concept is crucial for analyzing gravitational systems.
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Let's say we have three objects, moon, Earth and a ball.

Suppose that the ball is in a point in space such that the gravity from the moon cancels out the gravity from the Earth, so that the net force on the ball is zero. Also assume that the ball is at rest.

Then by Newton's laws, the ball will remain at rest.

My question: What is the potential energy of the ball? I can calculate the potential energy due to the moon and the potential energy due to the earth, but will they cancel each other out because they are due to opposing forces? Or do they add up?

Thanks.

BiP
 
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The potential energies are scalars--they add accordingly.
 

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