The gravitational potential energy of a two-particle system is derived

1.	The gravitational potential energy of a two-particle system is derived in this chapter as U = -Gm₁m₂/r. Does it follow from the equation that the potential energy for r = ∞ must be zero? Can we choose the potential energy for r = ∞ to be 20 J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r?
Answer» Yes. Since U is inversely proportional to r, at r = ∞ the gravitational potential energy must be zero. If we choose the potential energy at r = ∞ to be 20 J, we can not use this formula, because putting r = ∞, will not give the result 20 J. The required formula will be, U = -Gm_₁m_₂/r + 20.

The gravitational potential energy of a two-particle system is derived in this chapter as U = -Gm₁m₂/r. Does it follow from the equation that the potential energy for r = ∞ must be zero? Can we choose the potential energy for r = ∞ to be 20 J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r?

Answer»

Yes. Since U is inversely proportional to r, at r = ∞ the gravitational potential energy must be zero.

If we choose the potential energy at r = ∞ to be 20 J, we can not use this formula, because putting r = ∞, will not give the result 20 J.

The required formula will be, U = -Gm_₁m_₂/r + 20.

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