We saw that gravitational potential energy is relative. In other words, one must

Question

We saw that gravitational potential energy is relative. In other words, one must define a zero height, or reference position, and give potential energies relative to this reference position. Normally, the reference position is the ground. Is this choice arbitrary, or is there an inherent advantage in choosing the ground as the reference position? There are other forms of potential energy, such as chemical potential energy or spring potential energy. Do all forms of potential energy require a defined reference value, or is the need for a reference unique to gravitational potential energy?

Explanation / Answer

The general expression for gravitational potential energy arises from the law of gravity and is equal to the work done against gravity to bring a mass to a given point in space. Because of the inverse square nature of the gravity force, the force approaches zero for large distances, and it makes sense to choose the zero of gravitational potential energy at an infinite distance away. The gravitational potential energy near a planet is then negative, since gravity does positive work as the mass approaches. This negative potential is indicative of a "bound state"; once a mass is near a large body, it is trapped until something can provide enough energy to allow it to escape. The general form of the gravitational potential energy of mass m is:

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