Specific potential energy

In classical mechanics and gravitational physics, massic gravitational potential energy (MGPE) is a fundamental concept that relates to the gravitational potential a body possesses due to its position in a gravitational field relative to a reference point. This energy is associated with the gravitational force acting on a body and its displacement within the gravitational field. It depends on the height of a body and the strength of the gravitational field. The term "massic" in this context refers to the gravitational energy per unit mass.

Definition
The massic gravitational potential energy (MGPE) of an object is defined as the gravitational potential at a location which is the gravitational potential energy (GPE) at that location per unit mass (m):
 * $$MGPE = {GPE\over m}$$

In some situations, the equations can be simplified by assuming a field that is nearly independent of position. For instance, in a region close to the surface of the Earth, the gravitational acceleration, g, can be considered constant. In that case, the difference in potential energy from one height to another is, to a good approximation, linearly related to the difference in height (∆h): $$MGPE \approx g\Delta h.$$

Massic gravitational potential energy is typically measured in Joules per kilogram (J/kg) in the International System of Units. The dimensional formula for massic gravitational potential energy is [L]²[T]-2, consistent with energy measurements.

Key Concepts

 * Frame of reference: The choice of reference point is arbitrary but is crucial for determining the potential energy. Commonly, the Earth's surface is chosen as a reference, and heights are measured vertically above it.
 * Zero Potential Energy at Infinity: As an object moves infinitely far away from the gravitational source, its potential energy approaches zero. This choice simplifies calculations and is a convention in many physics problems.