# Gravitational Potential Energy

on . Posted in Classical Mechanics

Gravitational potential energy, abbreviated as $$PE_g$$, also called, gravitational energy, is the energy an object possesses due to its position within a gravitational field.  It's a type of potential energy associated with the height of an object above a reference point, such as the Earth's surface.  Gravitational potential energy is an important concept in physics and is used to describe the energy stored in an object based on its position in a gravitational field.

Gravitational potential energy is a scalar quantity, meaning it has magnitude but not direction.  It's important to note that the reference point for gravitational potential energy can be chosen arbitrarily, but it's common to use the Earth's surface as the reference point.

When an object is raised to a higher height within a gravitational field, it gains gravitational potential energy.  The energy is stored in the object and can be released when the object falls back to a lower height.  For example, when you lift an object, you do work against gravity and increase its gravitational potential energy.  When you release the object, its potential energy is converted into kinetic energy as it accelerates downward.  Gravitational potential energy is often encountered in scenarios involving falling objects, such as objects dropped from a certain height or objects on an inclined plane.  It's a concept that's used in various fields, including physics, engineering, and environmental science.

### Gravitational Potential Energy formula

$$U = m \; g \; h$$     (Gravitational Potential Energy)

$$m = U \;/\; g \; h$$

$$g = U \;/\; m \; h$$

$$h = U \;/\; m \; g$$

Symbol English Metric
$$PE_g$$ = gravitational energy $$lbf-ft$$ $$J$$
$$m$$ = mass $$lbm$$ $$kg$$
$$g$$ = gravitational field $$t\;/\;sec^2$$ $$m\;/\;s^2$$
$$h$$ = height $$ft$$ $$m$$