Gravitational Potential Energy

Mechanics · 1853

Equation: U = mgh (near a surface); U = −GMm/r (in general)
Field: Mechanics
Year: 1853

Symbols

U potential energy · m the mass raised · g the local gravitational acceleration · h height above a chosen zero · G the gravitational constant · M the attracting mass · r distance between centres

Significance

Energy stored by position in a gravitational field: what a raised weight, a reservoir behind a dam or a satellite in a high orbit can give back. The mgh form is the −GMm/r form linearised near a planet's surface. Rankine named it in 1853. Hydroelectric turbines run on the first form; escape velocity and the vis-viva equation on the second.

Machines

Pelton Wheel Francis Turbine Kaplan Turbine

Requires

Work

Required By

Conservation of Mechanical Energy Escape Velocity Hydraulic Power

Referenced by

equation

Conservation of Mechanical Energy Escape Velocity Hydraulic Power Work

machine

Francis Turbine Kaplan Turbine Pelton Wheel

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.