Britannica Sources used in this answer

How is an equipotential surface connected to the geoid?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

Diagram showing the deflection of the vertical from the geoid to the ellipsoid or spheroid, with labeled lines for geoid, spheroid, rock surface, ocean, and geoid height in a geology context. — geoid Deflection of the vertical from the geoid to the spheroid.

The geoid is defined as a specific equipotential surface of Earth's gravitational field. An equipotential surface is characterized by a constant potential function across its entire extent, which accounts for both the gravitational attraction of Earth's mass and the centrifugal repulsion resulting from the planet's rotation.12

The connection between the two is as follows:

Definition: The geoid is the particular equipotential surface that coincides with mean sea level over the oceans.12
Gravity: Because the geoid is an equipotential surface, the local direction of gravity is everywhere perpendicular (normal) to it.12
Practical Application: In geodesy, geodetic leveling relies on this relationship; a spirit level is set tangential to an equipotential surface, allowing for the measurement of elevations relative to the geoid.2

While the geoid is mathematically an equipotential surface, it is irregular rather than a simple geometric shape due to variations in Earth's internal density and mass distribution.12