What best defines the geoid?

The geoid is best defined as the irregular shape the surface of the ocean takes under gravity. This definition reflects that the geoid represents an equipotential surface of the Earth's gravity field, essentially depicting how the Earth's surface would appear if the oceans were adjusted to follow the gravitational pull of the Earth without influences like winds or tides.

In practice, while the geoid is not a perfect or smooth surface, it closely approximates mean sea level and takes into account variations in Earth's gravitational field. These variations arise from factors such as the Earth's topography and density differences within the Earth, which affect gravity.

The notion of it being a constant height across all regions is misleading, as the geoid varies significantly due to these gravitational differences. A perfect mathematical surface suggests an idealized surface, rather than the actual physical and uneven shape defined by the geoid. Similarly, describing the geoid as the physical shape of the Earth's surface does not accurately convey its specific role in representing gravitational potential rather than a direct topographical reference.