A geoid is a mathematical object exactly representing the

Earth's surface, with all of its bumps and divots.

In

geodesy, the geoid is more carefully defined: This is an

equipotential surface representing

mean sea level around the Earth. This is not

*quite* the same as an

ellipsoid: There are all sorts of

anomalies in the Earth's gravity field, caused by

continents among other things, each of which affects the shape of the geoid. The Earth is sort of

pear-shaped.