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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.

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