Most people think of the Earth as being a sphere. For most purposes that’s close enough, but it’s actually a spheroid, something close to but not precisely a perfect sphere. It bulges in the middle (as so many of us do) due to its spin, the Moon’s gravity warps it, the continents and oceans distort the shape. And the surface gravity changes with all this too; it’s different on top of the highest mountain, for example, compared to its strength in Death Valley.

So if you could map out the average shape of the Earth’s gravity, a shape where the gravity is the same no matter where you stood on it, what would it look like?

It would look like this:

That is a (somewhat exaggerated for easy viewing) map of the Earth’s geoid, produced by the European Space Agency’s GOCE satellite. A good way to think of the geoid is the shape a global ocean would take if it were governed only by gravity, and not currents or tides or anything else. If the Earth’s gravity were a little stronger in one place, water would flow toward it, and if it were weaker water would ...