The geoid does not precisely follow mean sea level, nor does it exactly correspond with the topography of the dry land. It is irregular like the terrestrial surface. It is bumpy. Uneven distribution of the mass of the planet makes it maddeningly so, because if the solid earth had no internal anomalies of density, the geoid would be smooth and almost exactly ellipsoidal. In that case, the reference ellipsoid could fit the geoid to near perfection and the lives of geodesists would be much simpler. But like the earth itself, the geoid defies such mathematical consistency and departs from true ellipsoidal form by as much as 100 meters in places.

### The Modern Geocentric Datum

Three distinct figures are involved in a geodetic datum for latitude, longitude, and height: the geoid, the reference ellipsoid, and the topographic surface. Due in large measure to the ascendancy of satellite geodesy, it has become highly desirable that they share a common center.

While the level surface of the geoid provides a solid foundation for the definitions of heights and the topographic surface of the earth is necessarily where measurements are made, neither can serve as the reference surface for geodetic positions.

From the continents to the floors of the oceans, the solid earth’s actual surface is too irregular to be represented by a simple mathematical statement. The geoid, which is sometimes under, and sometimes above, the surface of the earth, has an overall shape that also defies any concise geometrical definition. But the ellipsoid not only has the same general shape as the earth, but, unlike the other two figures, can be described simply and completely in mathematical terms.

Therefore, a global geocentric system has been developed based on the ellipsoid adopted by the *International Union of Geodesy and Geophysics (IUGG)* in 1979. It is called the *Geodetic Reference System 1980 (GRS80)*. Its semimajor axis, *a*, is 6378.137 km long and is probably within a few meters of the earth’s actual equatorial radius. Its flattening, *f*, is 1/298.25722 and likely deviates only slightly from the true value, a considerable improvement over Newton’s calculation of a flattening ratio of 1/230. But then, he did not have orbital data from near-earth satellites to check his work.

Here we have an image of three figures, one is the topographic surface of the Earth that we walk around on, and the next in the red dashed line is the ellipsoid, and the third in the blue wavy line is the geoid. The geoid doesn't follow mean sea level, doesn't correspond with a topographic surface. It's irregular. It does have peaks and valleys. It's bumpy because of the uneven mass of the planet. If the solid Earth didn't have these changes in density, the geoid and the ellipsoid would be the same thing. However, the geoid actually departs from the ellipsoid up to 100 meters in some places.

The figures involved in a latitude, and longitude, and height, are the geoid, the reference ellipsoid, and the Earth itself.

The goal is to have the reference ellipsoid, we use for satellite geodesy, to be geocentric. From the continents to the floors of the ocean, the solid Earth is too irregular to be represented by a simple mathematical statement. The geoid, sometimes under, sometimes above the surface of the Earth, has an overall shape that also defies any concise geometrical definition. However, the ellipsoid not only has the same general shape as the Earth, but unlike the other two figures can be described simply and completely in mathematical terms. That is why we use the ellipsoid as a reference. Therefore, a global geocentric system has been developed based on the ellipsoid adopted by the International Union of Geodesy and Geophysics. It's called the Geodetic Reference System, GRS 80.