**Earth Shape**

Earth shape

- The earth's equatorial and polar radiis vary by 22 km out of 6400, or about 1/300. The equatorial radius a is about 6378 km, and the polar radius b about 6356 km (we actually know them to about cm precision).
- Total relief, Mt. Everest (+9 km) to Marianas trench (-11 km), about 20 km, so also about 1/300
- Geoid relief only ±100 m, due to mass imbalances in the mantle.

The sphere is actually very good approximation, but as a tribute to our precision we must consider departures from a sphere for any map of an area smaller than a continent, and anytime we need precise coordinates such as rocket launches (where we also need to know the gravity field), property surveys, and locating things like oil wells.

**Spheroid**: adequate for small scale maps of the entire world or a
hemisphere.

**Ellipsoid**: more complex mathematics,
defined as part of the horizontal **datum**

The Geoid (gravity equipotential surface, mean sea level) has many oceanographic applications, and is how we currently have complete bathymetric coverage in the oceans.

*Last revision *
*11/13/2017*