# Relation between GOCE gravity model and Earth shape

There are a couple of viral videos claiming that "NASA shows that Earth is shaped like potato". The source of such videos is 3D visualization of data collected by GOCE satellite (full animation, video by ESA with comments).

It still unclear to me what is shown on this animation. As I understand, the color represents gravity intensity, but what is represented by shape? My assumptions are:

• Earth shape (with sea level)

• Earth shape (with seabed level)

• A hypothetical shape taken by the ocean water under gravity forces only which is also interpolated across the continents

So what is the correct interpretation of this model? And also are surface bumps exaggerated on animation (as stated here)? Links to explanation by GOCE team or other experts are appreciated.

• @JCRM - Except it wouldn't shape the sea surface like that. The depictions of the geoid as an extremely misshapen potato are highly exaggerated. Imagine shrinking the Earth to the size of a basketball (or a globe). This would shrink the 21.4 km out-of-round nature of the Earth and the 20 km deviation between the bottom of the Marianas Trench and the top of Mount Everest to 0.4 millimeters, or about 5 human hairs. That's possibly noticeable. The 200 meter variations in the geoid height shrinks to 4 µm, or about the size of a bacterium. That's not noticeable at all. Aug 13, 2018 at 17:09
• @DavidHammen It is the sea level shape (the third os the OPs options) and as they represent deviations of +/1 100 meters, of course they are scaled.
– user20636
Aug 14, 2018 at 8:47
• The GOCE User Toolkit is available to download I would expect it is possible to generate a scale version using that
– user20636
Aug 14, 2018 at 9:08

The bumps in a depiction of the geoid aren't just exaggerated. They are vastly exaggerated.

The Earth is very close to spherical, with the largest deviation from spherical being the Earth's equatorial bulge. The North Pole is 21.4 km closer to the center of the Earth than are places at sea level at the equator. That's a tiny fraction (about 1/3 of 1%) of the 6378.137 km equatorial radius of the Earth. If you were playing with a volleyball that was out of round to this tiny extent, you would not notice it.

The next largest variations are mountains versus deep sea trenches. The deepest part of the Mariana Trench is 10.994 km below sea level while the peak of Mount Everest is 8.848 km above sea level, a difference of almost 20 km. These are local rather than global variations. The variations in a volleyball due the seams and little blemishes in the plates are much larger.

What the geoid attempts to measure is mean sea level. An Earth devoid of mountains, deep sea trenches, and continents would be covered by a globe-spanning ocean. The Earth's shape (mean sea level) would be very close to an ellipsoid if the underlying rock had the same density profile from any point all the way down to the core-mantle boundary. The equatorial bulge would still be there; this bulge results from the Earth's daily rotation.

The geoid height variations depicted in various images show the deviation of mean sea level from that idealized ellipsoidal shape. These variations are very small, ranging from about -100 meters to +100 meters. Notice how much smaller that range is compared to the variations between the deepest parts of the ocean and the tallest mountains or between the equator and the North Pole. The only way to depict these small geoid height variations graphically is to exaggerate them, and not just a little bit, but many, many times over.

• Relevant XKCD Aug 13, 2018 at 19:16
• Pet peeve, why say 'about 1/3 of 1%' when you can say 0.3% instead? Aug 14, 2018 at 11:24
• As a final remark, Scientific American article cites GOCE mission manager saying that amplification factor is 7000: blogs.scientificamerican.com/observations/… Aug 15, 2018 at 0:56