# What's the distance between the center of mass and geometrical center of Earth (CM-CF offset)?

I asked the same question on Physics StackExchange site. I now know that there are several types of "center" and I can tell, I'm interested in the CM-CF offset (CM = geocenter, CF = center of figure).

Wu, Ray, and van Dam, "Geocenter motion and its geodetic and geophysical implications," Journal of Geodynamics 58 (2012): 44-61.

Based on Fig. 2 in the paper above, I calculated that the distance is 9 meters. However this 9 meters seems too small to me. In addition it's about geocenter motion, but on he vertical axis, it says "meters" and not "meters/year" or "meters / 1000 years" or something similar. On Fig. 5, it's clear that Δt = 1 month. But I don't understand what's Δt for Fig. 2. If there is at all...

I also found in this paper http://goo.gl/pPWD8l On page 174 it says that this offset is 0.8 km. However, it's 1995 data while the other article was published in 2012.

So I'm really confused now, I think I misunderstood something. I'm not a geophysicist, please help me out.

• If the Earth were a pure ellipsoid, these should coincide, so the difference would be due to mountains, continents, etc?
– user967
Mar 15, 2016 at 15:17
• If the Earth were a pure ellipsoid, CM and CF should not necessarily coincide, they could differ due to in homogeneous density, but yes the main difference would be due to mountains and continents. Mar 15, 2016 at 21:55
• Considering the center of mass of just Earth is often pointless. The fact is that when talking about the center of mass, we need to consider the barycenter (center of mass of two of more bodies that are orbiting each other) of the Earth-Moon system. In our case, the larger body, Earth, simply "wobbles" slightly, instead of appearing to orbit a common center of mass. The barycenter of the Earth–Moon system on average is located 4671 km from the center of Earth (inside Earth, as the planet has a radius of around 6378 km). Mar 18, 2016 at 1:02
• I'm asking about the Earth only system, without the Moon. Just read into the first paper I linked above, you can see that the CM of the Earth-only system is actually used in some cases Mar 18, 2016 at 20:47

There is no inconsistency between the 2012 paper and the older reference(s).

Fig. 2 arbitrarily sets all the components (x,y,z) of all the displacement vectors of all the centers to zero at the beginning of the time period (about 123,000 years ago).

Furthermore the 2012 article states:

The horizontal movement of topography associated with plate motion will then change the CF. Over time, these slow phenomena can create large offsets, up to hundreds of meters, between CM and CF. When the evolution of the internal load is reasonably inferred from other sources, then these processes may be able to explain a significant bulk of the current static offset between CM and CF.

Planetary Sciences, table 1.2, says the distance between CF and CM is 0.80 km, citing to Yoder 1995.

See also Evidence for convection in planetary interiors from first-order topography The Moon March 1973, Volume 7, pages 172-180

It has been known for some time that a center of mass-center of figure offset exists for the Earth (e.g. Jeffreys, 1962). From a spherical harmonic analysis of the Earth's topography with the oceans replaced by an equivalent mass of rock, Balmino et al. (1972) find the center of mass displaced by 1.1 km from the center of figure in the direction 145°W long and 42 ° S lat.

And from the NASA memorandum Reports of planetary geology program - 1981:

For Earth, with its combination of sialic ([denisty]~2.7) and simatic ([density] 3.0-3.3) crusts, the CF is displaced toward 41.6°N, 34.7°E, in the direction of the Eurasian shield, and close to the center of the continental province at 46°N and 27°E (Bills and Ferrari, 1978).