# Do there exist reasonable numbers on the density/radius/mass of the various geological layers of the Earth?

I've been doing some math on the radius of the core (inner core in particular), and I keep getting what look like nonsense results. The composition is supposedly nearly all iron, close enough to it anyway... and I've been using (avg) densities as high as 13,000kg/m3. However, even with density this high I can't get a lower radius than about 2500km. This is using a 0.16 mass for the inner core.

Google returns a radius of 1220km for the inner core. It also returns a diameter of 1220km for the inner core.

I went so far as to reimplement this an an Excel spreadsheet to double check my code, and I get consistent results.

Is there a good source for the (rough is fine) densities, mass, and radii of the geological layers? I don't trust Google and Wikipedia at this point, and even if I find the answer somewhere else I won't know for sure if they're even close to correct.

One model that will help you is the admittedly dated (1981) Preliminary Reference Earth Model. It provides density models for the inner and outer core as functions of distance from the center of the Earth: $$\rho = \begin{cases} 13.0885 - 8.8381 x^2 & \quad \phantom{000}0\phantom{.0} \le r \le 1221.5 \\ 12.5815 - 1.2638 x - 3.6426 x^2 - 5.5281 x^3 & \quad 1221.5 \le r \le 3480.0 \end{cases}$$ where

• $$\rho$$ is the density in grams per cubic centimeter,
• $$r$$ is distance from the center of the Earth to the point of interest in kilometers, and
• $$x$$ is the normalized radius: $$x\equiv\frac r {6371}$$.

Note that this results in a slight density discontinuity at the boundary between the inner and outer core (1221.5 km). That's intentional. There have been later upgrades to the PREM, but the PREM is where it all starts.

Reference:

Dziewonski, Adam M., and Don L. Anderson. "Preliminary reference Earth model." Physics of the earth and planetary interiors 25.4 (1981): 297-356.

• To confirm though, 1220km is definitely the accepted boundary between the two? Roughly at least? My formula must have some sort of flaw in it then. – John O Nov 27 '18 at 2:18
• @JohnO - It's 1221.5 km according to the PREM. – David Hammen Nov 27 '18 at 6:37