If gravity exists, and the Earth is subject to the force of gravity, this mathematical note from my planetary science book should apply to earth:
"In chapter 8 we will derive the following equation for the pressure of overlying material, measured at some distance r out from the center of a planet with uniform mean density p with radius R:
Pr = [(2*Pi*G*p^2)/3]*(R^2 - r^2)
Now consider a planetesimal in whose central region the strength of the material, is greater than the pressure exerted by the overlying material. (Note that the strength S and the pressure Pr have the same units, newtons/meter^2). As long as S exceeds Pr in the central region, the planetesimal will be strong enough to retain any irregular shape [a flat shape in this case] it might acquire, say, by collisional fragmentation. But if the planetesimal grows to a size such that Pr begins to exceed then the central material will be crushed and the planet can begin to assume the spheroidal shape of hydrostatic equilibrium. If we set Pr equal to S for material 20% of the way out from the center (an arbitrary choice for distance), the equation reduces to the following condition for the largest planetesimal radius RMax that can sustain a substantially irregular shape:
S = 1.34(10^-10)p^2*RMax^2
(assuming SI units)
We might expect the inner regions of a reasonably large planetesimal to be made either of moderately strong rock (like chondritic meteorites) or of iron (like iron meteorites). For these two cases we have the following conditions:
(1) For a rocky planetesimal [earth!], strengths of chondritic stone meteorite range from about 6 x 10 to 4 x 10^8 N/m^2 (Wasson, 1974), and corresponding densities range from 2500 to 3800 kg/m^3, respectively. Using a representative strength and density of 2 x 10^8 N/m^2 abd 3500 kg/m^3 we find
RMax = 349 km
(2) For an iron-cored planetsimal, using an iron meteorites strength of 4 x 10^8 N/m^2 (Wasson, 1974) and the iron density of about 7870 kg/m^3, we find :
RMax = 220 km
These calculations suggest that the largest irregular planetesimals might be expected to line the the diameter range of 440 to 700 km. This prediction, though based on a simplified analysis, is in excellent agreement with empirical data, where the largest irregular asteroids and satellites show a well-defined upper diameter limit in the range of about 360 to 600 km. "
Wasson, J.T. 1974. Meteorites. New York: Springer-Verlag.
From the book Moon and Planets by William K. Hartmann, 5th edition. Published by Thomson- Brooks Cole. ISBN - 0-534-49393-9