[tpfqrkkk] Earth surface area

Approximating the shape of the earth as an oblate ellipsoid, we use the following values from wikipedia (which cites IERS):
a=6378136.6 meter
c=6356751.9 meter
f=298.25642^-1

Note that the values are not consistent.  If we compute flattening from a and c, we get f=298.25701^-1.

We can compute eccentricity from c and a:
e = sqrt(1-c^2/a^2) = 0.081819221

Or we can compute it from flattening:
e = sqrt(2*f-f^2) = 0.081819301

We use the following formula from Wikipedia for the surface area of an oblate ellipsoid to compute the area of the Earth in square meters:
2*Pi*a^2*(1+(1-e^2)/e*atanh(e))
= 5.1006556e14 m^2
= 5.1006555e14 m^2
using the two different values of eccentricity computed above.

We have tried to use significant digits correctly.  The above two values of the earth surface area are considerably higher precision than typically reported values of earth surface area, which usually give only 2 significant digits.

We have not made any corrections for general relativity.