I admit I trusted your math; you seem to be off by a factor of 4:

  You have: 510.1e6km^2/1073741824/1073741824
  You want: cm^2
   * 4.4244122
   / 0.22601872

Strangely enough, units lacks area_earth, so I used the number from https://iere.org/what-is-the-area-of-the-earth/

:D

I was starting with the length of the equator and assuming a spherical cow^Hplanet.

Did you perhaps use the diameter of the earth rather than the radius?

#PiIsWrong

https://www.tauday.com/

  You have: (40075km/tau)^2*4*pi/1073741824/1073741824
  You want: cm^2
   * 4.434018
   / 0.22552908