Earlier quoted context omitted.
I admit it, I was applying Cunningham’s Law. Disappointingly(?), you came to the same answer.
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/
I was starting with the length of the equator and assuming a spherical cow^Hplanet.