What? You're off by several orders of magnitude. The surface area of the earth is only 196 million square miles. Still very big, but nowhere near 510 trillion square miles.
The Earth's diameter is ~13000 km. Surface area is therefore 4 * pi * r^2 = 4 * pi * ((13000/2)^2) = 500 million square kilometres (which is, as you say, about 200 million square miles).
I suspect the parent is both confusing a million with a trillion and also miles with kilometres.
Neither. It's just such a habit to type miles. I meant 510 trillion square _meters_, which google and wolfram alpha tell me is correct.
In any case.. the reason I chose that is because that's probably close to a reasonable maximum single pixel resolution for tracking imagery. I wanted the scope of the problem to be obvious by choice of units; unfortunately, I screwed that part up. :(
I suspect the parent is both confusing a million with a trillion and also miles with kilometres.