Luc, you're absolutely right. However, TAS/10 is easier to work out than TAS/8 and since an approximation is all that's desired, I'd stick with the easier math.
Re-entry. I'm not being a smart-ass and you're not being smart. Since g is an acceleration, the SI units are meters per second squared. The ^ is often used to indicate "raised to the power" so ^2 is squared, not square root. As far as the variation of g with location on the planet, you are correct. I'll leave it to you to calculate how this pertains to the AOB formula.