Calculating the distance to the Sun requires careful, accurate observations

That's true, but with the scientific method, we also need to complete the rest of the equation. Testable, observable (i see a circle up there, not a sphere), measurable and repeatable.

So, since observations are not actually measuring the distance or the size, how did they come up with the number 93 Million and not 1 Billion or a hundred thousand? A laser? A bounced radio signal?