Yeah, I skipped over that a bit quickly. In theory, you could use the discrepancy between your disappearing-ship estimate and Eratosthenes-shadow estimate to estimate how far away the Sun is, then use that estimated distance plus the Sun’s angular width to estimate its size, then compare that to Earth’s size (which you’ve got an independent estimate of from disappearing-ship). I don’t have a great sense of how well this would work in practice, because of factors like refraction messing with your disappearing-ship estimate.
I don’t understand how you go from “the Sun is very big” to “the Sun is much bigger than the Earth”? The Earth is very big too!
Yeah, I skipped over that a bit quickly. In theory, you could use the discrepancy between your disappearing-ship estimate and Eratosthenes-shadow estimate to estimate how far away the Sun is, then use that estimated distance plus the Sun’s angular width to estimate its size, then compare that to Earth’s size (which you’ve got an independent estimate of from disappearing-ship). I don’t have a great sense of how well this would work in practice, because of factors like refraction messing with your disappearing-ship estimate.