On 2015-04-18 19:37, Warren D Smith wrote:
I had known that Aristarchus computed a good estimate of the size of the Earth using trigonometry. But I had not known that he also computed the sizes of, and distances to, the Moon & Sun. However, he got those numerically quite wrong, due to bad input data (his mathematics was ok). Nevertheless, he did correctly realize that the Sun was much bigger than the Earth, which led him to suggest the "Copernican" idea that the Sun was central with Earth rotating around it, rather than the reverse. Wikipedia says JW Draper contends he then ordered the planets correctly by distance to the central Sun.
When the Sun and crescent Moon are both visible, you can get a pretty good idea that the Sun is 400 times farther (and 400 times bigger) by the exact dimensions of the crescent, vs the Sun-Moon apparent angular separation. --rwg