[math-fun] Aristarchus of Samos, 300 BC
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. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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
On Sat, Apr 18, 2015 at 8:44 PM, rwg <rwg@sdf.org> wrote:
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
I don't get it. How do you get any indication of the Sun's size relative to the moon? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Oh, now I see. Never mind. On Sat, Apr 18, 2015 at 9:00 PM, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Apr 18, 2015 at 8:44 PM, rwg <rwg@sdf.org> wrote:
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
I don't get it. How do you get any indication of the Sun's size relative to the moon?
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
On 4/18/2015 9:00 PM, Mike Stay wrote:
Oh, now I see. Never mind.
On Sat, Apr 18, 2015 at 9:00 PM, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Apr 18, 2015 at 8:44 PM, rwg <rwg@sdf.org> wrote:
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 I don't get it. How do you get any indication of the Sun's size relative to the moon?
Aristarchus estimated the ratio of the distance to the Sun relative to the distance to the Moon by measuring the angle between the Sun and Moon at half-moon. So the Moon, Earth, Sun formed a right triangle with the Moon at the right angle and the Earth-to-Sun leg as the hypotenuse. Brent
On 2015-04-18 22:06, meekerdb wrote:
On 4/18/2015 9:00 PM, Mike Stay wrote:
Oh, now I see. Never mind.
On Sat, Apr 18, 2015 at 9:00 PM, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Apr 18, 2015 at 8:44 PM, rwg <rwg@sdf.org> wrote:
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.
rwg>>>> 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 I don't get it. How do you get any indication of the Sun's size relative to the moon?
BMeeker> Aristarchus estimated the ratio of the distance to the Sun relative to
the distance to the Moon by measuring the angle between the Sun and Moon at half-moon. So the Moon, Earth, Sun formed a right triangle with the Moon at the right angle and the Earth-to-Sun leg as the hypotenuse.
Brent
______________________ That should have worked! An error analysis should show how bad his measurements had to be to miss by a factor > 20. How could it be that sensitive?
Once he knew the aspect ratio was > 18, despite living on the island of Pythagoras he could have punted the half-full constraint by using the small-angle, isosceles approximation on thinner, or even thicker crescents. If he had some way to measure them. I wonder if, like Archimedes, his writings were overwritten by Muslim prayers. Or earlier burnt by butthole Romans. --rwg
participants (4)
-
meekerdb -
Mike Stay -
rwg -
Warren D Smith