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I’ve been looking for a resource for a long time but haven’t found much. What I am curious about is how people 500+ years ago predicted solar / lunar eclipses (

I’ve been looking for a resource for a long time but haven’t found much. What I am curious about is how people 500+ years ago predicted solar / lunar eclipses (for example). Columbus was able to persuade some islanders that he was some sort of god by making the moon darken/turn red at a predicted time due to an almanac he happened to have. Would I be able to make the same prediction using only math and whatever instruments could measure the positions of the sun and moon that accurately? What instruments and equations do I use?

fluoridation 3y ago
If you're starting from scratch you would need some way to determine the apparent position of the Sun and the Moon. Probably some kind of long tube that you can rotate precisely. Ancient people would use buildings for that purpose. Then you need to make observations probably over several, possibly many, years to determine the Earth's perihelion and apohelion (at least their timing), the length of the year, and the precession. For the Moon you determine its orbital period and plane, and if you want to know whether the eclipse will be partial or total from a given location you also need the perigee and apogee (again, at least their timing). Once you have all the data you find all the times when the Moon crosses the ecliptic plane (about once every 14 days), which are the only times when eclipses can happen. You discard the times when the Moon will not be aligned with the Earth and the Sun. You will be left with a handful of times per year when an eclipse is possible. If the eclipse is solar you compute the orientation of the Earth to see where it will be visible from. It's all trigonometry and linear algebra.
Miiko 3y ago
My understanding is that at Columbus time they did not measured sun / moon positions, but instead based their predictions on the eclipse cycles - if you have long enough record of past eclipses, you can notice that they are not random but the same timing sequence repeats after some time: https://en.wikipedia.org/wiki/Eclipse_cycle https://en.wikipedia.org/wiki/Eclipse_cycle

fluoridation 3y ago

If you're starting from scratch you would need some way to determine the apparent position of the Sun and the Moon. Probably some kind of long tube that you can rotate precisely. Ancient people would use buildings for that purpose. Then you need to make observations probably over several, possibly many, years to determine the Earth's perihelion and apohelion (at least their timing), the length of the year, and the precession. For the Moon you determine its orbital period and plane, and if you want to know whether the eclipse will be partial or total from a given location you also need the perigee and apogee (again, at least their timing). Once you have all the data you find all the times when the Moon crosses the ecliptic plane (about once every 14 days), which are the only times when eclipses can happen. You discard the times when the Moon will not be aligned with the Earth and the Sun. You will be left with a handful of times per year when an eclipse is possible. If the eclipse is solar you compute the orientation of the Earth to see where it will be visible from. It's all trigonometry and linear algebra.

Miiko 3y ago

My understanding is that at Columbus time they did not measured sun / moon positions, but instead based their predictions on the eclipse cycles - if you have long enough record of past eclipses, you can notice that they are not random but the same timing sequence repeats after some time: https://en.wikipedia.org/wiki/Eclipse_cycle https://en.wikipedia.org/wiki/Eclipse_cycle