Stop avoiding. Research please.
Here is the page on timeanddate that describes how to use their solar data:
https://www.timeanddate.com/astronomy/about-sun-calculator.htmlFrom that page:
"Accuracy
Times are rounded to the nearest minute and should generally match closely with those listed in the annual Astronomical Almanac published jointly by H.M. Nautical Almanac Office in the U.K. and the Naval Observatory in the U.S.
A sample set of 150 records consisting of times for sunrise, sunset, and start and end times for civil, nautical, and astronomical twilight was compared with times listed in The Astronomical Almanac for 2007. Only two differed, both by only one minute, which means that just over 1.3 percent were different in that sample set."
And as for the Almanac mentioned, there is more info on Wikipedia:
https://en.wikipedia.org/wiki/Astronomical_AlmanacFrom that page:
"The Astronomical Almanac is the direct descendant of the British and American navigational almanacs. The British Nautical Almanac and Astronomical Ephemeris had been published since 1766, and was renamed The Astronomical Ephemeris in 1960. The American Ephemeris and Nautical Almanac had been published since 1852. In 1981 the British and American publications were combined under the title The Astronomical Almanac."
More info is here:
http://astro.ukho.gov.uk/nao/publicat/asa.htmlSo these publications have been used by navigators and astronomers for 250 years to accurately predict the position of the sun, moon and other celestial objects. As you probably know, before GPS and similar technologies, sailors and explorers used celestial navigation to successfully navigate the world. In order for such a system of navigation to work, you need to know where the sun and other celestial objects will be at a specified time to a fairly high degree of accuracy, so these almanacs were tested over hundreds of years and found to be accurate. And furthermore, for the hundreds of years that celestial navigation has proven to be so reliable, it was based on the geographic position of celestial bodies over a globe. That entire system of navigation is based on the round earth model.
Here is an excerpt from this page on Wikipedia about celestial navigation:
https://en.wikipedia.org/wiki/Celestial_navigation"Celestial navigation is the use of angular measurements (sights) between celestial bodies and the visible horizon to locate one's position on the globe, on land as well as at sea. At a given time, any celestial body is located directly over one point on the Earth's surface. The longitude of that point is known as the celestial body’s geographic position (GP),
the location of which can be determined from (a year long observation of the stars at that location and subsequent shared) tables in the Nautical or Air Almanac for that year." (emphasis added)
So the almanacs were initially created from repeated observations until the calculators became accurate enough to be reliable.
Seems like a pretty reliable system overall. Do you see any flaws in their process?