Calc Eclipse Any Loc: What Softwares Do?

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Prasanna Suman
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How can I calculate eclipse (any), for any location on earth? Not using any software, because I know that. But I want to know what these softwares do?
 
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The ancient people would use the Saros cycle to compute eclipses. Google for that. I don't know how accurate the ancients were. I'm guessing that they knew what dates the eclipses would occur on, and approximately what part of the world. But to get modern-day predictions (i.e. Shanghi will be 122 km north of centerline, and will receive 5:18 seconds of totality beginning at 11:42 AM), you'll need a computer.

I wrote an eclipse-predictor program for DOS using algorithms from a book. It was quite accurate. It would agree with the official predictions within minutes and a few kilometers. I didn't understand the math I borrowed. The code was thousands of lines long.
 
Thanks tony873004,
I read about Saros cycle and other ancient method used by Hindus. I actually wanted to know the modern method which the softwares use. Can I get a suggestion of a web page? Google's results were a bit flat. :(
 
This book will give you the math in computer code (BASIC). I can't find my copy at the moment, but the documentation is minimal. He gives a brief explanation as to what he's doing, but for the most part, the code is not documented. So you just have to trust that his math works (and it does!)

https://www.amazon.com/dp/052138995X/?tag=pfamazon01-20

Thinking about it, you probably can do it without a computer, but I expect it is lengthy. Even before the 20th century, people traveled to see eclipses and transits, so the methods had to be pretty good.
 
Thanks tony873004,
That's great, because I know is BASIC. Can I get the source code of your file, if I am not troubling you too much.
Thanks again.