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I can't seem to find this algorithm, if it exists. Can you calculate the longitude and latitude of where you are standing based on the date and the angle of the sun? Also, would the algorithm work for any date past or future?

Thanks for any help, AD

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Any longitude calculus needs a clock with the time of a place of known longitude, being it a mechanical or an astronomicl clock. Sun does not fulfill the role. The question as stated has no answer. –  Envite Jan 20 at 0:21
    
@Envite: My impression was that date was used in the sense implying that the local time is known. –  Alexey Bobrick Jan 20 at 14:09
    
@AlexeyBobrick Local time is of no help, you can get that from the Sun. You need time of a place of known longitude. Greenwich time, e.g. –  Envite Jan 20 at 15:43
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@Envite: Speaking of longitudes, you are right of course. For latitude the answer to your comment is yes and no. Yes, if you can wait and see how the Sun moves, and no in the opposite case. If you can wait, you can get the latitude from the position of the Sun at the noon. If you can only know the immediate position of the Sun, you would also need the local time to get the latitude. –  Alexey Bobrick Jan 20 at 16:41
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@AlexeyBobrick Yes, my comment is about longitude only. I fully agree with you about latitude. –  Envite Jan 20 at 16:44
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1 Answer

What you are looking for is the navigation method used by ships and aircraft before the advent of GPS. It requires not only an instrument for measuring the angle between the sun or a star (such as Polaris) and the horizon, but also an accurate time measurement, and charts that can be used to interpret the numbers. And of course an accurate chronometer -- you'll need to know the time at Greenwich Obervatory, in London.

The traditional instrument used for determining this angle is the sextant. Here is an article describing the use of a sextant for deterining one's position:

http://www.ehow.com/how_7562747_use-nautical-sextant.html

I suppose that an algorithm for doing what you are asking is available where good sextants are sold - as to the charts, well, perhaps there are downloadable charts somewhere.

Also, here is a good article on determining latitude and longitude by the stars. Latitude is what a sextant will tell you, longitude is determined differently. For that you need two clocks: one set to GMT; one set to your local UTC time (NOT your timezone time). The method is described here: How to Calculate Longitude. Which brings us to the question of how to calculate your local solar time, which is described in this article How to Calculate Solar Time. Clearly you can't use this for navigation - it's convenient for human economics, but not finding your location.

Just to make it clear why you can't use local civil time for determining longitude is that the solar time is nearly the same on both Hawaii and Kodiak islands, but Hawaii's civil time is one hour after Kodiak's. And China stretches some 5,026 kilometers across the East Asian landmass, which is about 4 hours of solar time, but it all has the same civil time.

This question might better be asked in the Sailing SE. Oh, wait, there isn't one, yet.

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