Suppose, we know the length of the shadow of an object at some known time.

Can we use the this information to find position of the object (the longitude )?

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I deleted some argumentative comments. – David Z Nov 19 '11 at 1:28

Not without extra information...

If you know the length of the shadow and the time of day, you can't figure out the object's location. But you CAN narrow it down to a circle on the earth's surface, a circle with the sun at the center. If the shadow length happens to be exactly zero, of course, the circle reduces down to a point--the only point on the earth's surface where the sun is directly overhead at that moment.

If you know the length of the shadow and the latitude, then you can narrow down the longitude to two points.

If you know the length and direction of the shadow, you can locate the object (longitude and latitude) uniquely.

All this assumes the person is standing on a flat surface. If they might be on a slope, you can't infer anything.

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Does anyone know any research paper or example of this being done? I remember somebody mentioning it the show, Numbers. They manage to pinpoint a criminal through a video he took – Alexandre Cassagne Oct 27 '13 at 10:07
Can you say how to narrow down it to circle , with just knowing the time and length of shadow . "the mathematical calculations please " – gkshindia Jan 10 '15 at 15:07