How is the length of the shadow of a pole useful for determining the latitude of a place?

Answer 1

I believe it is credited to Eristothenes a greek scholar. ANyways it is not so simple but involves algebra and triginometry etc.

ANyways I have to refresh my memory but I believe he had come across some papers from another scholar who was located somewhere very south of his location and that this person wrote that at noon on the longest day of the year a stick in the ground casts no shadow. THus knowing where the sun was exactly over head (WEll roughly actualy) he could compute the relation of that location to his by placing a stick in the ground at a time of day that the sun is at its highest point and measure the shadow. Then the math.

Oh and using this knowledge Eristothenes gave use the longitudes and latitudes as well as the proof of a round earth (if I remember right)

Anyways the math is like this set a stick straight up and down and at the time of day where the sun is at its highest point you measure the shadow. This measurement and the hight of the stick are plugged into this equation

S_=_H_tan(_L-((tilt)_*_sin(360degrees_d_/365)_)">S= H tan( L-((tilt) * sin(360degrees d /365) )

S is length of shadow, H is pole height, tilt is the relationship of earths axis related to its orbit around the sun which is 23.5 degrees, and d is amount of days from the vernal equinox and L is the latitude we are looking for.

As you can see its better to just look on a map because thats alot of work when your trying to find your location. Thank god for Google maps.

Actually it is pretty neat being able to do this. You can throw your measurements into a computer program to do the math and then try and see how close you get to the actual location.

He was able to determine the circumfrence of the earth to within 1 percent of what we know it to be today.