On June 20 at 4:44 CDT in the northern hemisphere the sun will be vertically overhead at a geographic location in the northern hemisphere. If you are located precisely on a longitudinal line North of that 'zenith position' at some arbitrary northern latitude, you will have the opportunity to calculate the approximate circumference of the earth, assuming that it is spherically shaped.

...The two key numbers that are necessary are the angle that the shadow of a vertical pole or stick forms at precise!y 4:44 CDT, and also the geographic distance between the po!e location and the overhead sun zenith position, which is necessarily located further south of the pole/stick location.

The method was first described by the Greek mathematician Erathosthenes:

Erathosthenes.

An explanatory diagram:

Consequently, R, the radius of the earth, is found to be approximately = d/(tan A),

and the circumference C=2π R.

Where:

d is the longitudinal geographic distance between the two points.

A is the angle made by the shadow of the pole at the northern geographic position.

... It may be that this method would be more accurate when a shorter d measurement is possible, as opposed to a vertical stick positioned at an extreme northern latitude. The southern zenith position for my particular location is at approximately 23 degrees North latitude, and my shadow angle measurement position is at about 30 degrees North latitude. I seem to be located on about the same longitudinal line as the sun zenith position, thereby allowing a reasonably simple estimate of d.

...The two key numbers that are necessary are the angle that the shadow of a vertical pole or stick forms at precise!y 4:44 CDT, and also the geographic distance between the po!e location and the overhead sun zenith position, which is necessarily located further south of the pole/stick location.

The method was first described by the Greek mathematician Erathosthenes:

Erathosthenes.

An explanatory diagram:

Consequently, R, the radius of the earth, is found to be approximately = d/(tan A),

and the circumference C=2π R.

Where:

d is the longitudinal geographic distance between the two points.

A is the angle made by the shadow of the pole at the northern geographic position.

... It may be that this method would be more accurate when a shorter d measurement is possible, as opposed to a vertical stick positioned at an extreme northern latitude. The southern zenith position for my particular location is at approximately 23 degrees North latitude, and my shadow angle measurement position is at about 30 degrees North latitude. I seem to be located on about the same longitudinal line as the sun zenith position, thereby allowing a reasonably simple estimate of d.

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