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These are formulas for the circumference of a circle of given radius on the surface of the earth, measured in miles and in kilometers, with the radius of the circle being the arc of a great circle.
For example, as the earth's radius is 3959 miles, its circumference is 24875 to the nearest mile. If one goes 1/4 that, or 6219 miles in any direction, the locus is a circle which can be said to have a radius of r = 6219 miles. 2*pi*3959*sin(6219/3959) where the sine function uses radians gives the circumference of that circle: in this case the 24875-mile circumference of the earth, as 1/4 of the way around the earth, as the radius of the circle along the earth's surface produces a great circle as the circumference. That's the largest circle there can be on the surface. |
