Monday, February 9, 2015

Calculating a rough estimate of the Earth's radius from the old definition of meter

I sometimes have a hard time remembering the radius of the Earth. This tip shows how to derive the rough value if you don't remember the actual number.

According to Wikipedia, the 'Metre' was previously defined as follows:
"The other approach suggested defining the metre as one ten-millionth of the length of the Earth's meridian along a quadrant; that is, the distance from the Equator to the North Pole."
If we approximate the Earth as a perfect Circle, then according to the definition above, the Circumference (C) of the Earth would be 4 times 10 Million meters i.e.
C =  40 Million meters.
Circumference C and Radius R of a circle
From the standard circle equation and the circumference of the Earth (C) above, we can quickly derive the approximate radius (R) of the Earth i.e.

Solving for R = 0.5 * C / Pi, we get the Earth's radius of roughly 6370 kilometers, which is not far from the more accurate 6371 Km value.

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