How can we know the radius of earth just by looking at sunrise?
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awesome question
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Lie down and face the horizon (supine), as soon as you see the very TOP of the Sun disappear below the horizon, start the STOPWATCH
Stand-up as quickly as possible
Now here is the fun part, watch closely. It is magic; the Sun will have miraculously reappeared above the horizon!
As soon as the TOP of the Sun disappears again, stop the STOPWATCH. (In our case it took about 11.5 seconds)
Now you know angle rotated by earth (Ɵ) in 11.5 seconds, and you know your height H, you can use a little trigonometry to calculate the radius of the Earth R.
H you know, Ɵ you know the only unknown is Rin this equation which is radius of Earth which can be calculated easily by putting values of known in the above equation.
cos(0. 04791666 degrees) = R / (R + H)
R = H * cos(0.04791666 degrees) / (1 – cos(0.04791666 degrees))
R = 6.22 * 106106 m (close to the actual value of 6.38 * 106106 m) = 6220 km
Stand-up as quickly as possible
Now here is the fun part, watch closely. It is magic; the Sun will have miraculously reappeared above the horizon!
As soon as the TOP of the Sun disappears again, stop the STOPWATCH. (In our case it took about 11.5 seconds)
Now you know angle rotated by earth (Ɵ) in 11.5 seconds, and you know your height H, you can use a little trigonometry to calculate the radius of the Earth R.
H you know, Ɵ you know the only unknown is Rin this equation which is radius of Earth which can be calculated easily by putting values of known in the above equation.
cos(0. 04791666 degrees) = R / (R + H)
R = H * cos(0.04791666 degrees) / (1 – cos(0.04791666 degrees))
R = 6.22 * 106106 m (close to the actual value of 6.38 * 106106 m) = 6220 km
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6220 km...................
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