What is the arc length formula and how would it be used to find the radius of the earth?

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What is the arc length formula and how would it be used to find the radius of the earth?

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Answer 1 · 2016-04-17T13:35:14

If arc length (seemingly horizontal distance) between two locations on the equator, with longitude difference $θ^{o}$ $theta^o$ , is S km, the equatorial radius is $(\frac{S}{θ}) (\frac{180}{π}) k m$ $(S/theta)(180/pi) km$

Explanation:

The formula used is (circular arc length) = radius X (angle subtended at the center in radian)
Sample data, for explication:

If two locations, near the equator, in Brazil, have longitudes $45^{o} W and 55^{o} W$ $45^o W and 55^o W$ and the distance in-between is 1100 km, S = 1100 km, $θ = 10^{o}$ $theta=10^o$ .

Equatorial radius $R = (\frac{1100}{10}) (\frac{180}{π}) k m$ $R = (1100/10)(180/pi) km$ = 6302 km.

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What is the arc length formula and how would it be used to find the radius of the earth?

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