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

Question

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

1 Answer

Impact of this question

2761 views around the world

You can reuse this answer
Creative Commons License

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.

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question