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The question asks us to determine the length of a path on the surface of the earth connecting two locations having the same longitude.
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A =
(2r)pi * (# degrees in the arc/360)
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r = radius of arc on the surface the earth = rearth =6378 km (# degrees in the arc/360) = by looking at the picture next to the question we intuitively know what we will walk along half of any great circle connecting the North and South poles. Let's compute the number of degrees between the poles mathematically: # degrees in arc = lat2 - lat1 = (90 N) - (90 S). In order to subtract these two numbers, they must be expressed in terms of the same units - we may remember that (1) degree South is equal to (-1) degree North, so (90 S) = (-90 N) lat2 - lat1 = (90N) - (-90N) = 90 N + 90 N = 180 deg. |
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All units cancel except for km, so A will be in km, the unit for distance appropriate to the problem. |
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