The great circle distance (D) between any two points P and A on the
sphere is calculated with the following formula:
cos D = (sin p sin a) + (cos p cos a cos
|dl|)
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p and a are the latitudes of P and A
-
|dl| is the absolute value of the difference
in longitude between P and A
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 |
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Calculate the great circle distance between Paris (P) and Austin
(A):
Paris, France (48° 52' N, 02°
20' E)
Austin, Texas (30° 16' 09" N, 97°
44' 37" W)
|
1. Convert to decimal degrees:
-
Paris: 48.87° N, 02.33° E
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Austin: 30.27° N, 97.74° W
|
| 2. cos D = [sin(48.87) * sin(30.27)] + [cos(48.87)
* cos(30.27) * cos(|-97.74 - 2.33|)] |
| 3. cos D = [0.753 * 0.504] + [0.658 * 0.864 * -0.174]
= 0.281 |
| 4. D = cos-1 (0.281) = 73.68° |
| 5. D = 73.68° * 111.23 kilometers/degree
= 8,195.44 kilometers (5,092.03 miles) |