Theory question 109
Latitude and LongitudeTwo towns K and Q are on the parallel of latitude 46°N. The longitude of town K is 130°W and that of town Q is 103°. A third town P also on latitude 46°N is on longitude 23°E. Calculate: (i) the length of the parallel of latitude 46°N, to the nearest 100km, (ii) the distance K and Q, correct to the nearest 100km, (iii) the distance between Q and P measured along the parallel of latitude, to the nearest 10m. (Take π = 3.142, radius of the earth = 6400km).
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Radius of the parallel = R cos 46° = 6400 × 0.6947.
(i) Length = 2 × 3.142 × 6400 × 0.6947 = 27 938 km ≈ 27 900 km.
(ii) K (130°W) and Q (103°W): difference 27°. Distance = 27/360 × 27 938 = 2095 km ≈ 2100 km.
(iii) Q (103°W) and P (23°E): difference 103° + 23° = 126°. Distance = 126/360 × 27 938 = 9778 km ≈ 9780 km.
Distances along a parallel use the radius R cos(latitude); add longitudes on opposite sides of Greenwich.