Theory question 112
Latitude and LongitudeP and Q are two points on latitude 55°N and their longitudes are 33°W and 20°E respectively. Calculate the distance between P and Q measured along (a) the parallel of latitude; (b) a great circle. (Take π = 22/7 and radius of the earth = 6400km)
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Model answer
Difference in longitude = 33° + 20° = 53°
(a) Radius of the parallel = 6400 cos 55° = 3671 km
Distance = 53/360 × 2 × 22/7 × 6400 × cos 55° ≈ 3397 km (about 3400 km)
(b) Chord PQ = 2 × 6400 cos 55° × sin 26.5° ≈ 3277 km
Half the angle at the earth's centre: sin(θ/2) = 3277 ÷ (2 × 6400) = 0.2560, so θ ≈ 29.7°
Great-circle distance = 29.7/360 × 2 × 22/7 × 6400 ≈ 3316 km
Explanation
Along a parallel use the smaller radius R cos(latitude); along a great circle use the full earth radius.