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Question: 11 the shortest distance between two places on the surface...

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1.1 The shortest distance between two places on the surface of the earth is the Great Circle Distance, which, for a perfectly spherical earth, would be equal to the radius Reof the earth times the angle A subtended between vectors from the centre of the earth to the points on the surface Express the positions of points 1 and 2 on the surface of the earth in terms of Cartesian vectors about the centre of the earth, using 1 and фі to denote the latitude and longitude respectively for point 1 and likewise θ2 and φ2 for point2. Then take the dot product of the vectors to show that the cosine of the angle A is given by cos A-cos θ| cos θ2 cos (φ1-φ2) + sin θι sin θ2. Find the shortest distance in nautical miles between London (latitude 51.5° N, longitude 0) and Sydney in Australia (latitude 33.9° S, longitude 151.3° E) (Ans: 9170 nm)

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