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The straight line distance between two points on the Earth
3D graphic showing the relative positions of Sylhet & Florida on the planet. [Graphic: A Ahad, Earth image courtesy: ESA] Consider a 3D rectangular system of coordinates (x,y,z) passsing through the centre of the Earth as origin and two points on the Earth's surface, as shown in the above illustration. If we ignore the effects of a quantity known as the 'geometric flattening' (f), which defines the deviations in the Earth's shape from that of a perfect sphere (value of f is small - 0.00335281), then a first order approximation for rectangular coordinates of each point is:- x=a*cos(Lt)*cos(Ln) y=a*cos(Lt)*sin(Ln) z=a*sin(Lt) And the distance, D, between two points (x1,y1,z1) and (x2,y2,z2) is then given by D=SQRT[(x1-x2)^2+(y1-y2)^2+(z1-z2)^2]. Where, in the first set of equations above, a is the Earth's radius (equatorially, this is 6,378 km) and (Lt, Ln) denote the latitude and longitude of each point. Taking average latitudes and longitudes for central Florida as (+28.5 deg, W81.5 deg) and Sylhet as (+24.7 deg, E91.5 deg), the straight line distance between them works out at roughly 11,385 km as a 'first order' approximation. [Back to main article - Florida 2003] "Earth-Science" projects home page 
Copyright © 2003 Abdul Ahad. All rights reserved.
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