X Axis In Real Life
Consider as an example superimposing 3D Cartesian coordinates over all points on the Earth (i. e. geospatial 3D). What units make sense? Kilometers are ... Read more a good choice, since the original definition of the kilometer was geospatial. . . 10,000 km equalling the surface distance from the Equator to the North Pole. Where to place the origin? Based on symmetry, the gravitational center of the Earth suggests a natural landmark (which can be sensed via satellite orbits). Finally, how to orient X, Y and Z axis directions? The axis of Earth's spin provides a natural direction strongly associated with "up vs. down", so positive Z can adopt the direction from geocenter to North Pole. A location on the Equator is needed to define the X-axis, and the Prime Meridian stands out as a reference direction, so the X-axis takes the direction from geocenter out to [ 0 degrees longitude, 0 degrees latitude ]. Note that with 3 dimensions, and two perpendicular axes directions pinned down for X and Z, the Y-axis is determined by the first two choices. In order to obey the right hand rule, the Y-axis must point out from the geocenter to [ 90 degrees longitude, 0 degrees latitude ]. So what are the geocentric coordinates of the Empire State Building in New York City? Using [ longitude = â73. 985656, latitude = 40. 748433 ], Earth radius = 40,000/2Ï, and transforming from spherical --> Cartesian coordinates, you can estimate the geocentric coordinates of the Empire State Building, [ x, y, z ] = [ 1330. 53 km, â4635. 75 km, 4155. 46 km ]. GPS navigation relies on such geocentric coordinates.Read less
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