Monday, August 13, 2012

Navigating by Latitude and Longitude

  Navigation is easier if one can use just latitude and longitude to specify positions. Though the grids are not quite square there is the equivalent of the Pythagorean Theorem for distance and a correction for the true heading can be found. Here are some simplified formulas that can be used. The flattening for the ellipsoid is f, the geocentric latitude is φ and the geographic latitude is φg.
  The formula for the heading correction has a factor, κ, which is a simple function of the scaling factors in the Pythagorean Theorem. The following calculations give the corrected headings and distances for the Google Mars points used to find Curiosity's position. Points were chosen that could be easily spotted on both Google Mars and the photographic images of the landing site. The first three are associated with the nearby craters and the forth appears to be a large boulder or sarsen of some sort. It seems to cast a good shadow. It also might make a good marker.

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