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2.7 Shortest Distance to the Poles or Equator

Note: if you cannot remember what a meridian is, revise notes for 2.6 Modelling the World.

Finding the Shortest Distance using the Meridian

  • The shortest path between any point on the surface of the earth to the north or south pole, or the equator is along the meridian intersecting that point. By taking the section of the meridian between the relevant pole or equator and the point being solved for, we find an arc whose length is the shortest distance between the pole or equator and the position. The angle of that arc can be found using the latitude of that location.
  • We can modify our formula for arc length (from 2.1 Circles and Arcs) to be specific for this situation:

s_{\text {north pole }}=\frac{\pi 6400\left(90-l_{N}\right)}{180}=\frac{\pi 640\left(90-l_{N}\right)}{18}

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