[Math] Determining the distance between two points on the surface of the earth.

differential-geometrygeometry

Question is simple:

  1. Does the elliptical shape of the earth affect its radius? (Yes!!?)

  2. If it is true: How?

  3. How can I determine the exact distance between two points on the earth with this influence?

Notice: When I measure the distance between two points (the arc length) on any circle the length radius is unique at any point. So what about the earth? The equatorial radius of earth (from the center of the earth to the equator) is larger than the polar radius.

Also:

Can I use $d= r$ $\Delta \theta$ to determine distance between two points on the surface of the earth ?

Best Answer

In answer to question 3. Computing distance on an ellipsoid of revolution (oblate or prolate) is addressed in "Algorithms for geodesics". The algorithms given there are available in several different languages using GeographicLib. The methods are essentially exact for $|f|<1/50$ where $f$ is the flattening. (There's a C++ version of the algorithms which works for arbitrary values of $f$.)

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