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As far as I understand given a certain latitude the length of a degree of longitude is constant.

So using any distance calculator (I use Mathematica here) this equals: (circumference of the earth) 

GeoDistance[{0, 0}, {0, 1}]*360 = 40075km  
GeoDistance[{0, 0}, {0, 90}]*4 = 40075km

However, if we change the latitude to 15° for example, this happens: 

GeoDistance[{15, 0}, {15, 1}]*360 = 38718.1km  
GeoDistance[{15, 0}, {15, 90}]*4 = 38372.7km

Are these roundoff errors? Which one is correct?

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  • I wonder why this only happens on 15-degree. I´d expected the same for equator as semi-axes are of different lengths. – HimBromBeere Mar 7 '16 at 11:43
  • this also happends when I assume a spherical model of the earth: At 15° latitude: 1°*360=38666.2km, 90°*4=38321.8km – Sebastian Lehmann Mar 7 '16 at 12:20
  • You are calculating with rhumb line ( en.wikipedia.org/wiki/Rhumb_line ), so along the lat/long grid – Giacomo Catenazzi Mar 7 '16 at 13:37
  • @GiacomoCatenazzi No, not the rhumb line, which means crossing at the same angle. When you move from point A on a given latitude to point B on the same latitude, following the great circle, you leave from point a at x degrees and arrive at B at -x degrees. – Tom Brunberg Mar 7 '16 at 13:50
  • @TomBrunberg - yes, and the great circle is the answer to the question (and the answer is already accepted). But it seems that OP used something like the Rhumb line to calculate the distances (360 times walking one 1 degree), which caused interpretation problems. – Giacomo Catenazzi Mar 7 '16 at 13:58
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When you calculate the distance between two points it means the distance following the great circle through the points. It is not the same as the latitude "line" (or parallels). On the northern hemisphere the great circle bends northward. Think about the distance between 45°, 0° and 45°, 180° the shortest distance goes via the north pole. See here for an explanation of great circle distance.

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  • Thank you for your answer. So the first calculation 38718.1km for 15° latitude matches the question: "what is the circumference of a given latitude "line"?" better. – Sebastian Lehmann Mar 7 '16 at 13:36
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    Better than the second one, but neither matches the circumference at 15° lat. exactly. GeoDistance is not the correct function to use. – Tom Brunberg Mar 7 '16 at 13:43

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