confused about distances on the wgs-84 ellipsoid

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?

• I wonder why this only happens on 15-degree. I´d expected the same for equator as semi-axes are of different lengths. Mar 7, 2016 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 Mar 7, 2016 at 12:20
• You are calculating with rhumb line ( en.wikipedia.org/wiki/Rhumb_line ), so along the lat/long grid Mar 7, 2016 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. Mar 7, 2016 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. Mar 7, 2016 at 13:58

1 Answer

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.

• 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. Mar 7, 2016 at 13:36
• Better than the second one, but neither matches the circumference at 15° lat. exactly. GeoDistance is not the correct function to use. Mar 7, 2016 at 13:43