# 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. – 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