How accurate is approximating the Earth as a sphere?

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What level of error do I encounter when approximating the earth as a sphere? Specifically, when dealing with the location of points and, for example, the great circle distances between them.

Are there any studies on the average and worst case error compared to an ellipsoid? I'm wondering how much accuracy I'd be sacrificing if I go with a sphere for the sake of easier calculations.

My particular scenario involves directly mapping WGS84 coordinates as if they were coordinates on a perfect sphere (with the mean radius defined by the IUGG) without any transformation.



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