Jun 2018

This problem is now closed. Keep an eye out for the Sept Issue Problem

A Problem of Global Proportions

What geodetic latitude represents 75% of the GRS 80 ellipsoid’s volume from South to North? Determine to nearest second.

grs80 b


   Sol'n    Date    Bonus    Total  Name   Date Rec'd     Comments
10 4
Norm Hanson 18 Jun  Slightly off because Norm used an incorrect semi-minor axis value and computed the geocentric latitude.
2 8 5  15  Larry Schmit  02 Jul  Larry admitted his “son Tim did most of the work.” They attempted a triple integral but their solution was a little short on details. Their latitude (also geocentric), was off by quite a bit.

What’s the difference between geodetic and geocentric latitude? Nothing, if you’re on a sphere. On an ellipsoid, the geocentric latitude, Ψ, is the angle from the semi-major axis to a line connecting the surface point and semi-major and -minor axes intersection. The geodetic latitude, Φ, is the angle from the semi-major axis to the normal through the surface point (a normal is perpendicular to the ellipsoid).


They are related through the equation:


At 0° and 90° N and S, geodetic and geocentric latitude are equal.

Problem Solution  


updated 20 Aug '18