If I recall correctly, it will still be a prolate ellipsoid, at least up to some critical rotational speed. You might be able to estimate the limiting condition by considering a thin disk and comparing the gravitational attraction of an element on the edge of the disk to v^2/R. -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Henry Baker Sent: Tuesday, February 08, 2011 11:20 PM To: math-fun@mailman.xmission.com Subject: [math-fun] Earth = mathematical ellipsoid ?? One of the standard GPS models of the Earth is that of an "ellipsoid", where a cross-section through the N-S pole is an ellipse. http://en.wikipedia.org/wiki/Reference_ellipsoid But I seem to recall that a fast-rotating body of liquid produces a funny discus-like form. Given a molten liquid of "constant density" -- e.g., mercury -- held together by Newtonian gravity, what mathematical shape does it assume as it rotates faster & faster? How fast can it rotate before the ellipsoidal shape no longer applies? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun