A spheroid is an Ellipsoid

(1) 
with two Semimajor Axes equal. Orient the Ellipse so that the and axes are
equal, then

(2) 

(3) 
where is the equatorial Radius and is the polar Radius. Here is the colatitude, so take
to express in terms of latitude.

(4) 
Rewriting
gives

(5) 

(6) 
so

(7) 
If , the spheroid is Oblate. If , the spheroid is Prolate. If , the spheroid degenerates to a Sphere.
See also Darwinde Sitter Spheroid, Ellipsoid, Oblate Spheroid, Prolate Spheroid
© 19969 Eric W. Weisstein
19990526