Explicitly computing geodetic coordinates from Cartesian coordinates

Earth, Planets and Space

Table 1. Solution of p in the region of the polar axis.

Region	Real number solutions	Complex number solutions	Right real number solution
Outside the evolute	P₁, P₂, P₃, P₄	none	P ₁
On the evolute	P₁, P₂, P₃, P₄ (P₂ = P₄)	none	P ₁
Inside the evolute*	P₁, P₂	P₃, P₄	P ₁

Note: * denotes that it does not include the region near the center of the Earth.