The satellite is orbiting Earth in a fixed elliptical orbit. It must have 3D coordinates to account for whether a telescope on the Earth can see it (but not as part of these equations). The Earth is at/near one focus of this elliptical orbit. So I'm pretty much looking for something of this form where the equations are in terms of time since 'perihelion' and constants about the ellipse such as a, b, eccentricity, and so on: rho(t) = ... theta(t) = ... phi(t) = ... Thanks for all your help.