What is $\phi '$ in orbital mechanics?
This appears to be the geocentric latitude ($\psi$), which is the angle between the equatorial plane and the point on the surface of the ellipse. It can be calculated from the geodetic latitude (also known as the geographic latitude) ($\phi$) and the eccentricity of the ellipse ($e$):
$$\psi(\phi)=\tan^{-1}\left(\left(1-e^2\right)\tan\phi\right)$$
If $e=0$, then the two lattitudes are the same, because the focus is at the center of the ellipse.



Image courtesy of Wikipedia user Wmc824 under the Creative Commons Attribution 3.0 Unported license.

It might make more sense to use this latitude to describe the position of an orbiting object, but the vector from the focus to the object's position $(r,\theta)$ is perpendicular to the tangential component of the object's velocity vector, meaning that the geodetic latitude may be better.