Envelopes for orbits around axially symmetric sources with spheroidal shape

We introduce a method to obtain the envelopes of eccentric orbits in axially symmetric potentials, $\Phi(R,z)$, endowed with $z$-symmetry reflection. By making transformation $z\rightarrow a+\sqrt{a^{2}+ z^{2}}$, $a>0$, we compute resulting mass density, referred here as \emph{effective density} $\rho_{\rm ef}(R,z;a)$, order calculate $Z(R)$ meridional plane $(R,z)$. find that they obey approximated formula $Z(R)\propto [\Sigma_{\rm ef}(R;a\approx 0)]^{-1/3}$, where $\Sigma_{\rm ef}(R;a)$ is integrated surface density associated ef}(R,z;a)$. As examples consider dynamics two potentials: monopole plus quadrupole and Kalnajs disc.