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Using the approach of autonomous Hamiltonian dynamical system, we attempt toestimate the as yet unknown upper limit on the size of the galactic halosurrounding galaxies (lenses). The key to determine the size of the halo is todetermine the maximum radius up to which stable material circular orbits areadmissible. We shall illustrate the approach by considering a solution of theWeyl gravity containing a halo parameter $\gamma$. The upper limit for severalobserved lenses are calculated for a typical value of $gamma$ for definiteness,with and without the cosmological constant $\Lambda $. These lenses (all havingEinstein radius $R_{\text{E}}\approx 10^{23}$ cm) consistently yield an upperlimit $R_{\text{max}}^{\text{stable}}$($\simeq 4.25\times 10^{27}$ cm) insidethe de Sitter radius only when $\gamma$ is \textit{negative}, while a positive$\gamma$ yields $R_{\text{max}}^{\text{% stable}}$ always exceeding the deSitter radius.

Upper Limit on the Size of Galactic Halo via Hamiltonian Approach