We illustrate how the application of autonomous Hamiltonian dynamical system can definitively fix a sign for an otherwise indefinite sign of a certain astrophysical parameter. To illustrate it, we shall consider the Mannheim-Kazanasde Sitter solution of Weyl conformal gravity containing the parameter γ, which is believed to be significant in the galactic halo gravity. However, the sign of γ has so far been ambiguous. The strategy we adopt to fix it is to look for a finite maximum radius up to which the halo supports stable material circular orbits inside the de Sitter radius. The maximum radius for several observed lenses are calculated for both signs of γ, and with the observed value of cosmological constant Λ. These lenses (all having approximately the Einstein radius R E ≈ 10 23 cm) consistently yield a maximum radius (R max stable ≃ 4.25 × 10 27cm) inside the de Sitter radius of the universe only when γ is negative, while a positive γ yields R max stable always exceeding the de Sitter radius. © 2012 IACS.