Conformal Weyl gravity and perihelion precession

We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric of the static, spherically symmetric solution discovered by Mannheim and Kazanas [Astrophys. J. 342, 635 (1989)]. To this end we employ a procedure similar to that used by Weinberg for the Schwarzschild solution, which has also been used recently to study the solar system effects of the cosmological constant Lambda. We show that besides the general relativistic terms obtained earlier from the Schwarzschild-de Sitter solution, the expression for the perihelion shift includes a negative contribution which arises from the linear term gamma r in the metric. Using data for perihelion shift observations, we obtain constraints on the value of the constant gamma similar to that obtained earlier using galactic rotational curves.