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.

• Received 1 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.084008