Gravitomagnetic effects in conformal gravity

Gravitomagnetic effects are characterized by two phenomena: first, the geodetic effect which describes the precession of the spin of a gyroscope in a free orbit around a massive object, and second the Lense-Thirring effect which describes the precession of the orbital plane about a rotating source mass. We calculate both these effects in the fourth-order theory of conformal Weyl gravity for the test case of circular orbits. We show that for the geodetic effect a linear term arises which may be interesting for high radial orbits, whereas for the Lense-Thirring effect the additional term has a diminishing effect for most orbits. Circular orbits are also considered in general leading up to a generalization of Kepler's third law.