The Flyby Anomaly in an Extended Whitehead’s Theory

In this paper, we consider an extended version of Whitehead s theory of gravity in connection with the flyby anomaly. Whitehead s theory is a linear approximation defined in a background Minkowski spacetime, which gives the same solutions as standard general relativity for the Schwarzschild and Kerr metrics cast in Kerr Schild coordinates. For a long time and because it gives the same results for the three classical tests perihelion advance, light bending and gravitational redshift it was considered a viable alternative to general relativity, but as it is really a linear approximation, it fails in more stringent tests. The model considered in this paper is a formal generalization of Whitehead s theory, including all possible bilinear forms. In the resulting theory, a circulating vector field of force in the low velocities approximation for a rotating planet is deduced, in addition to Newtonian gravity. This extra force gives rise to small variations in the asymptotic velocities of flybys around the Earth to be compared to the recently reported flyby anomaly.