The flyby anomaly and the effect of a topological torsion current

•Determines the general condition of equilibrium of a rotating gravitational and/or electromagnetic system.•New dynamical equation of motion with an unforseen topological torsion current.•The topological torsion current explains the anomalous acceleration detected in spacecrafts.•It may be the missing link between linear and angular motions.

A new variational technique determines the general condition of equilibrium of a rotating gravitational or electromagnetic system (or both) and provides a modified dynamical equation of motion from where it emerges a so-far unforseen topological torsion current (TTC) (Pinheiro, 2013) [63]. We suggest that the TTC may explain, in a simple and direct way, the anomalous acceleration detected in spacecrafts during close planetary flybys. In addition, we theorize that TTC may represent a novel relationship between linear momentum and angular motion through the agency of a vector potential.