Flyby Anomaly in the Variation Principle of General Relativity

The anomalous velocity deviation in the osculating planetary flyby attracts enough attention as a problem of General Relativity. In connection of rotating weak field massive source the Lense Thirring metric is diagonalized to find the equation of motion from action invariance Hamilton principle in pure relativistic theory. The computation for near Earth flyby shows energy anomaly over the asymptotic in and out velocity obeying Anderson's empirical formula.