On the effect of ocean tides and tesseral harmonics on spacecraft flybys of the Earth

Abstract: The so-called flyby anomaly has encouraged several authors to analyze in detail the minor perturbative contributions to the trajectory of spacecraft performing a flyby manoeuvre. This anomaly consist of an unexplained increase or decrease of the asymptotic velocity of the spacecraft after a flyby of the Earth in the range of a few mm per second. Some order of magnitude estimations have been performed in recent years to dismiss many possible conventional effects as the source of such an anomaly but no explanation has been found yet. In this paper we perform a study of the perturbation induced by ocean tides in a flybying spacecraft by considering the time dependence of the location of the high tide as the Moon follows its orbit. We show that this effect implies a change of the spacecraft velocity of a few micrometers per second. We also consider the coupling of tesseral harmonics inhomogeneities and the rotation of the Earth and its impact of the spacecraft outgoing velocity. Significant corrections to the observed asymptotic velocities are found in this case but neither their sign nor their magnitude coincide with the anomalies. So, we can also rule this out as a conventional explanation.