Nonlocal tidal effects of the moon and numerical estimation of the secular drift rate for a GPS satellite

Abstract

In this study, we have analyzed several geometrical aspects of the concept of nonlocal-in-time kinetic energy by deriving the extended geodesic and geodesic deviation equations which are the basic stone to analyze tidal and lunar gravitational forces. We have used these equations to study nonlocal tidal effects of the moon. It was observed that nonlocality-in-time generates higher-order corrections to the gravitational tidal field and hence results on a modification of the drift rate of the moon. We have evaluated the maximal secular drift rate for a GPS satellite due to the tidal potential and compared the results with near Earth missions obtained from the Space-Time Explorer and QUantum Equivalence Space Test space mission and some recent relativistic studies. The numerical estimate of nonlocal-in-time parameter is obtained, although it is small, it proves that nonlocality-in-time may have besides the kinetic aspect a geometrical feature.