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.

在这项研究中，我们通过推导扩展的测地线和测地线偏差方程，分析了非局部时间动能概念的几个几何方面，这些方程是分析潮汐和月球引力的基础。我们已经使用这些方程来研究月球的非局地潮汐效应。据观察，非定域性对引力潮汐场产生了更高阶的修正，因此导致了月球漂移率的改变。我们已经评估了 GPS 卫星由于潮汐势引起的最大长期漂移率，并将结果与​​从时空探索者和量子等效空间测试太空任务获得的近地任务以及最近的一些相对论研究进行了比较。获得了非局部时间参数的数值估计，虽然它很小，