Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8239Research ArticleEstimation of the Relativistic Phase-Shift Formula Applicability to Jupiter’s Satellite SystemAnisimovA VInstitute of Gravitation and CosmologyAnisimovav1987@rambler.ruPeoples’ Friendship University of Russia15032014313814408092016Copyright © 2014,2014In this work an estimate of the relativistic phase shift of space body satellite rotation observed from a remote planet is compared with the classical perturbation of the satellite orbit by other space bodies. The calculations are exemplified by Jupiter’s satellites. A satellite of the Amalthea group interacting with the Galilean satellites is chosen. The interaction of this satellite with the rest of its group is negligible as compared to that with external satellites, since the mass of any internal satellite is much less than that of external ones. A gravitational interaction of Jupiter’s satellite system has been considered within the weak-interaction approximation for inner satellites neglecting Galilean satellites’ action on the phase. Jupiter’s system is chosen since it has many satellites whose mutual interaction is rather strong due to small distances between them and their large mass, besides Jupiter is rather close to us, so it is possible to observe directly its satellites in a telescope and to check data empirically. A gravitational deviation of the chosen inner satellite is calculated to match against the value obtained from the relativistic phase shift formula. The relativistic shift between real and observable phases is given by a formula obtained by A. P. Yefremov in the framework of Quaternion theory. The formula for correction to the phase is a relativistic effect of time delay. The classical correction is estimated using celestial mechanics. An effect of the Galilean satellites on the inner satellites is considered. The phase correction is compared with the value predicted by Quaternion theory of relativity. In conclusion applicability of this formula has been discussed.relativistic effectsphase shiftJupiter ’s satellite systemAmaltheaquaternionic relativityformulae estimationрелятивистские эффектысдвиг фазысистема спутников ЮпитераАмальтеякватернионная теория относительностипроверка формулы[Ефремов А. П. Кватернионные пространства, системы отсчёта и поля. - М.: РУДН, 2005.][Yefremov A. P. Quaternions: Algebra, Geometry and Physical Theories // Hypercomplex Numbers in Geometry and Physics. - 2004. - Vol. 1.][Ландау Л. Д., Лившиц Е. М. Теоретическая физика. Т. I - «Механика». - М.: Наука, 1988.][Yefremov A. P. Quaternion Model of Relativity: Solutions for Non-Inertial Motions and New Effects // Advanced Science Letters. - 2008. - Vol. 1.]