Физика UDC 531.352, 53.01 Estimation of the Relativistic Phase-Shift Formula Applicability to Jupiter’s Satellite System A. V. Anisimov Institute of Gravitation and Cosmology Peoples’ Friendship University of Russia 6, Miklukho-Maklaya Str., Moscow, Russian Federation, 117198 In 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. <...> A satellite of the Amalthea group interacting with the Galilean satellites is chosen. <...> 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. <...> 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. <...> 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. <...> Key words and phrases: relativistic effects, phase shift, Jupiter ’s satellite system, Amalthea, quaternionic relativity, formulae estimation. 1. <...> They are: light ray deflection by gravity sources, time delay of the objects moving relative to the observer etc. <...> This work is devoted to estimation of the relativistic effect illustrated by Jupiter’s There exists a problem of determining space body coordinates due to a plethora of satellites. <...> Section 2 includes description of the algebra of quaternions and biquaternions and the main notions of General relativity in terms of hypercomplex number algebra. <...> Quaternions and Fundamentals of Quaternion Special Relativity formula for the relativistic shift. <...> The quaternion calculation is based on four units, Received 15th June, 2014. <...> Now we shall discuss in detail the fundamentals of the theory to find the final Anisimov A. V. Estimation of the Relativistic Phase-Shift Formula . . . 139 one is a scalar and three are vectors q1, q2, q3, satisfying the multiplication rules [2]: 1qk = qk1 = qk; qkql = −δkl +εkliqj. <...> In Einstein’s theory of relativity the interval is <...>