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Thermal activity of the Enceladus Vadym Kostiuk A lot of heart was found on Saturn’s moon Enceladus by means of spacecraft Cassini which significantly exceeds accounts which emerge from the conditions of thermal equilibrium of the solar radiation. With help of it, there is an inner satellite ocean of water in the southern polar region of the moon which is the source of the geysers. The aim of our research is the dynamic study of the geysers of Enceladus the substance of which is the main source of E ring of Saturn and calculation of a tidal acceleration and comparison with the results of tidal acceleration of other physically similar satellites of giant planets. In addition we tried to identify the typical trajectory of particles which fly out from the geysers of the south pole of Enceladus and partially get in E ring of Saturn. For this purpose we determined appropriate vector of speed of release of substance from the geysers of Enceladus based on the integral of energy which links the speed of the motion on the orbit with chronocentric length and width of the E ring. Besides we tried to access the possible inclination of orbits particles of the substance which was erupted from the geysers of Enceladus near its south pole based on the integral of moment of impulse. To illustrate the possible trajectories of motion of the particles after getting out from the gravitation field of Enceladus we built a computer model based on the classic task of two bodies. We used the method of spheres of action of planets in the external gravitation field of the Sun.