This thesis devoted to research the dynamics of satellites in binary and multiple systems of small bodies. The basis of the study is the unique computer simulation performed by the author, and observations of asteroids in near-Earth space received on OMT-800 telescope in Astronomical Observatory of Odessa I.I. Mechnikov National University. In the thesis used an analytical calculation of stability of satellites movement in binary and triple asteroid systems. The purpose of the thesis is to study the dynamics of satellites, asteroids, implementation methodologies of determination the expansion coefficients of the gravitational field of asteroid components and research contribution of periodic disturbances in the annual evolution of asteroid systems orbits. The main methods: optical astrometric observations of asteroids, computer modeling of a binary and multiple asteroid systems based on numerical integration of the equations of motion in the coordinates by Everhart fifteenth order. For interpretation of the obtained values, periodogramial analysis used. Implemented new software to search for unknown objects in the Solar system, thus improving penetrating capability of the telescope OMT-800 from 19 Mag to 21 Mag. As a result of survey observations of binary and multiple Solar system bodies two new small bodies was discovered. One of them identified as previously lost asteroid. Conditions of systems gap calculated for 168 binary and multiple systems of Solar system small bodies. 10 orbital, 26 spin-orbital and 28 spin-spinal resonances founded in selected binary and multiple systems. The first time calculated the mass, the semi-major axis, the orbital period, resonances of hypothetical shepherd satellite of the asteroid (10199) Chariklo. The first time five coefficients of expansions of gravitational field in spherical functions calculated for selected asteroid systems. Not all values are consistent with results previously obtained in previous work. Probably this connected with difference of data and methods of obtaining them. The numerical model of motion was built for systems of binary and multiple small bodies of the Solar system. The model takes into account gravity of the Sun and the major planets, small bodies' asymmetry, the sunlight pressure considering the shadow function. The model allows to find some of the features of the evolution of satellites orbits The numerical model approbated on binary and multiple small bodies of the Solar system: (45) Eugenia, (87) Sylvia, (90) Antiope, (66391) 1999 KW4, (134340) Pluto, (136108) Haumea, (136617) 1994 CC, (153591) 2001 SN263, (385446) Manwe. Obtained changes Keplerian orbital elements for range 100 years and 1000 years generally confirms the results obtained by other authors. Annual changes in certain Keplerian orbital elements founded. For all orbital elements calculated values of periodical changes and suggested possible causes of their origin. Also, found in the same periodic oscillations in Keplerian orbital elements of the same satellite. Based on the developed model of asteroid system became possible to obtain photometric characteristics of the system observed from Earth. Comparison of asteroid light curves with model values will identify structural features and physical properties of surfaces of small bodies. Keywords: Asteroid system, satellite shepherd, resonances in asteroid systems, orbital evolution of asteroids satellites.
