E. D. Kuznetsov

Light pressure effect on the orbital evolution of objects moving in the neighborhood of low-order resonances

The hardware-software complex of the SBG telescope of the Kourovka astronomical observatory of the Ural Federal University is described. The area-to-mass ratio of high-orbit objects was estimated from the results of positional observations at the SBG telescope. Positions and sizes of resonance zones are determined from the numerical simulation results depending on the area-to-mass ratio in the case of low-order resonances (1 : 1, 1 : 2, and 1 : 3). Secular perturbations of semimajor axes of orbits, caused by the Poynting-Robertson effect, are estimated in the neighborhood of low-order resonance zones at different area-to-mass ratios.

Expansion of the Hamiltonian of the planetary problem into the Poisson series in elements of the second Poincare system

The Hamiltonian of the N-planetary problem is written in the Jacobi coordinates using the second system of Poincare elements. The Hamiltonian is expanded into the Poisson series for the four-planet system. The computer algebra system Piranha is used for analytical transformations. Obtained expansions provide the Hamiltonian expression accuracy up to the third degree of the small parameter for giant planets of the Solar System and up to the second degree of the small parameter for extrasolar planetary systems. The ratio of sums of masses of the planets to the star mass can be selected as a small parameter.

The Hori–Deprit method for averaged motion equations of the planetary problem in elements of the second Poincaré system

We consider an algorithm to construct averaged motion equations for four-planetary systems by means of the Hori–Deprit method. We obtain the generating function of the transformation, change-variable functions and right-hand sides of the equations of motion in elements of the second Poincaré system. Analytical computations are implemented by means of the Piranha echeloned Poisson processor. The obtained equations are to be used to investigate the orbital evolution of giant planets of the Solar system and various extrasolar planetary systems.

Effect of the high-order resonances on the orbital evolution of objects near geostationary orbit

The area-to-mass ratio of high-orbit space objects is estimated on the basis of positional observations from the SBG telescope at the Kourovka astronomical observatory of the Ural Federal University. The properties of regions where high-order resonances are located are analyzed. The position and sizes of the resonance zones depending on the area-to-mass ratio of objects are determined on the basis of numerical modeling. It is shown that a system transits through the high-order resonances due to secular perturbations of the semimajor axis under the Poynting-Robertson effect. The high-order resonances weakly influence the formation of the stochastic trajectories. The stochastic properties are mostly manifested in evolution of the semimajor axis of the orbit.

Orbital Evolution of the Sun–Jupiter–Saturn–Uranus–Neptune Four-Planet System on Long-Time Scales

The four-planet problem is solved by constructing an averaged semi-analytical theory of secondorder motion by planetary masses. A discussion is given of the results obtained by numerical integration of the averaged equations of motion for the Sun–Jupiter–Saturn–Uranus–Neptune system over a time interval of 10 Gyr. The integration is based on high-order Runge–Kutta and Everhart methods. The motion of the planets is almost periodic in nature. The eccentricities and inclinations of the planetary orbits remain small. Short-period perturbations remain small over the entire interval of integration. Conclusions are drawn about the resonant properties of the motion. Estimates are given for the accuracy of the numerical integration.

On the long-period evolution of the sun-synchronous orbits

The dynamic evolution of sun-synchronous orbits at a time interval of 20 years is considered. The numerical motion simulation has been carried out using the Celestial Mechanics software package developed at the Institute of Astronomy of the University of Bern. The dependence of the dynamic evolution on the initial value of the ascending node longitude is examined for two families of sun-synchronous orbits with altitudes of 751 and 1191 km. Variations of the semimajor axis and orbit inclination are obtained depending on the initial value of the ascending node longitude. Recommendations on the selection of orbits, in which spent sun-synchronous satellites can be moved, are formulated. Minimal changes of elements over a time interval of 20 years have been observed for orbits in which at the initial time the angle between the orbit ascending node and the direction of the Sun measured along the equator have been close to 90° or 270°. In this case, the semimajor axis of the orbit is not experiencing secular perturbations arising from the satellite’s passage through the Earth’s shadow.

Dynamical evolution of objects on highly elliptical orbits near high-order resonance zones

Both analytical and numerical results are used to study high-order resonance regions in the vicinity of Molnya-type orbits. Based on data of numerical simulations, long-term orbital evolution are studied for objects in highly elliptical orbits depending on their area-to-mass ratio. The Poynting–Robertson effect causes a secular decrease in the semi-major axis of a spherically symmetrical satellite. Under the Poynting–Robertson effect, objects pass through the regions of high-order resonances. The Poynting–Robertson effect and secular perturbations of the semi-major axis lead to the formation of weak stochastic trajectories.