Nina A. Solovaya

Orbital evolution of Jupiter's 8th satellite

Abstract The orbitai evolution of Pasiphae,the 8th satellite of Jupiter, has been investigated. Its osculating orbit for the epoch 29 October 1983 was numerically integrated over the interval of 20,000 years. Within the investigated time interval also the question of the Hills stability has been studied. The Jacobian constant, generalized to the avegaged elliptic problem. calculated from position and velocities obtained by numerical integration, changes less then the order of 10−8 The dominant pertubations by the Sun to the satellite allow us to use the intermediate orbit of the averaged elliptic three-body problem for investigation of the evolutionary change in the motion of the satellite. The mean motion of the agreement of perijove and the ascending node of the satellite are defined by analytical formulae, using the osculating non-Keplerian ellipse with moving node and perijove, and changing eccentricity. The results obtained according to this theory are comparable with those calculated from the numerical integration.

An Extra-Solar Planet in a Double Stellar System: The Modelling of Insufficient Orbital Elements

The modelling of the insufficient orbital elements of extra-solar planets (EPs) re- volving around one component in a binary star system is investigated in the present paper. This problem is considered in the frame of the three-body problem using the analytical theory of Orlov & Solovaya (1998). In the general case, the motion is defined by the masses of the components and by the six pairs of the initial values of the Keplerian elements. For EPs, it is not possible to obtain the complete set of elements for the orbit, in particular, the ascending node and the angle of the inclination. So, it is possible the two different variants of orbital evolution of EPs depend on the initial conditions. In one case, the orbit is unstable. Using the stability conditions of Solovaya & Pittich (2004), which are presented by the angle of the mutual inclination of the orbits between the EP and distant star, we varied unknown angular elements and defined the regions with possible values of the elements for which the motion of EP stays stable. We applied these calculations to the particular specific EPs: HD19994b, HD196885Ab and HD222404b.

Application of the Nonrestricted Three-Bodies Problem to the Stellar System ξ UMa

The present study concerns the application of an analytical theory of the stellar three- - bodies problem to the triple stellar system ξ UMa, whose components move along short-period orbits with periods of 2 years and 60 years. For this purpose the solution of the simplified canonical system of differential equations obtained in terms of hyperelliptic integrals by Hamilton-Jacobi method was used. The precision of the solution was increased by addition of short-periodic terms computed from the formulae of the transformation by von Zeipel’s method.

Model orbits of asteroid 3040 Kozai

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn.The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.

Evolution of Asteroidal Orbits with High Inclinations

The 20,000 years orbital evolution of massless fictitious asteroids located at a border of the Hill’s gravitational sphere has been investigated. The eleven orbits with the eccentricities from 0.0 to 0.4 in five groups of inclinations from 40° to 80° were numerically integrated with planetary perturbations of six major planets, using the numerical integration n-body program with the Everhart’s integrator RA15. For each group time evolution of orbital elements of the asteroids is presented.