OUP accepted manuscript

Abstract

The aim of this article is to determine the dynamical parameters of the asteroid ( 22) Kalliope with its satellite Linus, based on astrometric observations of this system. We use a model of the motion taking into account the gravitational influence of the primary's axisymmetric non-sphericity. This factor leads to precession of the line of apsides of the satellite, as well as precession of its orbit around the primary's axis of symmetry. The axisymmetric gravitational field of the primary is formed by the time-averaged field of the fast-rotating body of Kalliope. All available observations of the Kalliope-Linus system were divided into groups, each containing observations close in time. For each group, parameters of the fixed Keplerian orbit were determined. Thus, the behaviour of the satellite's orbit axis over about 16-yr time intervals was studied. Contrary to the expected uniform precession of the orbital plane, we discovered abnormal prograde motion of the ascending node in the first seven years, which became retrograde in the next nine years. The amplitude of the change is about 120 • . We make an attempt to explain such motion by effects not taken into account in the adopted dynamical model. It is shown that effects not taken into account cannot explain the oscillatory motion of the orbital node found. Using 121 available observations, two formal solutions for all fitted parameters were determined.

Determination of the orbits of 62 moons of asteroids based on astrometric observations.

“…The direction of this precession axis can only be found from astrometric observations. We tried to implement such a determination of perturbations for the moon Linus of the asteroid ( 22) Kalliope in a previous paper (Emelyanov et al 2019).…”

“…The determination of the precession of the axis of the moon's orbit was made in Emelyanov et al (2019) for the asteroid system (22) Kalliope in the observation's time interval of approximately 16 yr. The positions of the orbit's axis determined from observations show that the axis rotates in the same direction for the first 7 yr, and then turns in the opposite direction.…”

“…The task is complicated by the fact that we have to consider the combined effect of the attraction of the Sun and the influence of the nonsphericity of the main component. Estimates of the influence of the attraction of the Sun in the orbital motion of the moon of an asteroid were made in Emelyanov et al (2019). As can be clearly seen from the formulas shown in Emelyanov et al (2019), the magnitude of the perturbations from the attraction of the Sun is proportional to the parameter μ defined by the relation…”

“…Estimates of the influence of the attraction of the Sun in the orbital motion of the moon of an asteroid were made in Emelyanov et al (2019). As can be clearly seen from the formulas shown in Emelyanov et al (2019), the magnitude of the perturbations from the attraction of the Sun is proportional to the parameter μ defined by the relation…”