In this work, we study the current state of asteroid in the dominant region of v6 secular resonance. These resonances occur when there is a commensurability between the g or s frequency of precession of perihelion or node of a given asteroid and the g6 or s6 frequencies of precession of Saturn planet.
In the dynamics of the v6 resonance, the resonant argument σ6 = g – g6 may circulate or librate. An orbit is considered in circulating state if the resonant argument varies from 0◦ to 360◦ and considered in libration state if the resonant argument is oscillating around a equilibrium point. For the libration state resonances of order one, two equilibria points are possible: one around 0◦ and other around 180◦. In the first case, we say that the libration is aligned and in the second case it is anti-aligned.
We used the analytical method of Yoshikawa, to estimate a possible region of the v6 resonance. In this resonant region, we identified 4137 likely candidates from the AstDys catalog. We performed numerical integrations considering gravitational forces of the all the planets over an integration time of 20 Myr to identify asteroids population in pure libration states (anti-aligned and aligned) in this region. We, for the first time, identified a population of 7 asteroids in pure aligned libration located in the central belt. We study the stability of this new population, by integrating the orbits of its members both forward and backward in time.
An analysis using the algorithm of Hierarchical Clustering Method (HCM), was performed to identify the families of: Euphrosyne, 1995 FRI, Tina, Luciene and Svea, which are close or inside of the v6 secular resonance. In this work, we showed that 81% of its members of Svea’s family are in pure anti-aligned libration state and it is therefore the third family mostly affected by the v6 resonance in the main belt.