On the instability of Saturn’s hypothetical retrograde co-orbitals

Abstract

ABSTRACT We find an interesting fact that fictitious retrograde co-orbitals of Saturn, or small bodies inside the retrograde 1:1 resonance with Saturn, are highly unstable in our numerical simulations. It is shown that, in the presence of Jupiter, the retrograde co-orbitals will get ejected from Saturn’s co-orbital space within a time-scale of 10 Myr. This scenario reminds us of the instability of Saturn Trojans caused by both the great inequality and the secular resonances. Therefore, we carry out in-depth inspections of both mechanisms and prove that the retrograde resonance overlap, raised by great inequality, cannot serve as an explanation for the instability of the retrograde co-orbitals, due to the weakness of the retrograde 2:5 resonance with Jupiter at low eccentricity. However, we discover that both ν5 and ν6 secular resonances contribute to the slow growth of the eccentricity and are therefore possibly the primary causes of the instability inside Saturn’s retrograde co-orbital space.