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 timescale 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 on both mechanisms and prove that the retrograde resonance overlap , raised by Great Inequality , can not serve as an explanation for the instability of retrograde co-orbitals , due to the weakness of the retrograde 2:5 resonance with Jupiter at a low eccentricity .
However , we discover that both \nu _ { 5 } and \nu _ { 6 } secular resonances contribute to the slow growth of the eccentricity , therefore , are possibly the primary causes of the instability inside Saturn ’ s retrograde co-orbital space .