Dynamics of the 11:10 Corotation and Lindblad resonances with Mimas, and application to Anthe

The short-term, resonant and long-term dynamics of Anthe (S/2007 S4), are investigated with the most recent published ephemeris of the Saturnian system. We identify and explain many components in the time variations of the elements of Anthe as being caused by the joined effects of the Corotation resonance, the secular precessions of the orbits of Anthe and Mimas due to the effects of the oblateness of Saturn and long-term mutual interactions. Firstly, it is shown that the current resonant state of the pair Mimas-Anthe is characterized uniquely by the stable libration of the corotation angle phi(1) = 11 lambda(A) - 10 lambda(m) - pi(M) around zero, where A, M, lambda, pi refer to Anthe, Mimas, mean longitude and longitude of the pericenter, respectively. We find that only the comtation angle clij is stably librating, while all other arguments for the other sub-resonances (including the angular combination 11 lambda(A) - 10 lambda(m) - pi(A) - Omega(A) + Omega(M), where Omega is the longitude of the ascending node) are circulating on long time scales. This is consistent with the absence of chaos in Anthe's orbit. In the second part of this work, we map the 11:10 Mimas-Anthe resonance in the eccentricity-semi-major axis phase space. We identify non-chaotic regions around both the Corotation and Lindblad resonances, which are separated by chaotic zones. The orbit of Anthe is located deeply inside the stable regions of the Comtation resonance.