# Secular resonances between bodies on close orbits II: prograde and retrograde orbits for irregular satellites

## TL;DR

This paper extends the analysis of secular resonances to both prograde and retrograde irregular satellite orbits, providing a generalized model and confirming the persistence and impact of these resonances through numerical simulations.

## Contribution

The authors generalize the semianalytical model of secular resonances to include both orbit directions and validate it with numerical simulations, revealing the extent and survivability of these resonances.

## Key findings

- Over 20% of phase space affected near Himalia
- Over 40% of phase space affected near Phoebe
- 10-60% of particles captured in resonances

## Abstract

In extending the analysis of the four secular resonances between close orbits in Li and Christou (Celest Mech Dyn Astron 125:133-160, 2016) (Paper I), we generalise the semianalytical model so that it applies to both prograde and retrograde orbits with a one to one map between the resonances in the two regimes. We propose the general form of the critical angle to be a linear combination of apsidal and nodal differences between the two orbits $ b_1 \Delta \varpi + b_2 \Delta \Omega $, forming a collection of secular resonances in which the ones studied in Paper I are among the strongest. Test of the model in the orbital vicinity of massive satellites with physical and orbital parameters similar to those of the irregular satellites Himalia at Jupiter and Phoebe at Saturn shows that $> 20\%$ and $> 40\%$ of phase space is affected by these resonances, respectively. The survivability of the resonances is confirmed using numerical integration of the full Newtonian equations of motion. We observe that the lowest order resonances with $b_1+|b_2|\le 3$ persist, while even higher order resonances, up to $b_1+|b_2|\ge 7$, survive. Depending on the mass, between $10\%-60\%$ of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.