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

• Published in: Celestial mechanics and dynamical astronomy 2017-09, Vol.129 (1-2), p.1-23
• Main Authors: Li, Daohai, Christou, Apostolos A.
• Format: Article
• Language: English
• Subjects: Aerospace Technology and Astronautics; Astrophysics; Astrophysics and Astroparticles; Classical Mechanics; Critical angle; Dynamical Systems and Ergodic Theory; Equations of motion; Geophysics/Geodesy; Himalia; Jupiter; Jupiter satellites; Mathematical models; Numerical analysis; Numerical integration; Orbital resonances (celestial mechanics); Orbits; Original Article; Phoebe; Physics; Physics and Astronomy; Retrograde orbits; Satellite imagery; Satellites; Saturn; Survivability
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-017-9763-y

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 Δ ϖ + b 2 Δ Ω , 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 | ≤ 3 persist, while even higher-order resonances, up to b 1 + | b 2 | ≥ 7 , survive. Depending on the mass, between 10 and 60% of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.