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

Secular resonances between bodies on close orbits II: prograde and retrograde orbits for... 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 $$ b_1 \Delta \varpi + b_2 \Delta \varOmega $$ 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 $${>}20$$ > 20 and $${>}40\%$$ > 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 $$b_1+|b_2|\le 3$$ b 1 + | b 2 | ≤ 3 persist, while even higher-order resonances, up to $$b_1+|b_2|\ge 7$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Celestial Mechanics and Dynamical Astronomy Springer Journals

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

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Physics; Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics
ISSN
0923-2958
eISSN
1572-9478
D.O.I.
10.1007/s10569-017-9763-y
Publisher site
See Article on Publisher Site

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 $$ b_1 \Delta \varpi + b_2 \Delta \varOmega $$ 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 $${>}20$$ > 20 and $${>}40\%$$ > 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 $$b_1+|b_2|\le 3$$ b 1 + | b 2 | ≤ 3 persist, while even higher-order resonances, up to $$b_1+|b_2|\ge 7$$ 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.

Journal

Celestial Mechanics and Dynamical AstronomySpringer Journals

Published: Apr 18, 2017

References

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