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Secular resonances between bodies on close orbits: a case study of the Himalia prograde group of jovian irregular satellites
Earth and Planetary Astrophysics · Submitted 16 Mar 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The gravitational interaction between two objects on similar orbits can effect noticeable changes in the orbital evolution even if the ratio of their masses to that of the central body is vanishingly small.
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The abstract, sentence by sentence
The gravitational interaction between two objects on similar orbits can effect noticeable changes in the orbital evolution even if the ratio of their masses to that of the central body is vanishingly small. Christou (2005) observed an occasional resonant lock in the differential node $\Delta \Omega$ between two members in the Himalia irregular satellite group of Jupiter in the $N$-body simulations (corresponding mass ratio $\sim 10^{-9}$). Using a semianalytical approach, we have reproduced this phenomenon. We also demonstrate the existence of two additional types of resonance, involving angle differences $\Delta\omega$ and $\Delta (\Omega+\varpi)$ between two group members. These resonances cause secular oscillations in eccentricity and/or inclination on timescales $\sim$ 1 Myr. We locate these resonances in $(a,e,i)$ space and analyse their topological structure. In subsequent $N$-body simulations, we confirm these three resonances and find a fourth one involving $\Delta \varpi$. In addition, we study the occurrence rates and the stability of the four resonances from a statistical perspective by integrating 1000 test particles for 100 Myr. We find $\sim 10-30$ librators for each of the resonances. Particularly, the nodal resonance found by Christou is the most stable: 2 particles are observed to stay in libration for the entire integration.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The gravitational interaction between two objects on similar orbits can effect noticeable changes in the orbital evolution even if the ratio of their masses to that of the central body is vanishingly small. | background 1.00 | 0.08 | 0.11 | asserted 0.60 |
| s1 | Christou (2005) observed an occasional resonant lock in the differential node $\Delta \Omega$ between two members in the Himalia irregular satellite group of Jupiter in the $N$-body simulations (corresponding mass ratio $\sim 10^{-9}$). | background 0.98 | 0.05 | 0.07 | asserted 0.94 |
| s2 | Using a semianalytical approach, we have reproduced this phenomenon. | method 0.54 | 0.96 | 0.06 | asserted 1.00 |
| s3 | We also demonstrate the existence of two additional types of resonance, involving angle differences $\Delta\omega$ and $\Delta (\Omega+\varpi)$ between two group members. | result 0.69 | 0.95 | 0.21 | asserted 1.00 |
| s4 | These resonances cause secular oscillations in eccentricity and/or inclination on timescales $\sim$ 1 Myr. | result 0.93 | 0.75 | 0.22 | asserted 1.00 |
| s5 | We locate these resonances in $(a,e,i)$ space and analyse their topological structure. | contribution 0.80 | 0.95 | 0.06 | asserted 0.95 |
| s6 | In subsequent $N$-body simulations, we confirm these three resonances and find a fourth one involving $\Delta \varpi$. | result 0.86 | 0.97 | 0.14 | asserted 1.00 |
| s7 | In addition, we study the occurrence rates and the stability of the four resonances from a statistical perspective by integrating 1000 test particles for 100 Myr. | method 0.82 | 0.97 | 0.06 | asserted 0.94 |
| s8 | We find $\sim 10-30$ librators for each of the resonances. | result 1.00 | 0.96 | 0.14 | asserted 1.00 |
| s9 | Particularly, the nodal resonance found by Christou is the most stable: 2 particles are observed to stay in libration for the entire integration. | result 1.00 | 0.93 | 0.20 | asserted 1.00 |
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Original abstract
The gravitational interaction between two objects on similar orbits can effect noticeable changes in the orbital evolution even if the ratio of their masses to that of the central body is vanishingly small. Christou (2005) observed an occasional resonant lock in the differential node $\Delta \Omega$ between two members in the Himalia irregular satellite group of Jupiter in the $N$-body simulations (corresponding mass ratio $\sim 10^{-9}$). Using a semianalytical approach, we have reproduced this phenomenon. We also demonstrate the existence of two additional types of resonance, involving angle differences $\Delta\omega$ and $\Delta (\Omega+\varpi)$ between two group members. These resonances cause secular oscillations in eccentricity and/or inclination on timescales $\sim$ 1 Myr. We locate these resonances in $(a,e,i)$ space and analyse their topological structure. In subsequent $N$-body simulations, we confirm these three resonances and find a fourth one involving $\Delta \varpi$. In addition, we study the occurrence rates and the stability of the four resonances from a statistical perspective by integrating 1000 test particles for 100 Myr. We find $\sim 10-30$ librators for each of the resonances. Particularly, the nodal resonance found by Christou is the most stable: 2 particles are observed to stay in libration for the entire integration.
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