Secular dynamics of an exterior test particle: the inverse Kozai and other eccentricity–inclination resonances Article Swipe
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· 2017
· Open Access
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· DOI: https://doi.org/10.1093/mnras/stx3091
· OA: W2774074688
The behavior of an interior test particle in the secular 3-body problem has\nbeen studied extensively. A well-known feature is the Lidov-Kozai resonance in\nwhich the test particle's argument of periapse librates about $\\pm 90^\\circ$\nand large oscillations in eccentricity and inclination are possible. Less\nexplored is the inverse problem: the dynamics of an exterior test particle and\nan interior perturber. We survey numerically the inverse secular problem,\nexpanding the potential to hexadecapolar order and correcting an error in the\npublished expansion. Four secular resonances are uncovered that persist in full\n$N$-body treatments (in what follows, $\\varpi$ and $\\Omega$ are the longitudes\nof periapse and of ascending node, $\\omega$ is the argument of periapse, and\nsubscripts 1 and 2 refer to the inner perturber and outer test particle): (i)\nan orbit-flipping quadrupole resonance requiring a non-zero perturber\neccentricity $e_1$, in which $\\Omega_2-\\varpi_1$ librates about $\\pm 90^\\circ$;\n(ii) a hexadecapolar resonance (the "inverse Kozai" resonance) for perturbers\nthat are circular or nearly so and inclined by $I \\simeq 63^\\circ/117^\\circ$,\nin which $\\omega_2$ librates about $\\pm 90^\\circ$ and which can vary the\nparticle eccentricity by $\\Delta e_2 \\simeq 0.2$ and lead to orbit crossing;\n(iii) an octopole "apse-aligned" resonance at $I \\simeq 46^\\circ/107^\\circ$\nwherein $\\varpi_2 - \\varpi_1$ librates about $0^\\circ$ and $\\Delta e_2$ grows\nwith $e_1$; and (iv) an octopole resonance at $I \\simeq 73^\\circ/134^\\circ$\nwherein $\\varpi_2 + \\varpi_1 - 2 \\Omega_2$ librates about $0^\\circ$ and $\\Delta\ne_2$ can be as large as 0.3 for small $e_1 \\neq 0$. The more eccentric the\nperturber, the more the particle's eccentricity and inclination vary; also,\nmore polar orbits are more chaotic. Our inverse solutions may be applied to the\nKuiper belt and debris disks, circumbinary planets, and stellar systems.\n
