Secular resonance

A secular resonance is a type of orbital resonance between two bodies with synchronized precessional frequencies. In celestial mechanics, secular refers to the long-term motion of a system and resonance is when two periods or frequencies are a simple numerical ratio of small integers. Typically, the synchronized precessions in secular resonances are between the rates of change of the argument of the periapses or the rates of change of the longitude of the ascending nodes of two system bodies.[1] Secular resonances can be used to study the long-term orbital evolution of asteroids and their families within the asteroid belt (see the ν6 resonance below).

Description

Secular resonances occur when the precession of two orbits is synchronised (a precession of the perihelion, with frequency g, or the ascending node, with frequency s, or both). A small body (such as a small Solar System body) in secular resonance with a much larger one (e.g. a planet) will precess at the same rate as the large body. Over relatively short time periods (a million years, or so) a secular resonance will change the eccentricity and inclination of the small body.

One can distinguish between:

  • linear secular resonances between a body (no subscript) and a single other large perturbing body (e.g. a planet, subscript as numbered from the Sun), such as the ν6 = g − g6 secular resonance between asteroids and Saturn; and
  • nonlinear secular resonances, which are higher-order resonances, usually combination of linear resonances such as the z1 = (g − g6) + (s − s6), or the ν6 + ν5 = 2g − g6 − g5 resonances.[2]

ν6 resonance

A prominent example of a linear resonance is the ν6 secular resonance between asteroids and Saturn. Asteroids which approach it have their eccentricity slowly increased until they become Mars-crossers, at which point they are usually ejected from the asteroid belt due to a close encounter with Mars. This resonance forms the inner and "side" boundaries of the asteroid belt around 2 AU, and at inclinations of about 20°.

See also

References
  1. Murray, Carl D. (2000-02-13). Solar system dynamics. Dermott, S. F. Cambridge. ISBN 0521572959. OCLC 40857034.
  2. V. Carruba, et al. (2005). "On the V-type asteroids outside the Vesta family". Astronomy & Astrophysics. 441 (2): 819. arXiv:astro-ph/0506656. Bibcode:2005A&A...441..819C. doi:10.1051/0004-6361:20053355.
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