Secular resonance

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A secular resonance is a type of orbital resonance of two bodies with a synchronized precession. Secular resonances are used to study the long-time orbital evolution of asteroids and their families within the asteroid belt, where ν6 denotes such a resonance with respect to Saturn.


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.[1]

ν6 resonance[edit]

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[edit]


  1. ^ 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.