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 (such as 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 the 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 that approach Saturn have their eccentricity slowly increased until they become Mars-crossers, when they are usually ejected from the asteroid belt by a close encounter with Mars. The resonance forms the inner and "side" boundaries of the asteroid belt around 2 AU and at inclinations of about 20°.
^Murray, Carl D. (2000-02-13). Solar system dynamics. Dermott, S. F. Cambridge. ISBN0521572959. OCLC40857034.{{cite book}}: CS1 maint: location missing publisher (link)
