Secular resonance

A secular resonance is a type of orbital resonance.

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 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.

The effects of secular resonances are most studied in the context of the long-time evolution (millions of years or more) of minor planet orbits within the asteroid belt.

One can distinguish between

• linear secular resonances between a body and a single other large perturbing body (e.g. a planet), 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.

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

• Orbital resonance
• Asteroid belt