# What exactly are the "ν6 secular Sun-Jupiter-Saturn" and the "1:4 Sun-Jupiter" resonances?

In the recent Acta Astronautica article The edge of space: Revisiting the Karman Line, Harvard-Smithsonian Center for Astrophysics astronomer, Space SE contributor and "inverse namesake" of asteroid (4589) McDowell Johnathan C. McDowell lists a number of different boundaries in the solar system in section 3.2. One of them is described as the following:

The ν6 secular Sun-Jupiter-Saturn resonance which marks the conventional inner edge of the asteroid belt at 2.06 astronomical units (308 million km) from the Sun (26); it coincides with the 1:4 Sun-Jupiter resonance (27) and asteroid orbits near this resonance are unstable, soon perturbed to enter the inner solar system. Although there is no generally agreed definition, this location is a reasonable place to mark as the boundary between the inner and outer solar system.

What (the heck) are the ν6 secular Sun-Jupiter-Saturn and the 1:4 Sun-Jupiter resonances exactly?

The 1:4 (or 4:1) Jupiter resonance is a mean-motion resonance: an asteroid there takes 1/4 as long to orbit the Sun as Jupiter does. Perturbations by Jupiter at recurring ecliptic longitudes alter the asteroid's orbital period, so asteroids do not remain long in this state. The Kirkwood gaps in the asteroid belt include this and other mean-motion resonances with Jupiter.

The $$\nu_6$$ secular resonance (also called $$g = g_6$$) is more complex: in certain combinations of orbital period and inclination, an asteroid experiences perihelion precession at the same rate as Saturn (the 6th planet) does, resulting in a gradual increase of the asteroid's orbital eccentricity.

• This is very helpful, thank you! The Wikipedia article for secular resonance is so clear and concise that I don't think it's necessary to copy/paste here. But for the $\nu_6$ apsidal precession I'm still in "what the heck?" land. The Wikipedia article defines apsidal precession as precession of the line of apses and mentions Saturn, but I still have no idea how gravitational effects of the Sun + Saturn work together to affect an asteroid's orbit.
– uhoh
Oct 17, 2018 at 21:08
• Is this somehow related to the Sun's gravitational quadrupole moment as expressed by $J_2$, or the residual motion of the Sun around the solar system barycenter due to the other large planets, or something else about the Sun?
– uhoh
Oct 17, 2018 at 21:12
• Maybe Froeschle and Morbidelli 1994 could shed some light? Oct 18, 2018 at 4:09
• Yes! I'm in an airport now but I'll give that a thorough read later today. If it's possible to add that link to your answer, that would be great, thanks!
– uhoh
Oct 18, 2018 at 5:06
• My impression also. They seem to assume some background in classical perturbation theory. Oct 19, 2018 at 15:01