<p>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 <a href="https://en.wikipedia.org/wiki/Kirkwood_gap" rel="nofollow noreferrer">Kirkwood gaps</a> in the asteroid belt include this and other mean-motion resonances with Jupiter.</p>

<p>The <span class="math-container">$\nu_6$</span> <a href="https://en.wikipedia.org/wiki/Secular_resonance" rel="nofollow noreferrer">secular resonance</a> (also called <span class="math-container">$g = g_6$</span>) is more complex: in certain combinations of orbital period and inclination, an asteroid experiences <a href="https://en.wikipedia.org/wiki/Apsidal_precession" rel="nofollow noreferrer">perihelion precession</a> at the same rate as Saturn (the 6th planet) does, resulting in a gradual increase of the asteroid's orbital eccentricity.</p>

CC BY-SA 4.0
2018-10-17T21:08:43.440Z
This is very helpful, thank you! The Wikipedia article for [secular resonance](https://en.wikipedia.org/wiki/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
CC BY-SA 4.0
2018-10-17T21:12:06.410Z
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
CC BY-SA 4.0
2018-10-18T04:09:06.320Z
Maybe [Froeschle and Morbidelli 1994](http://adsabs.harvard.edu/abs/1994IAUS..160..189F) could shed some light?
Mike G
CC BY-SA 4.0
2018-10-18T05:06:05.497Z
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
CC BY-SA 4.0
2018-10-19T14:59:25.040Z
I've read through Froeschle and Morbidelli 1994 quickly, and have concluded that it's not a paper (or a topic) that you can read through quickly!
uhoh
CC BY-SA 4.0
2018-10-19T15:01:13.523Z
My impression also. They seem to assume some background in classical perturbation theory.
Mike G
CC BY-SA 4.0
2018-10-19T15:03:28.220Z
and considering how much faster computers are 25 years later, likely there are numerical tools available now that might address these in a different way.
uhoh
CC BY-SA 4.0
2018-10-17T19:06:07.893Z
2018-10-19T15:02:41.927Z
2018-10-19T15:02:41.927Z
Mike G
<p>In the recent Acta Astronautica article <a href="https://www.sciencedirect.com/science/article/pii/S0094576518308221" rel="nofollow noreferrer">The edge of space: Revisiting the Karman Line</a>, Harvard-Smithsonian Center for Astrophysics astronomer, <a href="https://space.stackexchange.com/a/21168/12102">Space SE contributor</a> and "inverse namesake" of <em>asteroid (4589) McDowell</em> 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:</p>

<blockquote>
  <p>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.</p>
</blockquote>

<p>What (the heck) are the <em>ν6 secular Sun-Jupiter-Saturn</em> and the <em>1:4 Sun-Jupiter</em> resonances exactly?</p>

<asteroids><orbital-mechanics><terminology><orbital-resonance>
What exactly are the "ν6 secular Sun-Jupiter-Saturn" and the "1:4 Sun-Jupiter" resonances?
uhoh
# What exactly are the "ν6 secular Sun-Jupiter-Saturn" and the "1:4 Sun-Jupiter" resonances?

(Asked by: username_0 on 2018-10-17)

In the recent Acta Astronautica article [The edge of space: Revisiting the Karman Line](https://www.sciencedirect.com/science/article/pii/S0094576518308221), Harvard-Smithsonian Center for Astrophysics astronomer, [Space SE contributor](https://space.stackexchange.com/a/21168/12102) 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?

**Tags:** asteroids, orbital-mechanics, terminology, orbital-resonance

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## 1 answers

### Answer by username_1 on 2018-10-17. Score: 4 | Accepted answer

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](https://en.wikipedia.org/wiki/Kirkwood_gap) in the asteroid belt include this and other mean-motion resonances with Jupiter.

The $\nu\_6$ [secular resonance](https://en.wikipedia.org/wiki/Secular_resonance) (also called $g = g\_6$) is more complex: in certain combinations of orbital period and inclination, an asteroid experiences [perihelion precession](https://en.wikipedia.org/wiki/Apsidal_precession) at the same rate as Saturn (the 6th planet) does, resulting in a gradual increase of the asteroid's orbital eccentricity.

> **Comments:**
> **username_0**: This is very helpful, thank you! The Wikipedia article for [secular resonance](https://en.wikipedia.org/wiki/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.  
> **username_0**: 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?  
> **username_1**: Maybe [Froeschle and Morbidelli 1994](http://adsabs.harvard.edu/abs/1994IAUS..160..189F) could shed some light?  
> **username_0**: 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!  
> **username_0**: I've read through Froeschle and Morbidelli 1994 quickly, and have concluded that it's not a paper (or a topic) that you can read through quickly!  
> **username_1**: My impression also. They seem to assume some background in classical perturbation theory.  
> **username_0**: and considering how much faster computers are 25 years later, likely there are numerical tools available now that might address these in a different way.  

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