# Oscillation in tilt of the solar system

I know that the solar system is tilted 62.6° to the plane of the galaxy. I'm curious whether this angle changes over time, and what are the extents and time frame of any such oscillations if they exist?

Upon reflection, I'm assuming that since such an oscillation would require a change in the overall angular momentum of the entire solar system, and that would necessitate a collective re-orientation of the orbit of every planet, dwarf planet, SSSB, etc. related to the Sun that it's unlikely that any such mechanism exists?

The tidal field of the Galaxy does lead to the oscillation of the plane of very wide binaries. The mechanism of this oscillation is identical to the Kozai-Lidov mechanism (the only difference is that in the case of KL oscillations the tidal field is generated by the averaged orbit of a tertiary stellar companion).

However, if you run the numbers, the timescale for these oscillations is extremely long for any of the planets (I forget how long exactly, but much longer than the age of the Universe). It's somewhat shorter for comets in the Oort Cloud, only a few billion years, because their orbits are much larger and so would tend to experience larger a larger tidal effect.

• That article says "...perturbation of the orbit of a satellite by the gravity of another body orbiting farther out." When you say "tidal field" do you mean the gradient of the overall field of the galaxy? Then at least according to your link, the KL mechinism per-se does not apply to the tilt of the ecliptic, and possibly your calculation is not correct. As stated there, it applies to the tilt of the Sun's orbit around the galactic center, if anything at all. In a wider context, the gradient of the local gravity field may have other structure besides the simplest global galactic description.
– uhoh
Jun 15 '16 at 5:55
• If there is a different, extended description of the KL mechanism that includes static gradients instead of other individual bodies that are moving with well defined orbital elements (e.g. $P_2, m_2, a_2, \epsilon_2$) , it would be great if you could mention it and add a reference. Thanks!
– uhoh
Jun 15 '16 at 6:07
• When I say the "tidal field" I indeed mean the gradient of the surrounding gravitational field. In the case of a hierarchical triple, this gradient is caused by the orbit-averaged potential of the tertiary star. However, the Galactic gravitational field also has a gradient which is not negligible at Oort Cloud distances. The inclination between the orbit and the direction of the gradient must be at least 39 degrees for the KL mechanism to be effective, however. This is why the inclination of the ecliptic to the Galactic plane is important. Jun 15 '16 at 16:44
• You are also right that the gradient may have other structure. In the simplest description, only the quadrupole moment of the gravitational field is important, but in many contexts the next order moment, the octupole moment is very important, too. See Lithwick et al. (2011) adsabs.harvard.edu/abs/2011ApJ...742...94L Lastly, all descriptions of the KL mechanism use a static gradient, even if they are written in terms of orbital elements. However, one paper that writes out the static gradient explicitly is Katz et al. (2011) adsabs.harvard.edu/abs/2011PhRvL.107r1101K Jun 15 '16 at 16:47
• Thanks for the information! I was thrown off by the use of the orbital elements of the outer body shown explicitly in the Wikipedia article here. The papers you cite are great - I can see right away that the calculations start by time-averaging the effect and expressing as a "pseudo" or "effective" potential. (Not sure which - if either - of those is actually correct here). Both are also in ArXiv where everyone can see them as well: Litwick, and Katz.
– uhoh
Jun 16 '16 at 1:36