Does the ecliptic plane change relative to the galactic plane?

Question

The equatorial plane moves over time with respect to the plane of the ecliptic (that's precession!). The ecliptic is at an angle with the galactic plane, but does this angle change over time? Does the ecliptic plane have a precession of sorts with respect to the galactic plane?

Answer 1

As mentioned by James K in this answer, the inclination of the ecliptic plane to the invariable plane of the Solar System varies by ~3°, over a very long time scale.

The invariable plane itself is very stable relative to the International Celestial Reference Frame (ICRF).

The ICRF creates a quasi-inertial frame of reference centered at the barycenter of the Solar System, whose axes are defined by the measured positions of extragalactic sources (mainly quasars) observed using very long baseline interferometry.

Although general relativity implies that there are no true inertial frames around gravitating bodies, the ICRF is important because it does not exhibit any measurable angular motion since the extragalactic sources used to define the ICRF are so far away. The ICRF is now the standard reference frame used to define the positions of the planets (including the Earth) and other astronomical objects.

As Wikipedia mentions, the invariable plane is perturbed due to the anisotropic loss of material from the Solar System, and the radiation of gravitational waves. It's also affected by torques exerted by neighbouring stars. But all of those perturbations are minute.

This excellent paper from the journal Astronomy & Astrophysics, The solar system’s invariable plane, by D. Souami and J. Souchay, (A&A 543, A133 (2012)) has a lot of information about the stability of the invariable plane. They calculate, using two different high precision ephemerides, that the variation of the inclination of the invariable plane relative to the ICRF is a little over 2 microarc-seconds per year.

With respect to the ICRF, we clearly observe a linear trend of $i$ as a function of time, at a rate of $-2".365252 × 10^{-6}/y$ ($-2".255406 × 10^{-6}/y$, respectively) over the entire available time span of the ephemeris DE405 (Fig. 2(a)) and INPOP10a (Fig. 2(b))

Temporal variations Δi and ΔΩ in the orientation of the invariable plane with respect to the ICRF, where Δi is given with respect to the equator of the ICRF by using DE405 a) and INPOP10a b), where ΔΩ is given with respect to the origin-equator of the ICRF by using of DE405 c) and INPOP10a d).

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That paper is fairly technical, and hopefully I haven't misinterpreted it. ;)