Does the invariable plane of the Solar system have axial precession?

[Hoon Sol]

TL;DR Summary

Does the invariable plane of the Solar system have axial precession? If so, how much and at what rate? I have wondered this for a while, but never found an answer.

As the title asks, does the invariable plane of the Solar system have axial precession? And if so, how much and at what rate?

I have tried to find an answer to these questions for a while now, but still haven't found any. I recently asked on reddit too, which pointed me to some speculation about how various galactic gravitational factors would likely yield a very small precession rate, but there was nothing conclusive, and certainly nothing about the rate or magnitude of the precession.

So, this seemed like the best public astrophysics-related forum I could find, and I hope perhaps someone here might know the answer.

 

[Astronuc]

TL;DR Summary: Does the invariable plane of the Solar system have axial precession? If so, how much and at what rate? I have wondered this for a while, but never found an answer.

As the title asks, does the invariable plane of the Solar system have axial precession? And if so, how much and at what rate?

One is asking about precession of the ecliptic. See the following:

Earth's precession was historically called the precession of the equinoxes, because the equinoxes moved westward along the ecliptic relative to the fixed stars, opposite to the yearly motion of the Sun along the ecliptic. Historically, the discovery of the precession of the equinoxes is usually attributed in the West to the 2nd-century-BC astronomer Hipparchus. With improvements in the ability to calculate the gravitational force between planets during the first half of the nineteenth century, it was recognized that the ecliptic itself moved slightly, which was named planetary precession, as early as 1863, while the dominant component was named lunisolar precession. Their combination was named general precession, instead of precession of the equinoxes.

https://en.wikipedia.org/wiki/Axial_precession
https://en.wikipedia.org/wiki/Ecliptic

Lunisolar precession is caused by the gravitational forces of the Moon and Sun on Earth's equatorial bulge, causing Earth's axis to move with respect to inertial space. Planetary precession (an advance) is due to the small angle between the gravitational force of the other planets on Earth and its orbital plane (the ecliptic), causing the plane of the ecliptic to shift slightly relative to inertial space. Lunisolar precession is about 500 times greater than planetary precession. In addition to the Moon and Sun, the other planets also cause a small movement of Earth's axis in inertial space, making the contrast in the terms lunisolar versus planetary misleading, so in 2006 the International Astronomical Union recommended that the dominant component be renamed the precession of the equator, and the minor component be renamed precession of the ecliptic, but their combination is still named general precession. Many references to the old terms exist in publications predating the change.

For the IAU article on the matter, see - https://www.iau.org/static/resolutions/IAU2006_Resol1.pdf

IAU page on Resolutions - https://www.iau.org/administration/resolutions/general_assemblies/

Objects with mass and angular momentum (rotation and revolution) will experience precession.
See - https://en.wikipedia.org/wiki/Apsidal_precession

 

[Hoon Sol]

One is asking about precession of the ecliptic. See the following:https://en.wikipedia.org/wiki/Axial_precession
https://en.wikipedia.org/wiki/EclipticFor the IAU article on the matter, see - https://www.iau.org/static/resolutions/IAU2006_Resol1.pdf

IAU page on Resolutions - https://www.iau.org/administration/resolutions/general_assemblies/

Objects with mass and angular momentum (rotation and revolution) will experience precession.
See - https://en.wikipedia.org/wiki/Apsidal_precession

I'm talking about the invariable plane, not the ecliptic.

 

[Astronuc]

I'm talking about the invariable plane, not the ecliptic.

My mistake. In that case, see

The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector. In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets (Jupiter, Saturn, Uranus, and Neptune). The invariable plane is within 0.5° of the orbital plane of Jupiter, and may be regarded as the weighted average of all planetary orbital and rotational planes.

https://en.wikipedia.org/wiki/Invariable_plane

The article provides some numbers for the inclinations of 4 giant plants projected to 142400 yrs and 168000 yrs compared to calculations from 2009.

See also - The solar system’s invariable plane, D. Souami and J. Souchay
https://www.aanda.org/articles/aa/full_html/2012/07/aa19011-12/aa19011-12.html

Results. We update the previous results on the determination of the orientation of the invariable plane with more accurate data, and a more complete analysis of the problem, taking into account the effect of the dwarf planet (1) Ceres as well as two of the biggest asteroids, (4) Vesta and (2) Pallas. We show that the inclusion of these last three bodies significantly improves the accuracy of determination of the invariable plane, whose orientation over a 100 y interval does not vary more than 0.1 mas in inclination, and 0.3 mas in longitude of the ascending node. Moreover, we determine the individual contributions of each body to the total angular momentum of the solar system, as well as the inclination and longitude of the node with respect to this latter plane.

See also - https://en.wikipedia.org/wiki/Laplace_plane

The Laplace plane or Laplacian plane of a planetary satellite, named after its discoverer Pierre-Simon Laplace (1749–1827), is a mean or reference plane about whose axis the instantaneous orbital plane of that satellite precesses.

Laplace's name is sometimes applied to the invariable plane, which is the plane perpendicular to a system's mean angular momentum vector, but the two should not be confused. They are equivalent only in the case where all perturbers and resonances are far from the precessing body.

Article references: https://iopscience.iop.org/article/10.1088/0004-6256/137/3/3706

The barycenters of the planets with respect to the sun are constantly changing. One could also calculate the influences of the nearest stars, e.g., Proxima Centauri.

See also
https://adsabs.harvard.edu/full/1982A&A...106..133B - this may answer your question.
https://farside.ph.utexas.edu/teaching/celestial/Celestial/node44.html

 

[harborsparrow]

It was my understanding that Wikipedia articles are not considered valid references in Physics Forums. Nor in my opinion should they be. I've been an author in Wikipedia since it began, and it has come to a situation where every article seems to be dominated and controlled by someone--and no one knows who these controllers ARE, what they expertise is, we know nothing. Do not take anything in Wikipedia as inherently true, no matter how many references have been tacked onto an article.

 

[Astronuc]

It was my understanding that Wikipedia articles are not considered valid references in Physics Forums.

Anyone can create/edit a Wikipedia article, and Wikipedia may not be controlled as other purportedly 'controlled' encyclopedic resources, e.g., Encyclopedia Britannica. That is why I look for and cite peer-reviewed articles from scientific journals, scientific organizations (e.g., IAU), and/or notes from university courses.

 

[berkeman]

It was my understanding that Wikipedia articles are not considered valid references in Physics Forums.

It depends on the subject, and is at the discretion of the Mentors. In most cases Wikipedia is a valid and useful reference. In the more complicated discussions, especially on contentious subjects, it probably will not be considered valid. In this case it's fine.

 

[Hoon Sol]

It was my understanding that Wikipedia articles are not considered valid references in Physics Forums. Nor in my opinion should they be. I've been an author in Wikipedia since it began, and it has come to a situation where every article seems to be dominated and controlled by someone--and no one knows who these controllers ARE, what they expertise is, we know nothing. Do not take anything in Wikipedia as inherently true, no matter how many references have been tacked onto an article.

Anyone can create/edit a Wikipedia article, and Wikipedia may not be controlled as other purportedly 'controlled' encyclopedic resources, e.g., Encyclopedia Britannica. That is why I look for and cite peer-reviewed articles from scientific journals, scientific organizations (e.g., IAU), and/or notes from university courses.

Wikipedia is fine, as long as you take what's written there with a grain of salt and actually check the sources. It's come a long way since its more unreliable beginnings.

That being said, I had already read those Wikipedia articles and am already quite familiar with their contents. The first of the other two papers referenced at least addresses the question, but doesn't really answer it. Perhaps no one knows at this point in time?

 

[harborsparrow]

Just a clarification about "Wikipedia is fine, as long as you take what's written there with a grain of salt and actually check the sources." The problem with "just check the sources" is that Wikipedia often leaves out important information that the article controllers consider to be controversial or they just don't like, for some reason, and no one can influence their choice of what information is most important to include. In my opinion, even if the information present in Wikipedia happens to be accurate, that does not mean that the overview of a topic in there is balanced or even reasonable. It's particularly bad for history (i.e., leaves out unpleasant things such as racism, caste violence, or past atrocities) but even for technical topics, it may omit important information such as whether or not a programming language is standardized and what implication that has for choosing that language for a long-term project. So it's problems are, in my opinion, more than just accuracy.

 

[Omega0]

So it's problems are, in my opinion, more than just accuracy.

I understand very well your point but nevertheless, it appears to me more like a citation problem. I think it is not a good advise to cite or even rely on a "moving target" - and this is not specific to your original question.

 

[Astronuc]

That being said, I had already read those articles and am already quite familiar with their contents. The second article referenced at least addresses the question, but doesn't really answer it. Perhaps no one knows at this point in time?

In the article by D. Souami and J. Souchay, the authors state

We show that the inclusion of these last three bodies significantly improves the accuracy of determination of the invariable plane, whose orientation over a 100 y interval does not vary more than 0.1 mas in inclination, and 0.3 mas in longitude of the ascending node.

Isn't that about what one is asking?

In the Wikipedia article on the Invariable Plane, there is a statement:

The invariable plane is derived from the sum of angular momenta, and is "invariable" over the entire system, while the Laplace plane for different orbiting objects within a system may be different. Laplace called the invariable plane the plane of maximum areas, where the "area" in this case is the product of the radius R and its time rate of change dR/dt, that is, its radial velocity, multiplied by the mass.

Then in a subsequent statement:

If all Solar System bodies were point masses, or were rigid bodies having spherically symmetric mass distributions, and further if there were no external effects due to the uneven gravitation of the Milky Way Galaxy, then an invariable plane defined on orbits alone would be truly invariable and would constitute an inertial frame of reference. But almost all are not, allowing the transfer of a very small amount of momenta from axial rotations to orbital revolutions due to tidal friction and to bodies being non-spherical. This causes a change in the magnitude of the orbital angular momentum, as well as a change in its direction (precession) because the rotational axes are not parallel to the orbital axes.

Nevertheless, these changes are exceedingly small compared to the total angular momentum of the system, which is very nearly conserved despite these effects.

This last statement, or set of sentences, seems consistent with the aforementioned article, and with the literature.

See Section 2 of Souami-Souchay article

Considering the solar system as isolated, its total angular momentum
vector is constant with respect to both spatial and time
coordinates. Thus, the invariable plane is defined as the plane
perpendicular to the total angular momentum vector of the solar
system that passes through its barycentre. Being fixed, it pro-
vides a permanent natural reference plane, whereas the ecliptic
slightly moves with time.

In this paper, we determine the orientation of the invariable
plane by setting its inclination and the longitude of its ascending
node with respect to both the ICRF (origin and equator) and the
ecliptic-equinox of the epoch J2000.0

Figure 2 and 3 provide some plots of their calculations for "Temporal variations Δi and ΔΩ in the orientation of the invariable plane" . . . .

Is the question with respect to the stability of the solar system and the planetary orbits? I don't know how often it comes up, but there is a paper from 2002.

 

[Astronuc]

continued from previous post

Long-term integrations and stability of planetary orbits in our Solar system, Takashi Ito, Kiyotaka Tanikawa, Monthly Notices of the Royal Astronomical Society, Volume 336, Issue 2, October 2002, Pages 483–500, https://doi.org/10.1046/j.1365-8711.2002.05765.

See this paper - Calibration of the angular momenta of the minor planets in the
solar system
https://arxiv.org/pdf/1909.11293.pdf
The authors state, "On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼ 50 − 140 mas." So is there a calculational error or issue in the models.

I would suspect that the precession of the invariable plane is relatively 'stable' or 'constant' over the time that we have been observing the solar system with a high level of accuracy, and it is certainly much easier to run a model/simulation for hundreds or thousands of years as compared to observation (experiment).

Also, consider what the invariable plane was during the 'Grand Tack' period.

Please consider the introduction in this paper - The Curiously Warped Mean Plane of the Kuiper Belt
https://iopscience.iop.org/article/10.3847/1538-3881/aa79ff
and this
https://iopscience.iop.org/article/10.3847/1538-3881/ac80f8/pdf

J2000 seems a common reference in these works. The invariable plane seems fixed, but that depends on the model. See that statement in the second paragraph on page 4, "The inclinations of Earthʼs and Mars’ orbits are referenced below in the invariable frame, i.e., relative to the invariable plane (perpendicular to the total angular momentum vector), a natural, common reference frame for solar system bodies. For example, the transformation of a state vector X from ECLIPJ2000 to the invariable plane is given by . . . ."

 

[Hoon Sol]

Just a clarification about "Wikipedia is fine, as long as you take what's written there with a grain of salt and actually check the sources." The problem with "just check the sources" is that Wikipedia often leaves out important information that the article controllers consider to be controversial or they just don't like, for some reason, and no one can influence their choice of what information is most important to include. In my opinion, even if the information present in Wikipedia happens to be accurate, that does not mean that the overview of a topic in there is balanced or even reasonable. It's particularly bad for history (i.e., leaves out unpleasant things such as racism, caste violence, or past atrocities) but even for technical topics, it may omit important information such as whether or not a programming language is standardized and what implication that has for choosing that language for a long-term project. So it's problems are, in my opinion, more than just accuracy.

I didn't say "just check the sources"; I said to take it with a grain of salt and check the sources. As you say, there are other ways to manipulate content, hence why the taking it with a grain of salt is equally important. No single source should be used authoritatively anyway, so in any case it's mostly a matter of weighting the importance of the information.

Also, of course for politically charged topics like history and such even this is going to be problematic; however, you of course have to discern what kind of topic is being discussed before making such a judgment. For a lot of physics it's most likely more reliable due to how there's little to no controversy, but of course even for some physics there might be ideologically driven content, like e.g. cosmology or nuclear power and such.

However, this is straying quite far from the topic of the thread at this point, I hope we can return.

continued from previous post

Long-term integrations and stability of planetary orbits in our Solar system, Takashi Ito, Kiyotaka Tanikawa, Monthly Notices of the Royal Astronomical Society, Volume 336, Issue 2, October 2002, Pages 483–500, https://doi.org/10.1046/j.1365-8711.2002.05765.

See this paper - Calibration of the angular momenta of the minor planets in the
solar system
https://arxiv.org/pdf/1909.11293.pdf
The authors state, "On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼ 50 − 140 mas." So is there a calculational error or issue in the models.

I would suspect that the precession of the invariable plane is relatively 'stable' or 'constant' over the time that we have been observing the solar system with a high level of accuracy, and it is certainly much easier to run a model/simulation for hundreds or thousands of years as compared to observation (experiment).

Also, consider what the invariable plane was during the 'Grand Tack' period.

Please consider the introduction in this paper - The Curiously Warped Mean Plane of the Kuiper Belt
https://iopscience.iop.org/article/10.3847/1538-3881/aa79ff
and this
https://iopscience.iop.org/article/10.3847/1538-3881/ac80f8/pdf

J2000 seems a common reference in these works. The invariable plane seems fixed, but that depends on the model. See that statement in the second paragraph on page 4, "The inclinations of Earthʼs and Mars’ orbits are referenced below in the invariable frame, i.e., relative to the invariable plane (perpendicular to the total angular momentum vector), a natural, common reference frame for solar system bodies. For example, the transformation of a state vector X from ECLIPJ2000 to the invariable plane is given by . . . ."

Thank you, this is good information. I see there's still very little knowledge about it. I'm primarily thinking in a galactic context too, as I'm interested in knowing about how the invariable plane might change throughout the movement around (and up and down in) the galaxy, but due to the long timescales that's obviously going to be even harder to get any good bounds on.

 

[Astronuc]

I'm interested in knowing about how the invariable plane might change throughout the movement around (and up and down in) the galaxy, but due to the long timescales that's obviously going to be even harder to get any good bounds on.

I believe folks are considering that aspect. It seems there are individuals and groups looking at the variation due to influences within the solar system (i.e., the major and minor planets, the many moons and asteroids, and more recently extending to the Kuiper Belt), and individuals and groups looking at larger scales, or galactic influences.

With respect to the latter (just as an example, and perhaps, not necessarily the best example), Angus Beane et al, "The Implications of Local Fluctuations in the Galactic Midplane for Dynamical Analysis in the Gaia Era", 2019 ApJ 883 103 DOI 10.3847/1538-4357/ab3d3c
https://iopscience.iop.org/article/10.3847/1538-4357/ab3d3c

Orbital properties of stars, computed from their six-dimensional phase-space measurements and an assumed Galactic potential, are used to understand the structure and evolution of the Galaxy. Stellar actions, computed from orbits, have the attractive quality of being invariant under certain assumptions and are therefore used as quantitative labels of a star's orbit. We report a subtle but important systematic error that is induced in the actions as a consequence of local midplane variations expected for the Milky Way. This error is difficult to model because it is non-Gaussian and bimodal, with neither mode peaking on the null value. An offset in the vertical position of the Galactic midplane of ∼15 pc for a thin disk-like orbit or ∼120 pc for a thick disk-like orbit induces a 25% systematic error in the vertical action Jz. In Feedback in Realistic Environments simulations of Milky Way-mass galaxies, these variations are on the order of ∼100 pc at the solar circle. . . .

Just for the sake of historical significance - JH Oort (1943) - The constants of precession and of galactic rotation - https://adsabs.harvard.edu/full/1943BAN.....9..424O

FRED L. WHIPPLE, EVIDENCE FOR A COMET BELT BEYOND NEPTUNE, PNAS, Volume 51 . Number 5 . May 15, 1964 - https://www.pnas.org/doi/pdf/10.1073/pnas.51.5.711
More on topic - Disrupting primordial planet signatures: the close encounter of two single-planet exosystems in the Galactic disc
https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2012.21552.x

I wonder if someone has done a calculation of say the 100 closest stars to the sun (Sol) and how they would affect the planetary orbits (angular momentum).

 

[Hoon Sol]

I believe folks are considering that aspect. It seems there are individuals and groups looking at the variation due to influences within the solar system (i.e., the major and minor planets, the many moons and asteroids, and more recently extending to the Kuiper Belt), and individuals and groups looking at larger scales, or galactic influences.

With respect to the latter (just as an example, and perhaps, not necessarily the best example), Angus Beane et al, "The Implications of Local Fluctuations in the Galactic Midplane for Dynamical Analysis in the Gaia Era", 2019 ApJ 883 103 DOI 10.3847/1538-4357/ab3d3c
https://iopscience.iop.org/article/10.3847/1538-4357/ab3d3cJust for the sake of historical significance - JH Oort (1943) - The constants of precession and of galactic rotation - https://adsabs.harvard.edu/full/1943BAN.....9..424O

FRED L. WHIPPLE, EVIDENCE FOR A COMET BELT BEYOND NEPTUNE, PNAS, Volume 51 . Number 5 . May 15, 1964 - https://www.pnas.org/doi/pdf/10.1073/pnas.51.5.711
More on topic - Disrupting primordial planet signatures: the close encounter of two single-planet exosystems in the Galactic disc
https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2012.21552.x

I wonder if someone has done a calculation of say the 100 closest stars to the sun (Sol) and how they would affect the planetary orbits (angular momentum).

Thank you for more good information. Something like the last thing you mentioned would indeed be very interesting to see; although I assume one would be most interested in the top X stars with the most gravitational influence on Sol (e.g. a star that's twice as far away would still have more of a gravitational effect if it were more than four times as massive, and so on) in this context. I can see how something like this could yield some idea of what the precession of the invariable plane could look like over the "short term" (i.e. not that short, still over the scale of tens or hundreds of thousands of years, if not millions or more, but still "shorter" than a comprehensive view of any regular precession the plane might have over many galactic orbits, if such a regular pattern were even to exist).

 

[Hornbein]

The variable plane should precess due to external gravitational sources but this would be very slow, so much so I would guess that it is swamped by complicating factors such as minuscule random changes in its angular momentum.