<p>Per <a href="https://astronomy.stackexchange.com/questions/57893/does-the-inclination-of-an-orbital-plane-change-due-to-pull-from-other-orbiting#comment132700_57893">@eshaya's comment</a>:</p>
<blockquote>
<p>Tidal dissipation from precessional forces brings orbiting objects into the lowest energy orbital plane</p>
</blockquote>

CC BY-SA 4.0
2024-06-15T12:59:55.730Z
Thank you, kind sir!
Miss Understands
CC BY-SA 4.0
2024-06-15T14:18:26.427Z
@Miss_Understands I think a follow-up question may be in order. [John Doty](https://astronomy.stackexchange.com/questions/57893/does-the-inclination-of-an-orbital-plane-change-due-to-pull-from-other-orbiting/57906?noredirect=1#comment132674_57893) didn't mean to say "google it", I think their point is that *after they had googled it*, they discovered "it's complicated". For example, there may be one mechanism for how planets eventually fall into a plane, and it may be somewhat different for asteroids, depending on where they are. Certainly comets (and therefore meteor showers) haven't.
uhoh
CC BY-SA 4.0
2024-06-15T14:21:26.643Z
@Miss_Understands our solar system's [Kuiper belt](https://en.wikipedia.org/wiki/Kuiper_belt) is mostly planarized, but its (suspected) [Oort cloud](https://en.wikipedia.org/wiki/Oort_cloud) is expected to me kind-of spherical still.
uhoh
CC BY-SA 4.0
2024-06-15T15:25:36.367Z
@johndoty "after they had googled it, they discovered "it's complicated" ===[ Well, I'm quite sure it's complicated. It's too many particles to model individually. You have to use a surface integral. But I  don't think  perturbations by other objects affects a general description  of tidal dissipation reducing inclination angle. I'm sure someone did this 100 years ago, to explain saturn. I'll go look it up thanx.
Miss Understands
CC BY-SA 4.0
2024-06-16T02:29:24.957Z
Hold on.  I am not sure that is the only answer.  An alternative might be that a ring of particles not at i=0 (equatorial plane) would evolve into a band above and below the equator by getting out of phase, collide with one another and settle at i = 0.  I think Goldreich liked this idea.  But, inclination dissipation is a reasonable mechanism.
eshaya
CC BY-SA 4.0
2024-06-16T03:10:19.070Z
@eshaya Agreed. If we look at [a list of Saturn's moons](https://en.wikipedia.org/wiki/Moons_of_Saturn#List) there's a lot going on, but perhaps the older ones were damped to 0° via tidal forces. [this answer](https://astronomy.stackexchange.com/a/25083/7982) talk about Jupiter circularizing its moons' orbits but I believe something similar can circularize. On the other hand, the myriads of of individual particles in Saturn's orbit might indeed require regular collisions as part of the planarizing effect. Please consider adding a new/better answer!
uhoh
CC BY-SA 4.0
2024-06-20T20:53:31.170Z
@Miss_Understands This is a minefield. Be vigilant. "The lowest energy orbital plane" implies not the global but a local minimum. In principle, tidal forces permit for stable configurations with a nonzero inclination.  See the paragraph after equation (165) in [this paper](https://ui.adsabs.harvard.edu/abs/2019CeMDA.131...30B/abstract). Methinks, this is the only way to explain the stability of Triton's inclined orbit.
Michael_1812
CC BY-SA 4.0
2024-06-20T21:51:45.893Z
I don't subscribe to Springer. Alas, I am frustrated in my quest. Anyway, I don't see how a nonzero inclination could be stable. The paper must be talking about something related. Copy the equation to here?
Miss Understands
CC BY-SA 4.0
2024-06-15T08:09:18.160Z
2024-06-15T08:09:18.160Z
uhoh
<p>If a ring of material forms in a plane inclined to the mean plane of a planet's system, forces could act to pull it toward the mean plane, initially causing precession.  These forces arise from the quadrupole moment and higher-order terms of the planet's density distribution (usually an equatorial bulge) and the distributions of other satellites and rings in the system.  These forces cause precession and do not initially pull the orbital plane into the mean because in order to align fully, it must first lose some orbital energy.</p>
<p>One mechanism for losing orbital energy is through the exchange of orbital energy. For example, the inclinations of nearby more massive objects could be increased slightly.</p>
<p>Another significant mechanism that influences the inclination is inclination dissipation, a type of tidal dissipation. Tidal dissipation, in general, is driven by the tidal bulges on a rotating object. The constant gravitational tugging between the ring particles and the planet's quadrupole moment or nearby moons causes periodic deformations, leading to time-varying forces that can alter the semi-major axis, eccentricity, inclination, and obliquity (tilt). The total losses in orbital dynamics will equal the heating from time-varying deformations, thus conserving energy.</p>
<p>On the other hand, nearly all moons of planets are in the equatorial planes of their host planet's system, even ones that are so far from their host planet that the timescales for inclination dissipation is longer than the age of the solar system.  Therefore, these moons could not have been randomly captured at random inclinations and brought down to the mean plane afterwards.  They must have formed in situ from dust/rock piles.  In the paper &quot;<a href="https://adsabs.harvard.edu/full/1965AJ.....70....5G" rel="nofollow noreferrer">Inclination of satellite orbits about an oblate precessing planet</a>&quot; (1965) by Peter Goldreich, he notes, towards the end,</p>
<blockquote>
<p>For example, suppose that in some manner or other all the particles
were put in a common orbital plane which was inclined to the equator
plane by some angle <span class="math-container">$\alpha$</span>.  Then, since the nodes of the individual
particle orbits would move at different rates, the particles would soon
cease to occupy one plane and instead fill a band about the planet.
This band would be symmetrical with respect to the equatorial plane
and would occupy the region outside of a double cone of half-angle
<span class="math-container">$\frac12 \pi - \alpha$</span> which has its axis coincident with the plane's
spin axis.  Hence, the only planar configuration of particles which
will endure is the one having <span class="math-container">$\alpha = \frac12 \pi$</span>.</p>
</blockquote>
<p>In time, collisions between the particles will turn the band into a thin disk.</p>

CC BY-SA 4.0
2024-06-19T01:03:56.963Z
Wow, Ty. I was mainly asking about the secular change in precession, not tugs by asteroids, but thanx for the answer: the ring particles would expand the disk from collisions into a less-dense, fuzzy disk. cool! I don't see why the alpha angle has that particular value though. (half pi). it seems arbitrary.
Miss Understands
CC BY-SA 4.0
2024-06-19T17:32:06.457Z
half pi = 90 degrees.  90 degrees from the pole or along the equator.
eshaya
CC BY-SA 4.0
2024-06-18T20:43:52.863Z
2024-06-18T20:49:30.437Z
2024-06-18T20:49:30.437Z
eshaya
<p>I don't mean precession. That's drift in the orbit around the center. I'm asking about drift of the tilt in the z-direction.</p>
<p>Saturn's ring particles are held in a tight disk because when they drift above it. they are pulled back like sheep wandering from a herd.</p>
<p>I thought that was what kept the sun in the galactic plane, but there was  a fistfight about that in another thread.</p>
<p>Each particle is in its own orbit, and that orbit exists in a plane. That plane is inclined relative to the mean plane. When the plane rotates, that's precession, though I see it as the orbit not being long enough to contain one summer-winter year, from a planet's point of view.</p>
<p>I'm asking about the orbital plane rotating around one of the other 2 axes.</p>
<p>QUESTION: Is it the case that over time, a lower-energy state would be tumbled into, in which all the objects' orbital planes align (after infinite time)?</p>
<p>Is there a name for that parameter?</p>

CC BY-SA 4.0
2024-06-13T16:05:02.163Z
A Google search for "evolution of orbital inclination" yields many results. It's complicated...
John Doty
CC BY-SA 4.0
2024-06-13T17:58:16.637Z
"Google it." Okay. Right.
Miss Understands
CC BY-SA 4.0
2024-06-13T18:29:27.710Z
I asked because it's not in any set of orbital elements I've seen (except maybe kozi oscillations). Since it involves gravitational  interaction, not with another particle but an extended  surface, that probably explains its absence. Still, the rate at which an orbit is pulled to the mean orbit has some numeric value.The evolution of rings depends on it. The thickness of the galaxy  depends on it.  I was just asking if this parameter is named. Apparently not.
Miss Understands
CC BY-SA 4.0
2024-06-13T20:15:23.847Z
I mean, it's trivial that comets can and do change their inclination by interacting with planets, especially Jupiter, but I don't know what you mean about a named parameter.
Darth Pseudonym
CC BY-SA 4.0
2024-06-13T21:15:49.623Z
Never mind. Again
Miss Understands
CC BY-SA 4.0
2024-06-13T21:18:36.310Z
I tried to close it but could only vote to close it.
Miss Understands
CC BY-SA 4.0
2024-06-14T01:51:24.563Z
Pure Kepler orbits only apply to 1 or 2 body systems. It can be useful to model more complicated systems as perturbed Kepler orbits, but those perturbations quickly get complicated if you want accurate results. I have some info on lunar motion here: https://astronomy.stackexchange.com/a/55112/16685 Eg, the Moon's mean inclination is ~5.14°, but its actual inclination varies by ~0.16° in a rather complex way. Also see https://adsabs.harvard.edu/full/1971AJ.....76..269D
PM 2Ring
CC BY-SA 4.0
2024-06-14T15:07:56.183Z
Tidal dissipation from precessional forces brings orbiting objects into the lowest energy orbital plane.
eshaya
CC BY-SA 4.0
2024-06-14T20:29:40.990Z
@eshaya TY! Jee-ziss, it's like pulling teeth here.Type that as an answer so I can declare it THE answer before I get banned for asking reasonable questions again.
Miss Understands
<orbital-elements><orbital-inclination>
Does the inclination of an orbital plane change due to pull from other orbiting objects?
Miss Understands
# Does the inclination of an orbital plane change due to pull from other orbiting objects?

(Asked by: username_0 on 2024-06-13)

I don't mean precession. That's drift in the orbit around the center. I'm asking about drift of the tilt in the z-direction.

Saturn's ring particles are held in a tight disk because when they drift above it. they are pulled back like sheep wandering from a herd.

I thought that was what kept the sun in the galactic plane, but there was a fistfight about that in another thread.

Each particle is in its own orbit, and that orbit exists in a plane. That plane is inclined relative to the mean plane. When the plane rotates, that's precession, though I see it as the orbit not being long enough to contain one summer-winter year, from a planet's point of view.

I'm asking about the orbital plane rotating around one of the other 2 axes.

QUESTION: Is it the case that over time, a lower-energy state would be tumbled into, in which all the objects' orbital planes align (after infinite time)?

Is there a name for that parameter?

**Tags:** orbital-elements, orbital-inclination

> **Comments:**
> **username_1**: A Google search for "evolution of orbital inclination" yields many results. It's complicated...  
> **username_0**: "Google it." Okay. Right.  
> **username_0**: I asked because it's not in any set of orbital elements I've seen (except maybe kozi oscillations). Since it involves gravitational  interaction, not with another particle but an extended  surface, that probably explains its absence. Still, the rate at which an orbit is pulled to the mean orbit has some numeric value.The evolution of rings depends on it. The thickness of the galaxy  depends on it.  I was just asking if this parameter is named. Apparently not.  
> **username_2**: I mean, it's trivial that comets can and do change their inclination by interacting with planets, especially Jupiter, but I don't know what you mean about a named parameter.  
> **username_0**: Never mind. Again  
> **username_0**: I tried to close it but could only vote to close it.  
> **username_3**: Pure Kepler orbits only apply to 1 or 2 body systems. It can be useful to model more complicated systems as perturbed Kepler orbits, but those perturbations quickly get complicated if you want accurate results. I have some info on lunar motion here: https://astronomy.stackexchange.com/a/55112/16685 Eg, the Moon's mean inclination is ~5.14°, but its actual inclination varies by ~0.16° in a rather complex way. Also see https://adsabs.harvard.edu/full/1971AJ.....76..269D  
> **username_4**: Tidal dissipation from precessional forces brings orbiting objects into the lowest energy orbital plane.  
> **username_0**: @username_4 TY! Jee-ziss, it's like pulling teeth here.Type that as an answer so I can declare it THE answer before I get banned for asking reasonable questions again.  

---

## 2 answers

### Answer by username_5 on 2024-06-15. Score: 1 | Accepted answer

Per [@username_4's comment](https://astronomy.stackexchange.com/questions/57893/does-the-inclination-of-an-orbital-plane-change-due-to-pull-from-other-orbiting#comment132700_57893):

> Tidal dissipation from precessional forces brings orbiting objects into the lowest energy orbital plane

> **Comments:**
> **username_0**: Thank you, kind sir!  
> **username_5**: @Miss_Understands I think a follow-up question may be in order. [username_1](https://astronomy.stackexchange.com/questions/57893/does-the-inclination-of-an-orbital-plane-change-due-to-pull-from-other-orbiting/57906?noredirect=1#comment132674_57893) didn't mean to say "google it", I think their point is that *after they had googled it*, they discovered "it's complicated". For example, there may be one mechanism for how planets eventually fall into a plane, and it may be somewhat different for asteroids, depending on where they are. Certainly comets (and therefore meteor showers) haven't.  
> **username_5**: @Miss_Understands our solar system's [Kuiper belt](https://en.wikipedia.org/wiki/Kuiper_belt) is mostly planarized, but its (suspected) [Oort cloud](https://en.wikipedia.org/wiki/Oort_cloud) is expected to me kind-of spherical still.  
> **username_0**: @johndoty "after they had googled it, they discovered "it's complicated" ===[ Well, I'm quite sure it's complicated. It's too many particles to model individually. You have to use a surface integral. But I  don't think  perturbations by other objects affects a general description  of tidal dissipation reducing inclination angle. I'm sure someone did this 100 years ago, to explain saturn. I'll go look it up thanx.  
> **username_4**: Hold on.  I am not sure that is the only answer.  An alternative might be that a ring of particles not at i=0 (equatorial plane) would evolve into a band above and below the equator by getting out of phase, collide with one another and settle at i = 0.  I think Goldreich liked this idea.  But, inclination dissipation is a reasonable mechanism.  
> **username_5**: @username_4 Agreed. If we look at [a list of Saturn's moons](https://en.wikipedia.org/wiki/Moons_of_Saturn#List) there's a lot going on, but perhaps the older ones were damped to 0° via tidal forces. [this answer](https://astronomy.stackexchange.com/a/25083/7982) talk about Jupiter circularizing its moons' orbits but I believe something similar can circularize. On the other hand, the myriads of of individual particles in Saturn's orbit might indeed require regular collisions as part of the planarizing effect. Please consider adding a new/better answer!  
> **username_6**: @Miss_Understands This is a minefield. Be vigilant. "The lowest energy orbital plane" implies not the global but a local minimum. In principle, tidal forces permit for stable configurations with a nonzero inclination.  See the paragraph after equation (165) in [this paper](https://ui.adsabs.harvard.edu/abs/2019CeMDA.131...30B/abstract). Methinks, this is the only way to explain the stability of Triton's inclined orbit.  
> **username_0**: I don't subscribe to Springer. Alas, I am frustrated in my quest. Anyway, I don't see how a nonzero inclination could be stable. The paper must be talking about something related. Copy the equation to here?  

---

### Answer by username_4 on 2024-06-18. Score: 4

If a ring of material forms in a plane inclined to the mean plane of a planet's system, forces could act to pull it toward the mean plane, initially causing precession. These forces arise from the quadrupole moment and higher-order terms of the planet's density distribution (usually an equatorial bulge) and the distributions of other satellites and rings in the system. These forces cause precession and do not initially pull the orbital plane into the mean because in order to align fully, it must first lose some orbital energy.

One mechanism for losing orbital energy is through the exchange of orbital energy. For example, the inclinations of nearby more massive objects could be increased slightly.

Another significant mechanism that influences the inclination is inclination dissipation, a type of tidal dissipation. Tidal dissipation, in general, is driven by the tidal bulges on a rotating object. The constant gravitational tugging between the ring particles and the planet's quadrupole moment or nearby moons causes periodic deformations, leading to time-varying forces that can alter the semi-major axis, eccentricity, inclination, and obliquity (tilt). The total losses in orbital dynamics will equal the heating from time-varying deformations, thus conserving energy.

On the other hand, nearly all moons of planets are in the equatorial planes of their host planet's system, even ones that are so far from their host planet that the timescales for inclination dissipation is longer than the age of the solar system. Therefore, these moons could not have been randomly captured at random inclinations and brought down to the mean plane afterwards. They must have formed in situ from dust/rock piles. In the paper "[Inclination of satellite orbits about an oblate precessing planet](https://adsabs.harvard.edu/full/1965AJ.....70....5G)" (1965) by Peter Goldreich, he notes, towards the end,

> For example, suppose that in some manner or other all the particles
> were put in a common orbital plane which was inclined to the equator
> plane by some angle $\alpha$. Then, since the nodes of the individual
> particle orbits would move at different rates, the particles would soon
> cease to occupy one plane and instead fill a band about the planet.
> This band would be symmetrical with respect to the equatorial plane
> and would occupy the region outside of a double cone of half-angle
> $\frac12 \pi - \alpha$ which has its axis coincident with the plane's
> spin axis. Hence, the only planar configuration of particles which
> will endure is the one having $\alpha = \frac12 \pi$.

In time, collisions between the particles will turn the band into a thin disk.

> **Comments:**
> **username_0**: Wow, Ty. I was mainly asking about the secular change in precession, not tugs by asteroids, but thanx for the answer: the ring particles would expand the disk from collisions into a less-dense, fuzzy disk. cool! I don't see why the alpha angle has that particular value though. (half pi). it seems arbitrary.  
> **username_4**: half pi = 90 degrees.  90 degrees from the pole or along the equator.  

---

