<p>The recent question <a href="https://astronomy.stackexchange.com/q/54051/7982">Can dark matter accumulate at Lagrange points?</a> mentions <a href="https://en.wikipedia.org/wiki/Kordylewski_cloud" rel="nofollow noreferrer">Kordylewski clouds</a> and that article begins:</p>
<blockquote>
<p>Kordylewski clouds are large concentrations of dust <strong>that exist</strong> at the L4 and L5 Lagrangian points of the Earth–Moon system.<sup>1,2,3</sup> They were first reported by Polish astronomer <a href="https://en.wikipedia.org/wiki/Kazimierz_Kordylewski" rel="nofollow noreferrer">Kazimierz Kordylewski</a> in the 1960s, <strong>and confirmed to exist by the Royal Astronomical Society in October 2018.</strong><sup>1,2,3</sup></p>
<hr />
<p><sup>1</sup>AAAS's Eureka Alert October 26, 2018: <a href="https://www.eurekalert.org/news-releases/652221" rel="nofollow noreferrer">Earth's dust cloud satellites confirmed</a></p>
<p><sup>2</sup>Slíz-Balogh, Judit; Barta, András; Horváth, Gábor (11 November 2018). &quot;<a href="https://doi.org/10.1093%2Fmnras%2Fsty2049" rel="nofollow noreferrer">Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth–Moon Lagrange point L5 – I. Three-dimensional celestial mechanical modelling of dust cloud formation</a>&quot;. Monthly Notices of the Royal Astronomical Society. 480 (4): 5550–5559. and <a href="https://arxiv.org/abs/1910.07466" rel="nofollow noreferrer">https://arxiv.org/abs/1910.07466</a>.</p>
<p><sup>3</sup>Slíz-Balogh, Judit; Barta, András; Horváth, Gábor (1 January 2019). &quot;<a href="https://doi.org/10.1093%2Fmnras%2Fsty2630" rel="nofollow noreferrer">Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth–Moon Lagrange point L5 – Part II. Imaging polarimetric observation: new evidence for the existence of Kordylewski dust cloud</a>&quot;. Monthly Notices of the Royal Astronomical Society. 482 (1): 762–770. and <a href="https://arxiv.org/abs/1910.07471" rel="nofollow noreferrer">https://arxiv.org/abs/1910.07471</a>.</p>
</blockquote>
<p>Discussion in comments on the previous question's page relate to the notion that for a buildup of material, items, particles or whatnots to occur at Earth-Moon Lagrange points, these things should have some kind of non-conservative or dissipative interaction - in other words be able to lose energy so they can &quot;fall in&quot; to Lagrange point-associated orbits and stay there for a while.</p>
<p>As I understand it, since <span class="math-container">$1/r^2$</span> forces (e.g. gravitational, electrostatic) are <a href="https://en.wikipedia.org/wiki/Conservative_force" rel="nofollow noreferrer">conservative</a> maybe something that dissipates energy (e.g. inelastic collisions converting some kinetic energy to thermal energy) might do the trick.</p>
<p>If this is all true (and I'm not saying it is) then I wonder:</p>
<p><strong>Question:</strong> Are dust-dust collisions necessary to explain Kordylewski Clouds at Earth-Moon L4/5? Aren't the cross-sections too small to be significant considering the low number density of dust particles and short timescales involved?</p>
<p>Perturbations in the Earth-Moon Lagrange point system are strong - the Moon's orbit is significantly elliptical (non CR3BP) and the Sun's gravitational perturbation will also be significant. And of course for dust at 1 AU pressure from sunlight and electrostatic effects related to the solar wind may be important.</p>
<p>I'm having a hard time believing that it's dust-dust collisions that are the driving force behind the formation of the Kordylewski clouds, so I'm asking to be &quot;straightened out&quot; on my thinking here.</p>
<p><strong>note:</strong> My current thinking is that collisions DO contribute to the accumulation of Trojan asteroids associated with the Sun-Jupiter L4/5 points. In this case all of the perturbing effects to dust with Earth-Moon L4/5 &quot;accumulations&quot; would not apply. Whether I'm right or wrong about that, the Trojans might be a good place to start before moving on to our local, dusty Kordylewski clouds.</p>

CC BY-SA 4.0
2023-06-22T14:49:41.810Z
You forget about interactions between photons and dust. a.k.a Poynting-Robertson drag.
ProfRob
CC BY-SA 4.0
2023-06-22T22:53:27.560Z
@ProfRob omission was actually deliberate, I didn't forget about it ([What is the origin of the dust near the sun?](https://astronomy.stackexchange.com/q/16707/7982)) If a particle is in heliocentric orbit photon pressure is radial just like the Sun's gravity so it's not really a perturber, but in the *Earth-Moon rotating frame* the Sun's gravity and photon pressure are now $1 \omega$ periodic perturbers (in the same direction) and for small enough dust could be comparable in magnitude. **I *guessed* P-R drag would be weak in comparison**, though still $1 \omega$ periodic. Was that incorrect?
uhoh
CC BY-SA 4.0
2023-08-14T22:44:13.227Z
@uhoh Poynting-Robertson drag is absolutely relevant; it’s a form of drag, and thus a form of dissipation. It’s not “radial”, as you seem to think.
Peter Erwin
CC BY-SA 4.0
2023-08-14T22:52:59.783Z
@PeterErwin I said *photon pressure* is radial; that sentence doesn't refer to Poynting-Robertson (P-R) drag. The following sentences do refer to P-R and say that "I guessed P-R drag would be weak in comparison" to photon pressure, and that's why I did not include it. I said this to address ProfRob's "You forgot about", explaining that I didn't forget about it, I simply dismissed it as too weak to be important in the context of accumulation of dust at the triangular Lagrange points, then asked if thinking of it as too weak was wrong - to which no reply came.
uhoh
CC BY-SA 4.0
2023-08-14T22:54:08.060Z
@PeterErwin do you think that the P-R effect is significant in the context of dust accumulation at L4/L5? If so, can you expand on that?
uhoh
CC BY-SA 4.0
2023-08-18T11:45:03.027Z
@uhoh P-R drag is an excellent way to bring dust particles orbiting outside the Earth's orbit to smaller radii, allowing them to cross the Earth's orbit and thus (potentially) be captured by L4/L5-associated orbits.
Peter Erwin
CC BY-SA 4.0
2023-08-18T22:12:23.000Z
@PeterErwin Yes, no dust means no accumulation, but I've asked specifically about the mechanisms of the "thus (potentially) be captured" part. I mean if you want to walk backwards we could include all the mechanisms that produce the dust particles too, and those that produced the nuclei of the atoms that are in the dust, but those don't help us with the accumulation mechanism.
uhoh
<solar-system><orbital-mechanics><dust>
Are dust-dust collisions necessary to explain Kordylewski clouds at Earth-Moon L4/5? Aren't the cross-sections, number density timescales too small?
uhoh
# Are dust-dust collisions necessary to explain Kordylewski clouds at Earth-Moon L4/5? Aren't the cross-sections, number density timescales too small?

(Asked by: username_0 on 2023-06-22)

The recent question [Can dark matter accumulate at Lagrange points?](https://astronomy.stackexchange.com/q/54051/7982) mentions [Kordylewski clouds](https://en.wikipedia.org/wiki/Kordylewski_cloud) and that article begins:

> Kordylewski clouds are large concentrations of dust **that exist** at the L4 and L5 Lagrangian points of the Earth–Moon system.1,2,3 They were first reported by Polish astronomer [Kazimierz Kordylewski](https://en.wikipedia.org/wiki/Kazimierz_Kordylewski) in the 1960s, **and confirmed to exist by the Royal Astronomical Society in October 2018.**1,2,3
>
> ---
>
> 1AAAS's Eureka Alert October 26, 2018: [Earth's dust cloud satellites confirmed](https://www.eurekalert.org/news-releases/652221)
>
> 2Slíz-Balogh, Judit; Barta, András; Horváth, Gábor (11 November 2018). "[Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth–Moon Lagrange point L5 – I. Three-dimensional celestial mechanical modelling of dust cloud formation](https://doi.org/10.1093%2Fmnras%2Fsty2049)". Monthly Notices of the Royal Astronomical Society. 480 (4): 5550–5559. and <https://arxiv.org/abs/1910.07466>.
>
> 3Slíz-Balogh, Judit; Barta, András; Horváth, Gábor (1 January 2019). "[Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth–Moon Lagrange point L5 – Part II. Imaging polarimetric observation: new evidence for the existence of Kordylewski dust cloud](https://doi.org/10.1093%2Fmnras%2Fsty2630)". Monthly Notices of the Royal Astronomical Society. 482 (1): 762–770. and <https://arxiv.org/abs/1910.07471>.

Discussion in comments on the previous question's page relate to the notion that for a buildup of material, items, particles or whatnots to occur at Earth-Moon Lagrange points, these things should have some kind of non-conservative or dissipative interaction - in other words be able to lose energy so they can "fall in" to Lagrange point-associated orbits and stay there for a while.

As I understand it, since $1/r^2$ forces (e.g. gravitational, electrostatic) are [conservative](https://en.wikipedia.org/wiki/Conservative_force) maybe something that dissipates energy (e.g. inelastic collisions converting some kinetic energy to thermal energy) might do the trick.

If this is all true (and I'm not saying it is) then I wonder:

**Question:** Are dust-dust collisions necessary to explain Kordylewski Clouds at Earth-Moon L4/5? Aren't the cross-sections too small to be significant considering the low number density of dust particles and short timescales involved?

Perturbations in the Earth-Moon Lagrange point system are strong - the Moon's orbit is significantly elliptical (non CR3BP) and the Sun's gravitational perturbation will also be significant. And of course for dust at 1 AU pressure from sunlight and electrostatic effects related to the solar wind may be important.

I'm having a hard time believing that it's dust-dust collisions that are the driving force behind the formation of the Kordylewski clouds, so I'm asking to be "straightened out" on my thinking here.

**note:** My current thinking is that collisions DO contribute to the accumulation of Trojan asteroids associated with the Sun-Jupiter L4/5 points. In this case all of the perturbing effects to dust with Earth-Moon L4/5 "accumulations" would not apply. Whether I'm right or wrong about that, the Trojans might be a good place to start before moving on to our local, dusty Kordylewski clouds.

**Tags:** solar-system, orbital-mechanics, dust

> **Comments:**
> **username_1**: You forget about interactions between photons and dust. a.k.a Poynting-Robertson drag.  
> **username_0**: @username_1 omission was actually deliberate, I didn't forget about it ([What is the origin of the dust near the sun?](https://astronomy.stackexchange.com/q/16707/7982)) If a particle is in heliocentric orbit photon pressure is radial just like the Sun's gravity so it's not really a perturber, but in the *Earth-Moon rotating frame* the Sun's gravity and photon pressure are now $1 \omega$ periodic perturbers (in the same direction) and for small enough dust could be comparable in magnitude. **I *guessed* P-R drag would be weak in comparison**, though still $1 \omega$ periodic. Was that incorrect?  
> **username_2**: @username_0 Poynting-Robertson drag is absolutely relevant; it’s a form of drag, and thus a form of dissipation. It’s not “radial”, as you seem to think.  
> **username_0**: @username_2 I said *photon pressure* is radial; that sentence doesn't refer to Poynting-Robertson (P-R) drag. The following sentences do refer to P-R and say that "I guessed P-R drag would be weak in comparison" to photon pressure, and that's why I did not include it. I said this to address username_1's "You forgot about", explaining that I didn't forget about it, I simply dismissed it as too weak to be important in the context of accumulation of dust at the triangular Lagrange points, then asked if thinking of it as too weak was wrong - to which no reply came.  
> **username_0**: @username_2 do you think that the P-R effect is significant in the context of dust accumulation at L4/L5? If so, can you expand on that?  
> **username_2**: @username_0 P-R drag is an excellent way to bring dust particles orbiting outside the Earth's orbit to smaller radii, allowing them to cross the Earth's orbit and thus (potentially) be captured by L4/L5-associated orbits.  
> **username_0**: @username_2 Yes, no dust means no accumulation, but I've asked specifically about the mechanisms of the "thus (potentially) be captured" part. I mean if you want to walk backwards we could include all the mechanisms that produce the dust particles too, and those that produced the nuclei of the atoms that are in the dust, but those don't help us with the accumulation mechanism.  

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