<p>I'll get to your question shortly, but first let's talk about the asteroids.</p>
<p>Asteroid sizes roughly follow a power law, <span class="math-container">$n \propto D^{-2.5}$</span>, where <span class="math-container">$n$</span> is the number of asteroids larger than diameter <span class="math-container">$D$</span>. Using the data given on <a href="https://en.wikipedia.org/wiki/Asteroid#Size_distribution" rel="noreferrer">Wikipedia</a>, I get <span class="math-container">$n \approx 10^5×D^{-2.5}$</span>, where <span class="math-container">$D$</span> is in kilometres.</p>
<p>Here's a log-log plot of the observed main belt asteroid size distribution, taken from <a href="https://www.researchgate.net/publication/45858498_Collisional_and_Rotational_Disruption_of_Asteroids" rel="noreferrer">Collisional and Rotational Disruption of Asteroids</a>, by Walsh, Kevin J.; Michel, Patrick; Richardson, Derek C. DOI:10.1166/asl.2011.1206</p>
<p><a href="https://i.sstatic.net/9mGky.png" rel="noreferrer"><img src="https://i.sstatic.net/9mGky.png" alt="Asteroid size distribution" /></a></p>
<blockquote>
<p>The size distribution of Main Belt asteroids, with the cumulative number larger than a given diameter plotted against diameter (km). Many different determinations of this relationship are shown, each drawing data from different sources. The larger trend emerges with two bumps, around ~5 km and ~100 km. </p>
</blockquote>
<p>That curve doesn't deviate very much from the line of best fit, over the 6 orders of magnitude shown. For smaller sizes, the slope drops slightly simply because the small asteroids are harder to observe.</p>
<p>The power law can be explained as the equilibrium resulting from two primary processes. Firstly, when two asteroids of similar size bump into each other, they tend to either bounce off each other or both asteroids shatter into smaller pieces. Secondly, when an asteroid hits a much larger asteroid, the small one tends to accrete onto the large one. There's a brief derivation of this process, with diagrams, on <a href="https://www.reddit.com/r/Physics/comments/bno1q0/why_the_size_distribution_of_asteroids_follow_a/" rel="noreferrer">Reddit</a>.</p>
<p>This equilibrium calculation assumes that the self-gravity of the asteroids is negligible. It also ignores the heat generated by collisions. For large asteroids / planetesimals, the gravity is <em>not</em> negligible, and the conversion of kinetic energy to heat can be substantial. These factors modify how the &quot;Kessler syndrome&quot; process affects large bodies.</p>
<p>The effects of heat are complicated. It can drive off volatiles, and it can cause the body to melt, which permits the components to be sorted gravitationally, that is, the heavier elements can sink towards the centre of the planetesimal, giving it a denser core. So when a planetesimal is large enough, it literally forges itself into a tougher body, more likely to survive disruption.</p>
<p>I should mention that most meteorites that we've examined don't show evidence of the effects of substantial heat during their formation.</p>
<p>Eventually, we ended up with a bunch of planets that were able to withstand the disruptive effects of the smaller bodies. Thus when the (hypothesised) collision between the proto-Earth and Theia occured, they didn't just shatter into numerous pieces like two small rocks would. Instead, the proto-Earth partly melted (and it already had substantial internal heat of formation), and we ended up with the Earth and the Moon (and probably a relatively small amount of loose material).</p>
<p>Still, the modern Solar system contains a <em>lot</em> of small material. We have a handful of planets, a couple of dozen moons, a few hundred large asteroids, and billions (or trillions) of small rocks and pebbles. And <em>vast</em> numbers of dust particles.</p>
<hr />
<p>Incidentally, not all of the Solar system dust is primordial, or created locally by the above processes. The Solar system is currently travelling through a dusty patch of the Milky Way: an interstellar dust cloud. Brian May found evidence of this in the 1970s, which he mentions in <em>A Survey of Radial Velocities in the Zodiacal Dust Cloud</em>. It took him a couple of decades to publish this info because he was busy being a rock star. ;) According to Dr May, at a distance of 20 AU or so (the orbital radius of Uranus), the zodiacal dust is dominated by interstellar dust, IIRC.</p>

CC BY-SA 4.0
2022-05-24T22:28:24.720Z
Does the fact that the motions are more ordered than satellites around the Earth also result in lower energy collisions?
ProfRob
CC BY-SA 4.0
2022-05-24T23:46:47.107Z
@ProfRob The motions became more orderly over time, as larger asteroids & planetesimals formed, which were capable of clearing their orbits, to some extent. In the early stages, things were quite chaotic, like motion in a gas, with gravity only playing a minor role, at least locally.
PM 2Ring
CC BY-SA 4.0
2022-05-26T23:24:32.337Z
@PM2Ring Most satellites in low Earth orbit are in highly inclined orbits.
David Hammen
CC BY-SA 4.0
2022-05-24T18:28:11.807Z
2022-05-24T18:28:11.807Z
PM 2Ring
<p>In 1978, Donald Kessler proposed that space pollution in orbit around the Earth could enter a collisional cascading state.  This means debris would collide with satellites, generating more debris, causing more collisions, until the whole orbital regime was peppered with debris.  This syndrome is referred to as <a href="https://en.wikipedia.org/wiki/Kessler_syndrome" rel="noreferrer">Kessler Syndrome</a>.</p>
<p>Kessler was inspired by modeling the evolution of our asteroid belt.</p>
<p>Question: <strong>Given the highly energetic and chaotic nature of our early Solar System, why weren't all the protoplanets torn apart in collisions?</strong>  Are there other star systems surrounded by a debris field rather than planets due to the syndrome?</p>

CC BY-SA 4.0
2022-05-24T19:17:53.957Z
You forgot that in the protoplanetary disc the dust is a minor component in terms of mass. Instead the mass is dominated by hydrogen and helium gas, which changes the dynamics of the solid component entirely: It damps eccentricities and inclinations and leads to dust-gas two-fluid instabilities which lead directly to the formation of asteroids.
AtmosphericPrisonEscape
CC BY-SA 4.0
2022-05-24T22:26:02.553Z
@AtmosphericPrisonEscape collisional cascades are an important component of solar system formation and can happen after the gas has gone.
ProfRob
CC BY-SA 4.0
2022-05-25T11:37:49.633Z
@ProfRob: Yes, true. But you neither contradicted my point or supported it, instead talking sideways.
AtmosphericPrisonEscape
<planetary-formation><collision><solar-system-evolution>
Why didn't Kessler Syndrome prevent planet formation?
Connor Garcia
# Why didn't Kessler Syndrome prevent planet formation?

(Asked by: username_0 on 2022-05-24)

In 1978, Donald Kessler proposed that space pollution in orbit around the Earth could enter a collisional cascading state. This means debris would collide with satellites, generating more debris, causing more collisions, until the whole orbital regime was peppered with debris. This syndrome is referred to as [Kessler Syndrome](https://en.wikipedia.org/wiki/Kessler_syndrome).

Kessler was inspired by modeling the evolution of our asteroid belt.

Question: **Given the highly energetic and chaotic nature of our early Solar System, why weren't all the protoplanets torn apart in collisions?** Are there other star systems surrounded by a debris field rather than planets due to the syndrome?

**Tags:** planetary-formation, collision, solar-system-evolution

> **Comments:**
> **username_1**: You forgot that in the protoplanetary disc the dust is a minor component in terms of mass. Instead the mass is dominated by hydrogen and helium gas, which changes the dynamics of the solid component entirely: It damps eccentricities and inclinations and leads to dust-gas two-fluid instabilities which lead directly to the formation of asteroids.  
> **username_2**: @username_1 collisional cascades are an important component of solar system formation and can happen after the gas has gone.  
> **username_1**: @username_2: Yes, true. But you neither contradicted my point or supported it, instead talking sideways.  

---

## 1 answers

### Answer by username_3 on 2022-05-24. Score: 8 | Accepted answer

I'll get to your question shortly, but first let's talk about the asteroids.

Asteroid sizes roughly follow a power law, $n \propto D^{-2.5}$, where $n$ is the number of asteroids larger than diameter $D$. Using the data given on [Wikipedia](https://en.wikipedia.org/wiki/Asteroid#Size_distribution), I get $n \approx 10^5×D^{-2.5}$, where $D$ is in kilometres.

Here's a log-log plot of the observed main belt asteroid size distribution, taken from [Collisional and Rotational Disruption of Asteroids](https://www.researchgate.net/publication/45858498_Collisional_and_Rotational_Disruption_of_Asteroids), by Walsh, Kevin J.; Michel, Patrick; Richardson, Derek C. DOI:10.1166/asl.2011.1206

[![Asteroid size distribution](https://i.sstatic.net/9mGky.png)](https://i.sstatic.net/9mGky.png)

> The size distribution of Main Belt asteroids, with the cumulative number larger than a given diameter plotted against diameter (km). Many different determinations of this relationship are shown, each drawing data from different sources. The larger trend emerges with two bumps, around ~5 km and ~100 km.

That curve doesn't deviate very much from the line of best fit, over the 6 orders of magnitude shown. For smaller sizes, the slope drops slightly simply because the small asteroids are harder to observe.

The power law can be explained as the equilibrium resulting from two primary processes. Firstly, when two asteroids of similar size bump into each other, they tend to either bounce off each other or both asteroids shatter into smaller pieces. Secondly, when an asteroid hits a much larger asteroid, the small one tends to accrete onto the large one. There's a brief derivation of this process, with diagrams, on [Reddit](https://www.reddit.com/r/Physics/comments/bno1q0/why_the_size_distribution_of_asteroids_follow_a/).

This equilibrium calculation assumes that the self-gravity of the asteroids is negligible. It also ignores the heat generated by collisions. For large asteroids / planetesimals, the gravity is *not* negligible, and the conversion of kinetic energy to heat can be substantial. These factors modify how the "Kessler syndrome" process affects large bodies.

The effects of heat are complicated. It can drive off volatiles, and it can cause the body to melt, which permits the components to be sorted gravitationally, that is, the heavier elements can sink towards the centre of the planetesimal, giving it a denser core. So when a planetesimal is large enough, it literally forges itself into a tougher body, more likely to survive disruption.

I should mention that most meteorites that we've examined don't show evidence of the effects of substantial heat during their formation.

Eventually, we ended up with a bunch of planets that were able to withstand the disruptive effects of the smaller bodies. Thus when the (hypothesised) collision between the proto-Earth and Theia occured, they didn't just shatter into numerous pieces like two small rocks would. Instead, the proto-Earth partly melted (and it already had substantial internal heat of formation), and we ended up with the Earth and the Moon (and probably a relatively small amount of loose material).

Still, the modern Solar system contains a *lot* of small material. We have a handful of planets, a couple of dozen moons, a few hundred large asteroids, and billions (or trillions) of small rocks and pebbles. And *vast* numbers of dust particles.

---

Incidentally, not all of the Solar system dust is primordial, or created locally by the above processes. The Solar system is currently travelling through a dusty patch of the Milky Way: an interstellar dust cloud. Brian May found evidence of this in the 1970s, which he mentions in *A Survey of Radial Velocities in the Zodiacal Dust Cloud*. It took him a couple of decades to publish this info because he was busy being a rock star. ;) According to Dr May, at a distance of 20 AU or so (the orbital radius of Uranus), the zodiacal dust is dominated by interstellar dust, IIRC.

> **Comments:**
> **username_2**: Does the fact that the motions are more ordered than satellites around the Earth also result in lower energy collisions?  
> **username_3**: @username_2 The motions became more orderly over time, as larger asteroids & planetesimals formed, which were capable of clearing their orbits, to some extent. In the early stages, things were quite chaotic, like motion in a gas, with gravity only playing a minor role, at least locally.  
> **username_4**: @PM2Ring Most satellites in low Earth orbit are in highly inclined orbits.  

---

