<p>In the early Solar System most orbits were circular.</p>
<p>The solid bodies in the Solar System condensed from a dense disc of gas and dust close to the Sun. Such a disc has many mechanisms for losing energy - i.e. dissipative mechanisms; primarily those resulting in the emission of radiation. Although such mechanisms reduce the energy of material in the disc they are are less able to remove angular momentum.</p>
<p>If we look at the specific energy (energy per unit mass, <span class="math-container">$E'$</span>) of an elliptical orbit and express it as a function of the specific angular momentum (angular momentum per unit mass, <span class="math-container">$L'$</span>) we find
<span class="math-container">$$ E' = -\frac{ (GM)^2 (1-e^2)}{2L'^2}\ , $$</span>
where <span class="math-container">$e$</span> is the eccentricity of the orbit.</p>
<p>If the specific angular momentum is fixed, then we see that the only way to reduce the specific energy, which is what happens in dissipative processes, is to reduce <span class="math-container">$e$</span> towards zero, towards a circular orbit. Equivalently, we see that a circular orbit is the lowest energy state for a given amount of angular momentum.</p>
<p>Any body orbiting in an environment where there are dissipative interactions will, on average, evolve towards having a circular orbit.</p>
<p>Thus, the material from which the planets formed was <em>already</em> orbiting close to the Sun, where it was dense enough to condense, and in a circular fashion thanks to the dissipative processes in the disc.</p>
<p>The planetary orbits are not perfecty circular because once the gas and dust clears, then the level of &quot;dissipativeness&quot; is reduced considerably and we expect then that individual mergers and collisions between proto-planetary bodies could well knock them out of a perfect circular orbit. This is a likely scenario for the inner Solar System planets</p>
<p>Parts of the outer Solar System also show higher eccentricities - e.g. some trans-Neptunian objects (Pluto, Sedna). But these are likely to have been scattered outwards by the migration of the larger giant planets during the epoch after the disc had dispersed but before the planets had settled into their current configuration (see  <a href="https://en.wikipedia.org/wiki/Nice_model" rel="noreferrer">the Nice model</a>). This also applies to the comets and the Oort cloud, which are thought to have been scattered from nearly circular orbits in the inner parts of the Solar System, where they formed, into the outer reaches of the Solar System (or beyond) by the migration of giant planets.</p>

CC BY-SA 4.0
2024-11-18T11:25:06.347Z
e and i damping for a body in the disc is not dominated by radiative processes - rather it's asymmetric gravitational torques, which can have a radiative component, but those function well in non-radiative simulations.
AtmosphericPrisonEscape
CC BY-SA 4.0
2024-11-18T11:49:08.780Z
"In a dense disc of gas and dust..." Radiative circularisation is surely key in this scenario @AtmosphericPrisonEscape ?   In terms of solid, macroscopic bodies, I'm sure that radiative dissipation becomes less important and I hedged my bets by saying "where there are dissipative interactions" - I assume dissipation is still a feature of the assymetric torquing process, otherwise where would the energy go?
ProfRob
CC BY-SA 4.0
2024-11-18T16:39:13.647Z
I would say that e and i damping are understudied in the radiative regime, with hints of "maybe it matters but radiation transport is expensive so we ignore it". Damping in the last two decades was often assumed to be viscous only (now we know that's a dodgy assumption, see ) with planets orbiting in isothermal discs. A recent overview can be found in the introduction to this paper https://www.aanda.org/articles/aa/full_html/2023/02/aa45196-22/aa45196-22.html 
Do you have a good reference that considers radiative circularization?
AtmosphericPrisonEscape
CC BY-SA 4.0
2024-11-18T16:43:33.907Z
@AtmosphericPrisonEscape accretion discs are cicularised by some sort of viscosity. The dissipated energy exits as radiation - this is why accretion discs are hot and we observe them.
ProfRob
CC BY-SA 4.0
2024-11-17T11:08:43.013Z
2024-11-17T11:15:50.923Z
2024-11-17T11:15:50.923Z
ProfRob
<p>A less scientific answer (based on probability): If some mass enters the gravity field of a sun (or is ejected from it), the path will be highly eccentric, but given many objects over a long time collisions will cause the paths to change (due to collisions or gravity effects when they get close enough), and as time goes by, the more circular orbits will survive with a much higher probability I guess.</p>

CC BY-SA 4.0
2024-11-18T09:57:04.350Z
2024-11-18T09:57:04.350Z
U. Windl
<p>I'm wondering why all the planet orbits are  circular when it seems to me they should almost all be eccentric.</p>
<p>Obviously, it's because that's the only stable orbit. But in those very early times when objects condensed and fell towards the Sun, they would be doing so from hundreds of millions or even billions of miles away. On that scale, the Sun is a teeny pinpoint less than a million miles wide. Almost everything would swing around it And either be ejected or would shoot back on a highly eccentric elliptical orbit.</p>
<p>It seems improbable that an orbit would commonly just happen to be very close to circular.</p>
<p>Yet we see nothing highly eccentric today except comets (whose eccentricity is an example of the above).</p>
<p>Is this assumption about the eccentricity of early orbits incorrect, did they all fall into the Sun, or did they all fall into planets that had circular orbits?</p>

CC BY-SA 4.0
2024-11-17T05:08:30.077Z
Here's a plot from https://en.wikipedia.org/wiki/Asteroid_belt of orbital inclination vs eccentricity for the numbered main-belt asteroids https://i.sstatic.net/dodSx.png For comparison, Earth's eccentricity is ~0.0167. OTOH, even an ellipse with eccentricity 0.2 still looks pretty circular, although the displacement of the focus from the centre is fairly obvious.
PM 2Ring
CC BY-SA 4.0
2024-11-17T05:22:26.720Z
Here's an example orbit with ec=1/5, with equal time steps between dots. https://i.sstatic.net/6nbY8FBM.png
PM 2Ring
CC BY-SA 4.0
2024-11-17T05:36:47.967Z
jesus, that's 1/5? wow.
Miss Understands
CC BY-SA 4.0
2024-11-17T05:44:26.030Z
Yep. Here's a condensed version of the plotting script. (The full version won't fit in a comment).
PM 2Ring
CC BY-SA 4.0
2024-11-17T05:44:39.730Z
https://sagecell.sagemath.org/?z=eJx9kkGP0zAQhe%5F5FU%5FLYcddlzaRQAJhiUu4pUJ7RezKsSe7ZtPYOM7S8uuR0zbQCz55RuNv3vOM5Q4vHHqOxEZiJz4WAFBDoYHCdo5svlZYIThssJtznY9wcAOiHp6YLg%5FzaXCnYJslrnM8kG2wAZVYgw1WMH6kWgixlGXij7%5FED%5F8QZxFZ00DUYJ2JJ8johgz5P3jRYOurnOug25FsLfAJJa%5FL6rpjPm1k%5FbJkj457i7ooXnWk23Qris9uSBy1SYXlDj62LpFWpQQbVW7eSexUWW0l9JT84xSsTqy%2D6H7ks7sOChorsJnDFgrjz5hIP1RYo3uoTjYORyi8skk%2DEumzySRyiUR7%5Foh0Mf0VCkFHvecUnXkMvU90OEpQkthKVKvghITxvY%5Fq5o3W%2Dkaic0%2Dj%2D83q%5FQlxD4VvhyMlVYt5MnWezNWmfD%5F3ulMYpz0F74ZE4cJ9npjcZreMYd4XiZAxPEx7jjox3V8Uvx2f%5FS8SfwBX5aHc&lang=sage
PM 2Ring
CC BY-SA 4.0
2024-11-17T05:56:12.777Z
@PM2Ring Damn, I didn't know you could do that in just that short code. It's 's C, right? I programmed in assembler or years, but I could have saved a lot of time with C. That += assignment operator is so cool!
Miss Understands
CC BY-SA 4.0
2024-11-17T06:01:18.733Z
No, that's [Sage](https://www.sagemath.org/), which is built on top of Python. That code is *mostly* Python, apart from the plotting functions.
PM 2Ring
CC BY-SA 4.0
2024-11-17T06:22:56.460Z
@PM2Ring Ah, so that's what python looks like! I read XKCD all the time, and I got the impression that it's legendary. But he's right about one thing, you can certainly pack a lot of procedure into a tiny program.
Miss Understands
CC BY-SA 4.0
2024-11-18T14:02:02.353Z
This question is similar to: [Why are most planetary orbits nearly circular](https://astronomy.stackexchange.com/questions/1979/why-are-most-planetary-orbits-nearly-circular). If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.
Beska
CC BY-SA 4.0
2024-11-19T11:13:42.050Z
"_objects condensed and fell towards the Sun_". You seem to assume that those objects appeared out of thin air, were static, and like an object you drop and falls to the floor, would have fallen towards the Sun. But those objects condensed out of components which were already in orbit, they were not static. Alternatively, you can consider that any object in orbit is perpetually "falling"... but at the same time its momentum keeps it from really falling and it continues on its orbit. If things actually "fell" towards the Sun, they would actually end up in the Sun, they would not fly past.
jcaron
CC BY-SA 4.0
2024-11-20T02:01:54.493Z
After reading both, this question *is not a duplicate* of the other question, and ProfRob's current answers to this question here is much more suitable to answer this question and much more informative. Closing as duplicate is counterproductive, so I'm **voting to leave open**
uhoh
<orbit><planet><solar-system><planetary-formation><eccentric-orbit>
In the early solar system, were most orbits highly eccentric?
Miss Understands
# In the early solar system, were most orbits highly eccentric?

(Asked by: username_0 on 2024-11-17)

I'm wondering why all the planet orbits are circular when it seems to me they should almost all be eccentric.

Obviously, it's because that's the only stable orbit. But in those very early times when objects condensed and fell towards the Sun, they would be doing so from hundreds of millions or even billions of miles away. On that scale, the Sun is a teeny pinpoint less than a million miles wide. Almost everything would swing around it And either be ejected or would shoot back on a highly eccentric elliptical orbit.

It seems improbable that an orbit would commonly just happen to be very close to circular.

Yet we see nothing highly eccentric today except comets (whose eccentricity is an example of the above).

Is this assumption about the eccentricity of early orbits incorrect, did they all fall into the Sun, or did they all fall into planets that had circular orbits?

**Tags:** orbit, planet, solar-system, planetary-formation, eccentric-orbit
> **Comments:**
> **username_1**: Here's a plot from https://en.wikipedia.org/wiki/Asteroid_belt of orbital inclination vs eccentricity for the numbered main-belt asteroids https://i.sstatic.net/dodSx.png For comparison, Earth's eccentricity is ~0.0167. OTOH, even an ellipse with eccentricity 0.2 still looks pretty circular, although the displacement of the focus from the centre is fairly obvious.  
> **username_1**: Here's an example orbit with ec=1/5, with equal time steps between dots. https://i.sstatic.net/6nbY8FBM.png  
> **username_0**: jesus, that's 1/5? wow.  
> **username_1**: Yep. Here's a condensed version of the plotting script. (The full version won't fit in a comment).  
> **username_1**: https://sagecell.sagemath.org/?z=eJx9kkGP0zAQhe%5F5FU%5FLYcddlzaRQAJhiUu4pUJ7RezKsSe7ZtPYOM7S8uuR0zbQCz55RuNv3vOM5Q4vHHqOxEZiJz4WAFBDoYHCdo5svlZYIThssJtznY9wcAOiHp6YLg%5FzaXCnYJslrnM8kG2wAZVYgw1WMH6kWgixlGXij7%5FED%5F8QZxFZ00DUYJ2JJ8johgz5P3jRYOurnOug25FsLfAJJa%5FL6rpjPm1k%5FbJkj457i7ooXnWk23Qris9uSBy1SYXlDj62LpFWpQQbVW7eSexUWW0l9JT84xSsTqy%2D6H7ks7sOChorsJnDFgrjz5hIP1RYo3uoTjYORyi8skk%2DEumzySRyiUR7%5Foh0Mf0VCkFHvecUnXkMvU90OEpQkthKVKvghITxvY%5Fq5o3W%2Dkaic0%2Dj%2D83q%5FQlxD4VvhyMlVYt5MnWezNWmfD%5F3ulMYpz0F74ZE4cJ9npjcZreMYd4XiZAxPEx7jjox3V8Uvx2f%5FS8SfwBX5aHc&lang=sage  
> **username_0**: @PM2Ring Damn, I didn't know you could do that in just that short code. It's 's C, right? I programmed in assembler or years, but I could have saved a lot of time with C. That += assignment operator is so cool!  
> **username_1**: No, that's [Sage](https://www.sagemath.org/), which is built on top of Python. That code is *mostly* Python, apart from the plotting functions.  
> **username_0**: @PM2Ring Ah, so that's what python looks like! I read XKCD all the time, and I got the impression that it's legendary. But he's right about one thing, you can certainly pack a lot of procedure into a tiny program.  
> **username_2**: This question is similar to: [Why are most planetary orbits nearly circular](https://astronomy.stackexchange.com/questions/1979/why-are-most-planetary-orbits-nearly-circular). If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.  
> **username_3**: "_objects condensed and fell towards the Sun_". You seem to assume that those objects appeared out of thin air, were static, and like an object you drop and falls to the floor, would have fallen towards the Sun. But those objects condensed out of components which were already in orbit, they were not static. Alternatively, you can consider that any object in orbit is perpetually "falling"... but at the same time its momentum keeps it from really falling and it continues on its orbit. If things actually "fell" towards the Sun, they would actually end up in the Sun, they would not fly past.  
> **username_4**: After reading both, this question *is not a duplicate* of the other question, and ProfRob's current answers to this question here is much more suitable to answer this question and much more informative. Closing as duplicate is counterproductive, so I'm **voting to leave open**  

---

## 2 answers

### Answer by username_5 on 2024-11-17. Score: 20

In the early Solar System most orbits were circular.

The solid bodies in the Solar System condensed from a dense disc of gas and dust close to the Sun. Such a disc has many mechanisms for losing energy - i.e. dissipative mechanisms; primarily those resulting in the emission of radiation. Although such mechanisms reduce the energy of material in the disc they are are less able to remove angular momentum.

If we look at the specific energy (energy per unit mass, $E'$) of an elliptical orbit and express it as a function of the specific angular momentum (angular momentum per unit mass, $L'$) we find
$$ E' = -\frac{ (GM)^2 (1-e^2)}{2L'^2}\ , $$
where $e$ is the eccentricity of the orbit.

If the specific angular momentum is fixed, then we see that the only way to reduce the specific energy, which is what happens in dissipative processes, is to reduce $e$ towards zero, towards a circular orbit. Equivalently, we see that a circular orbit is the lowest energy state for a given amount of angular momentum.

Any body orbiting in an environment where there are dissipative interactions will, on average, evolve towards having a circular orbit.

Thus, the material from which the planets formed was *already* orbiting close to the Sun, where it was dense enough to condense, and in a circular fashion thanks to the dissipative processes in the disc.

The planetary orbits are not perfecty circular because once the gas and dust clears, then the level of "dissipativeness" is reduced considerably and we expect then that individual mergers and collisions between proto-planetary bodies could well knock them out of a perfect circular orbit. This is a likely scenario for the inner Solar System planets

Parts of the outer Solar System also show higher eccentricities - e.g. some trans-Neptunian objects (Pluto, Sedna). But these are likely to have been scattered outwards by the migration of the larger giant planets during the epoch after the disc had dispersed but before the planets had settled into their current configuration (see [the Nice model](https://en.wikipedia.org/wiki/Nice_model)). This also applies to the comets and the Oort cloud, which are thought to have been scattered from nearly circular orbits in the inner parts of the Solar System, where they formed, into the outer reaches of the Solar System (or beyond) by the migration of giant planets.

> **Comments:**
> **username_6**: e and i damping for a body in the disc is not dominated by radiative processes - rather it's asymmetric gravitational torques, which can have a radiative component, but those function well in non-radiative simulations.  
> **username_5**: "In a dense disc of gas and dust..." Radiative circularisation is surely key in this scenario @AtmosphericPrisonEscape ?   In terms of solid, macroscopic bodies, I'm sure that radiative dissipation becomes less important and I hedged my bets by saying "where there are dissipative interactions" - I assume dissipation is still a feature of the assymetric torquing process, otherwise where would the energy go?  
> **username_6**: I would say that e and i damping are understudied in the radiative regime, with hints of "maybe it matters but radiation transport is expensive so we ignore it". Damping in the last two decades was often assumed to be viscous only (now we know that's a dodgy assumption, see ) with planets orbiting in isothermal discs. A recent overview can be found in the introduction to this paper https://www.aanda.org/articles/aa/full_html/2023/02/aa45196-22/aa45196-22.html  Do you have a good reference that considers radiative circularization?  
> **username_5**: @AtmosphericPrisonEscape accretion discs are cicularised by some sort of viscosity. The dissipated energy exits as radiation - this is why accretion discs are hot and we observe them.  

---

### Answer by username_7 on 2024-11-18. Score: 0

A less scientific answer (based on probability): If some mass enters the gravity field of a sun (or is ejected from it), the path will be highly eccentric, but given many objects over a long time collisions will cause the paths to change (due to collisions or gravity effects when they get close enough), and as time goes by, the more circular orbits will survive with a much higher probability I guess.


---

