<p>I want to point out that the Moon's orbit isn't circular now.   <a href="https://en.wikipedia.org/wiki/Orbit_of_the_Moon" rel="noreferrer">A 0.055 mean eccentricity</a> isn't that circular.  </p>

<p>But, onto your question.   I think you're making a bad assumption on the "must have started very elliptic.   Individual objects that are ejected from a planet need to follow their orbital path.   So any object flung from the earth would need likely either escape the Earth or fall back into it because you can't launch something, with a singular push, into a circular orbit.   All the individual bits of debris should have had highly eccentric orbits.</p>

<p>But the formation of the Moon was much more complicated than that.   First, it was enough matter to have it's own gravitational field, basically influencing itself, and the forming moon would be the combination of all those individual objects, so it wouldn't necessarily be eliptic at all.   The eccentricity of billions of objects could have (and likely did) cancel each other out to a large degree.  </p>

<p>Because the impact was off-center, it set the Earth spinning and most of the debris moved in the same direction around the Earth.   But the coalescing mass of material that didn't fall back to the Earth could have been in a reasonably circular orbit at formation.  </p>

<p>We should also define what number constitutes "highly" elliptic.   The Moon is thought to have started out 3-5 Earth Radii distant.   Any material that passed closer than 3 radii would have been inside the Roche limit and had a hard time coalescing into the Moon.    <a href="http://curious.astro.cornell.edu/about-us/37-our-solar-system/the-moon/the-moon-and-the-earth/31-how-close-was-the-moon-to-the-earth-when-it-formed-intermediate" rel="noreferrer">This article</a> suggests that the debris would have had a hard time being ejected further than 5 Earth Radii, though I'm not sure how that conclusion was reached.  But you have a few things going on.  Debris colliding with other debris, and some (presumably quite a bit) of debris falling back to the Earth and, mentioned above, the debris having a gravitational effect on itself.   Ultimately momentum needs to be conserved and calculating the formation of the Moon requires a super-computer, but in general I think the initial orbit could have been relatively circular.</p>

<p>If the Moon formed close to the Earth, which most models suggest it did and since it couldn't pass inside 3 Earth Radii and stay solid, those numbers put a limit on how eccentric the initial orbit probably was.   If we use the 5/3 Earth Radii as an estimate, Ra=5, Rp=3, then the eccentricity is 0.25, and that's an estimate for the upper limit of the initial eccentricity after formation.  It may well have been quite a bit less.</p>

<p><a href="https://i.sstatic.net/CH3qB.gif" rel="noreferrer"><img src="https://i.sstatic.net/CH3qB.gif" alt="http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/kep.gif"></a></p>

<p>But for the sake of argument, lets give the newly formed moon an eccentricity of .25 or, maybe a little higher with a <a href="http://www.lunarplanner.com/LunarPerigee/" rel="noreferrer">more distant apogee</a>, but we have to keep the perigee at 3 Earth radii or greater.   Your question still stands, how did the Moon's initial eccentricity become somewhat circular.</p>

<p>The answer is <a href="https://en.wikipedia.org/wiki/Tidal_circularization" rel="noreferrer">tidal circularization</a>.   I can't find a good article on it, but for many 2 body systems, tides circularize orbits.   It's well known that the tides on Earth, caused by the Moon's gravity rotate ahead of the Moon and this creates a tug on the moon that pushes (pulls?) the Moon into a higher orbit, further away from the Earth.   This same secondary effect circularizes the Moon's orbit because the closer the Moon is too the Earth, the greater the push.  The math behind this gets very complicated and it's above my paygrade to put numbers behind it and the Wikipedia article I've linked is very lacking, so I invite anyone to provide more details if they can. But Tidal circularization is a commonly accepted theory and given the strength of the tides early on, it's likely any eccentricity in the Moon's orbit circularized relatively quickly, at least, astronomically speaking.   (Tens of millions of years is a long time to you and me, but not to a stable orbit).</p>

CC BY-SA 3.0
2017-08-26T19:52:58.247Z
`A 0.055 mean eccentricity isn't that circular.` Point well taken. `The eccentricity of billions of objects could have (and likely did) cancel each other out to a large degree.` I think this is wrong. In a closed system, the center of mass never changes. 1 particle with 0.5 e might hit one with 0.2 e and together they become 0.35 e, **but their perigee started off the same and remains the same.** The perigee has to be raised somehow or else the coalescing body will already be inside its own roche limit, and indeed, the expanding radius of the body might even directly scrape into Earth.
DrZ214
CC BY-SA 3.0
2017-08-26T19:57:06.093Z
Nevertheless, +1 for your answer as it is well-explained. You made it clear that I'm actually asking two things. The first part is how the body raised its perigee so as not to break up by roche limit. The second part is how the orbit actually circularized (by which I mean how it became **more** circular, not necessarily a perfect circle). You answered that by tidal interactions with the bulge of Earth and Moon, and indeed, the Moon is still moving away from us (and lowering it's eccentricity?) to this day. But the first part still remains open in my mind. I should proly edit the OP a bit.
DrZ214
CC BY-SA 3.0
2017-08-26T20:03:05.657Z
@DrZ214 Actually, because of the Sun, as the Moon moves further away from the Earth, it's (mean) eccentricity increases.  This happens very slowly, of-course, but the Moon was likely was more circular 2 or 3 and maybe even 4 billion years ago when it was closer to the Earth.   It probably circularized fairly quickly because that close to the Earth, the tidal forces were very strong - at least, that's my understanding, but I can't do the math.   If there's an orbital math wizard reading this, I invite them to chime in.
userLTK
CC BY-SA 3.0
2017-08-26T20:24:11.897Z
@DrZ214 On your first comment.   You may be right on two objects, but this is a wave of debris ejected.   It's worth noting that the Earth lost mass in the ejection too, so while a typical ejection would be highly elliptical (or if above escape velocity, would just fly away) much of the debris ejected probably did enter orbits around the Earth, and after that, you have collisions and gravity assists and it's a mathematical mess.  probably a bunch of debris fell back to the Earth but the debris that stayed in orbit, I think it could have started out somewhat circular (but I'm mostly guessing)
userLTK
CC BY-SA 3.0
2017-08-26T11:34:31.657Z
2017-08-26T11:34:31.657Z
userLTK
<p>Well, I don't really think the GI Hypothesis can answer the orbital plan of the moon, I would say that the circular orbit of the moon today regarding the GIH is also due to other variables, like Jupiter, the Sun, etc... If the GIH is true, then the moon should still be on a quite elliptical orbit still, since the gravitational forces of other celestial bodies are not strong enough to transformer the orbit in the 4 million years since (Concerning my personal knowledge on gravity and the impact it has on long duration of time)</p>

CC BY-SA 3.0
2017-08-26T19:29:51.857Z
It's actually 4 **billion** years, not million. But all the GIH models I've read about say that the coallescing of the Moon takes no longer than 100 years. Presumably the orbit must have circularized a little bit by then or the big ball would scrape against Earth at perigee.
DrZ214
CC BY-SA 3.0
2017-08-26T19:53:32.723Z
The sun doesn't circularize the Moon's orbit, it perturbs it.   As the Moon moves further from the earth, towards the unstable region of the hill sphere, it's orbit will grow more and more eccentric and inconsistent.   As it is, the Moon has one of the most irregular orbits of any large body in the solar-system with just a 19 year orbital cycle (or 235 synodic orbits).  That's very short and it's because of the Sun's significant perturbations on the moon.   Somewhat related answer here  https://astronomy.stackexchange.com/questions/10946/why-doesnt-the-sun-pull-the-moon-away-from-earth
userLTK
CC BY-SA 3.0
2017-08-26T09:01:54.233Z
2017-08-26T09:01:54.233Z
Michael P. Jouanneau
<blockquote>
  <p>Does the Giant Impact Hypothesis explain how the Moon circularized its orbit?</p>
</blockquote>

<p>No, it does not.</p>

<p>The giant impact hypothesis says that the Moon formed a handful of Earth radii from the center of the Earth. The Moon currently orbits about 60 Earth radii from the center of the Earth. This means that whether the Moon's initial orbit was highly eccentric or almost circular is irrelevant with regard to the Moon's current orbit.</p>

<blockquote>
  <p>A debris field from any impact would at first follow a very elliptical orbit, with a perigee very close to the surface of the Earth and an apogee much farther away.</p>
</blockquote>

<p>That is incorrect. A debris field will circularize itself rather quickly. Collisions put some particles on an escape trajectory, other particles on a collision trajectory, with what's left tending toward having nearly circular orbits.</p>

CC BY-SA 3.0
2017-08-29T18:17:32.937Z
`A debris field will circularize itself rather quickly. Collisions put some particles on an escape trajectory, other particles on a collision trajectory, with what's left tending toward having nearly circular orbits.` Source? Every sim I've seen shows the debris very elliptical and indeed the coalescing ball gets pulled apart tidally with each orbit. I don't see how you can say that when an orbiting object will always return to its same point. The point I'm emphasizing here is perigee. Perigee starts very low and something outside the Earth-debris system is needed to perturb/raise it.
DrZ214
CC BY-SA 3.0
2017-08-30T20:40:42.023Z
@DrZ214 - The initial debris field from the giant impact would have been extremely hot, over 3000 kelvin. That would have made the debris a mix of most gas and liquid, with the liquid torn into droplets via tidal stresses. The gas component circularized quickly due to pressure, and given the small size of the droplets, this would have made the droplets highly subject to drag. The protolunar disk would have circularized itself very quickly.
David Hammen
CC BY-SA 3.0
2017-08-29T08:40:33.027Z
2017-08-29T08:40:33.027Z
David Hammen
<p>I just read most of Wikipedia's <a href="https://en.wikipedia.org/wiki/Giant-impact_hypothesis" rel="nofollow noreferrer">article on the Giant Impact Hypothesis</a>. Basically a large object impacts Earth and creates debris that soon coalesces into the Moon.</p>

<p>But there is something I did not find mentioned: <strong>How would the Moon get its circular orbit?</strong></p>

<p>A debris field from any impact would at first follow a very elliptical orbit, with a perigee very close to the surface of the Earth and an apogee much farther away. In orbital mechanics, where you start is where you end up. In fact it doesn't even have to be where you start. Pick any point in the orbit and you will return there again. In other words, the original elliptical orbit doesn't change its shape.</p>

<p>...Unless there are pertubations or impacts that change your velocity. How exactly did that happen? Does the GIH just assume something else did that fortuitously?</p>

<p>I've also seen youtube video simulations like <a href="https://www.youtube.com/watch?v=cn5vh7hZ2o0" rel="nofollow noreferrer">this</a>. It's hard to tell if the camera angle is changing or if the orbital plane is unstable (how?), but you can clearly see the debris goes around and impacts the surface again and again. I.e., <strong>the orbit remains highly elliptical. I've never seen a simulation that shows the debris circularizing.</strong></p>

<p>I also want to note that this question is highly relavent not just to the Moon, but many other things like orbital capture as well. I've never understood orbital capture theories as they all seem to leave out how the initial elliptical orbit later becomes circular, e.g., Triton.</p>

<orbit><the-moon><orbital-migration><eccentric-orbit><theia>
Does the Giant Impact Hypothesis explain how the Moon circularized its orbit?
DrZ214
# Does the Giant Impact Hypothesis explain how the Moon circularized its orbit?

(Asked by: username_0 on 2017-08-26)

I just read most of Wikipedia's [article on the Giant Impact Hypothesis](https://en.wikipedia.org/wiki/Giant-impact_hypothesis). Basically a large object impacts Earth and creates debris that soon coalesces into the Moon.

But there is something I did not find mentioned: **How would the Moon get its circular orbit?**

A debris field from any impact would at first follow a very elliptical orbit, with a perigee very close to the surface of the Earth and an apogee much farther away. In orbital mechanics, where you start is where you end up. In fact it doesn't even have to be where you start. Pick any point in the orbit and you will return there again. In other words, the original elliptical orbit doesn't change its shape.

...Unless there are pertubations or impacts that change your velocity. How exactly did that happen? Does the GIH just assume something else did that fortuitously?

I've also seen youtube video simulations like [this](https://www.youtube.com/watch?v=cn5vh7hZ2o0). It's hard to tell if the camera angle is changing or if the orbital plane is unstable (how?), but you can clearly see the debris goes around and impacts the surface again and again. I.e., **the orbit remains highly elliptical. I've never seen a simulation that shows the debris circularizing.**

I also want to note that this question is highly relavent not just to the Moon, but many other things like orbital capture as well. I've never understood orbital capture theories as they all seem to leave out how the initial elliptical orbit later becomes circular, e.g., Triton.

**Tags:** orbit, the-moon, orbital-migration, eccentric-orbit, theia

---

## 3 answers

### Answer by username_1 on 2017-08-26. Score: 10

I want to point out that the Moon's orbit isn't circular now. [A 0.055 mean eccentricity](https://en.wikipedia.org/wiki/Orbit_of_the_Moon) isn't that circular.

But, onto your question. I think you're making a bad assumption on the "must have started very elliptic. Individual objects that are ejected from a planet need to follow their orbital path. So any object flung from the earth would need likely either escape the Earth or fall back into it because you can't launch something, with a singular push, into a circular orbit. All the individual bits of debris should have had highly eccentric orbits.

But the formation of the Moon was much more complicated than that. First, it was enough matter to have it's own gravitational field, basically influencing itself, and the forming moon would be the combination of all those individual objects, so it wouldn't necessarily be eliptic at all. The eccentricity of billions of objects could have (and likely did) cancel each other out to a large degree.

Because the impact was off-center, it set the Earth spinning and most of the debris moved in the same direction around the Earth. But the coalescing mass of material that didn't fall back to the Earth could have been in a reasonably circular orbit at formation.

We should also define what number constitutes "highly" elliptic. The Moon is thought to have started out 3-5 Earth Radii distant. Any material that passed closer than 3 radii would have been inside the Roche limit and had a hard time coalescing into the Moon. [This article](http://curious.astro.cornell.edu/about-us/37-our-solar-system/the-moon/the-moon-and-the-earth/31-how-close-was-the-moon-to-the-earth-when-it-formed-intermediate) suggests that the debris would have had a hard time being ejected further than 5 Earth Radii, though I'm not sure how that conclusion was reached. But you have a few things going on. Debris colliding with other debris, and some (presumably quite a bit) of debris falling back to the Earth and, mentioned above, the debris having a gravitational effect on itself. Ultimately momentum needs to be conserved and calculating the formation of the Moon requires a super-computer, but in general I think the initial orbit could have been relatively circular.

If the Moon formed close to the Earth, which most models suggest it did and since it couldn't pass inside 3 Earth Radii and stay solid, those numbers put a limit on how eccentric the initial orbit probably was. If we use the 5/3 Earth Radii as an estimate, Ra=5, Rp=3, then the eccentricity is 0.25, and that's an estimate for the upper limit of the initial eccentricity after formation. It may well have been quite a bit less.

[![http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/kep.gif](https://i.sstatic.net/CH3qB.gif)](https://i.sstatic.net/CH3qB.gif)

But for the sake of argument, lets give the newly formed moon an eccentricity of .25 or, maybe a little higher with a [more distant apogee](http://www.lunarplanner.com/LunarPerigee/), but we have to keep the perigee at 3 Earth radii or greater. Your question still stands, how did the Moon's initial eccentricity become somewhat circular.

The answer is [tidal circularization](https://en.wikipedia.org/wiki/Tidal_circularization). I can't find a good article on it, but for many 2 body systems, tides circularize orbits. It's well known that the tides on Earth, caused by the Moon's gravity rotate ahead of the Moon and this creates a tug on the moon that pushes (pulls?) the Moon into a higher orbit, further away from the Earth. This same secondary effect circularizes the Moon's orbit because the closer the Moon is too the Earth, the greater the push. The math behind this gets very complicated and it's above my paygrade to put numbers behind it and the Wikipedia article I've linked is very lacking, so I invite anyone to provide more details if they can. But Tidal circularization is a commonly accepted theory and given the strength of the tides early on, it's likely any eccentricity in the Moon's orbit circularized relatively quickly, at least, astronomically speaking. (Tens of millions of years is a long time to you and me, but not to a stable orbit).

> **Comments:**
> **username_0**: `A 0.055 mean eccentricity isn't that circular.` Point well taken. `The eccentricity of billions of objects could have (and likely did) cancel each other out to a large degree.` I think this is wrong. In a closed system, the center of mass never changes. 1 particle with 0.5 e might hit one with 0.2 e and together they become 0.35 e, **but their perigee started off the same and remains the same.** The perigee has to be raised somehow or else the coalescing body will already be inside its own roche limit, and indeed, the expanding radius of the body might even directly scrape into Earth.  
> **username_0**: Nevertheless, +1 for your answer as it is well-explained. You made it clear that I'm actually asking two things. The first part is how the body raised its perigee so as not to break up by roche limit. The second part is how the orbit actually circularized (by which I mean how it became **more** circular, not necessarily a perfect circle). You answered that by tidal interactions with the bulge of Earth and Moon, and indeed, the Moon is still moving away from us (and lowering it's eccentricity?) to this day. But the first part still remains open in my mind. I should proly edit the OP a bit.  
> **username_1**: @DrZ214 Actually, because of the Sun, as the Moon moves further away from the Earth, it's (mean) eccentricity increases.  This happens very slowly, of-course, but the Moon was likely was more circular 2 or 3 and maybe even 4 billion years ago when it was closer to the Earth.   It probably circularized fairly quickly because that close to the Earth, the tidal forces were very strong - at least, that's my understanding, but I can't do the math.   If there's an orbital math wizard reading this, I invite them to chime in.  
> **username_1**: @DrZ214 On your first comment.   You may be right on two objects, but this is a wave of debris ejected.   It's worth noting that the Earth lost mass in the ejection too, so while a typical ejection would be highly elliptical (or if above escape velocity, would just fly away) much of the debris ejected probably did enter orbits around the Earth, and after that, you have collisions and gravity assists and it's a mathematical mess.  probably a bunch of debris fell back to the Earth but the debris that stayed in orbit, I think it could have started out somewhat circular (but I'm mostly guessing)  

---

### Answer by username_2 on 2017-08-26. Score: 3

Well, I don't really think the GI Hypothesis can answer the orbital plan of the moon, I would say that the circular orbit of the moon today regarding the GIH is also due to other variables, like Jupiter, the Sun, etc... If the GIH is true, then the moon should still be on a quite elliptical orbit still, since the gravitational forces of other celestial bodies are not strong enough to transformer the orbit in the 4 million years since (Concerning my personal knowledge on gravity and the impact it has on long duration of time)

> **Comments:**
> **username_0**: It's actually 4 **billion** years, not million. But all the GIH models I've read about say that the coallescing of the Moon takes no longer than 100 years. Presumably the orbit must have circularized a little bit by then or the big ball would scrape against Earth at perigee.  
> **username_1**: The sun doesn't circularize the Moon's orbit, it perturbs it.   As the Moon moves further from the earth, towards the unstable region of the hill sphere, it's orbit will grow more and more eccentric and inconsistent.   As it is, the Moon has one of the most irregular orbits of any large body in the solar-system with just a 19 year orbital cycle (or 235 synodic orbits).  That's very short and it's because of the Sun's significant perturbations on the moon.   Somewhat related answer here  https://astronomy.stackexchange.com/questions/10946/why-doesnt-the-sun-pull-the-moon-away-from-earth  

---

### Answer by username_3 on 2017-08-29. Score: 3

> Does the Giant Impact Hypothesis explain how the Moon circularized its orbit?

No, it does not.

The giant impact hypothesis says that the Moon formed a handful of Earth radii from the center of the Earth. The Moon currently orbits about 60 Earth radii from the center of the Earth. This means that whether the Moon's initial orbit was highly eccentric or almost circular is irrelevant with regard to the Moon's current orbit.

> A debris field from any impact would at first follow a very elliptical orbit, with a perigee very close to the surface of the Earth and an apogee much farther away.

That is incorrect. A debris field will circularize itself rather quickly. Collisions put some particles on an escape trajectory, other particles on a collision trajectory, with what's left tending toward having nearly circular orbits.

> **Comments:**
> **username_0**: `A debris field will circularize itself rather quickly. Collisions put some particles on an escape trajectory, other particles on a collision trajectory, with what's left tending toward having nearly circular orbits.` Source? Every sim I've seen shows the debris very elliptical and indeed the coalescing ball gets pulled apart tidally with each orbit. I don't see how you can say that when an orbiting object will always return to its same point. The point I'm emphasizing here is perigee. Perigee starts very low and something outside the Earth-debris system is needed to perturb/raise it.  
> **username_3**: @DrZ214 - The initial debris field from the giant impact would have been extremely hot, over 3000 kelvin. That would have made the debris a mix of most gas and liquid, with the liquid torn into droplets via tidal stresses. The gas component circularized quickly due to pressure, and given the small size of the droplets, this would have made the droplets highly subject to drag. The protolunar disk would have circularized itself very quickly.  

---

