<p>A full-text search using the astronomical-literature collection on the <a href="https://ui.adsabs.harvard.edu" rel="noreferrer">Astrophysics Data System</a> (more complete and more astronomy-specific than Google Scholar) yields 10,845 hits for "Lagrange point" and <a href="https://ui.adsabs.harvard.edu/search/filter_database_fq_database=AND&amp;filter_database_fq_database=database%3A%22astronomy%22&amp;fq=%7B!type%3Daqp%20v%3D%24fq_database%7D&amp;fq_database=database%3A%22astronomy%22&amp;q=collection%3Aastronomy%20full%3A%22libration%20point%22&amp;sort=date%20desc%2C%20bibcode%20desc&amp;p_=0" rel="noreferrer">2,302 for "libration point"</a> (not sure how long that URL will be valid, but it's easy enough to redo the search). So it's clear the former is more common than the latter. </p>

<p>Nonetheless, my impression from looking at article titles is that use of the "Lagrangian" sense of "libration point" significantly outnumbers the "lunar" sense that Hale prefers.</p>

<p>And it's clear that actual astronomers and physicists have been using "libration point" to refer "Lagrange point" since at least the beginning of the 20th Century. E.g., in <a href="https://iopscience.iop.org/article/10.1086/123342" rel="noreferrer">Trunpler (1923), "Search for Small Planets at the Triangle Points of Mercury and the Sun"</a>, the Lagrange points are referred to interchangeably as "triangle points", "libration points", and "Lagrange's libration points." And <a href="https://academic.oup.com/mnras/article/63/8/436/1009014" rel="noreferrer">Plummer (1903), "On Oscillating Satellites"</a>, refers to "points of libration" when discussing what are clearly the Lagrange points in the 3-body problem (e.g., "the three collinear points of libration").</p>

<p>So, yes, astronomers often refer to Lagrange points as "libration points", and have for at least a century; Hale is clearly wrong.</p>

CC BY-SA 4.0
2020-04-27T12:38:48.560Z
Wow what a thorough investigation! I think this really sets the issue to rest once and for all. Thank you very much!
uhoh
CC BY-SA 4.0
2020-04-27T12:56:51.020Z
I went and added a short comment to Wayne Hale's blog post; perhaps it will appear later.
Peter Erwin
CC BY-SA 4.0
2020-04-27T12:59:52.990Z
There are some NASA folk in Space SE that might be able to contact directly for you if you're interested, but I think the comment feature is the way to go; it's probably set up for review.
uhoh
CC BY-SA 4.0
2020-04-27T13:09:26.753Z
I also discovered that, in my one paper dealing with celestial mechanics theory ([Erwin & Sparke 1999](https://iopscience.iop.org/article/10.1086/307557/fulltext/)), I referred to "the outer (L4 and L5) Lagrangian libration points". So there's another data point on usage by astronomers ;-).
Peter Erwin
CC BY-SA 4.0
2020-04-28T11:00:35.177Z
not quite as glamorous, I've just used "librate" in a question; [When will DSCOVR appear too close to the Sun for reliable downlinking?](https://space.stackexchange.com/q/43758/12102) and since you've mentioned "Resonance Definitions" these two are unanswered; [1:1 resonance of two planets around a star in close proximity - approximate perturbative mathematical treatments?](https://astronomy.stackexchange.com/q/25878/7982) and also [Just how “locked” are resonant-chains of exoplanets thought to be?](https://astronomy.stackexchange.com/q/23980/7982)
uhoh
CC BY-SA 4.0
2020-04-27T12:35:56.077Z
2020-04-27T12:35:56.077Z
Peter Erwin
<p>In <a href="https://space.stackexchange.com/a/43568/12102">this answer</a> to <em>Who called the Lagrangian points as “Libration” points and and why was the terminology “Libration” used?</em> I described my feeling that Lagrangian points were also sometimes called &quot;libration points&quot; because for the the linearized equations of motion in the circular restricted three body problem at least some of these were equilibrium points where a small displacement would result in oscillatory motion and some of these are called halo orbits and Lissajous orbits. We know some of these are unstable even in CR3BP but for a few periods at least they are oscillatory.</p>
<p>Then I wrote:</p>
<p><strong>Interestingly</strong> former NASA engineer, flight director and Space Shuttle program manager, <a href="https://en.wikipedia.org/wiki/Wayne_Hale" rel="nofollow noreferrer">Wayne Hale</a>'s October 2019 blog post <a href="https://waynehale.wordpress.com/2019/10/16/definition-of-terms/" rel="nofollow noreferrer">Definition of Terms</a> covers this very question, <strong>and seems to disagree with this viewpoint!</strong></p>
<p>I recommend reading the full post for sure, but to summarize the post shows some &quot;libration points&quot; of the Moon, where <a href="https://en.wikipedia.org/wiki/Libration#Lunar_libration" rel="nofollow noreferrer">lunar libration</a> is maximum.</p>
<blockquote>
<p>The spot on the edge of the moon that is tilted the most toward an earthly observer is called ‘the libration point’.</p>
<p>Have you heard that term before?  I bet you have but in a different context.</p>
<p>Joseph-Louis Lagrange (1736-1813) was an Italian mathematician who played a large part in the development of the metric measurement system (SI) in post-revolutionary France.  He also studied orbital mechanics involving three bodies (e.g. sun/earth/moon) and mathematically proved there are locations around such an orbit which are gravitationally stable.  These points are called Lagrange points in his honor.  There are typically 5 such points and I will leave it to the student to research their locations.</p>
<p>As you can see Lagrange points and Libration points are quite different and literally have nothing to do with each other.</p>
<p>But if you read any number of popular media stories – and even several NASA technical papers – there appears to be confusion and the terms are used interchangeably.  This is so widespread that some dictionaries have started changing the definitions to keep up with what appears to be popular usage.</p>
<p>STOP THAT!</p>
<p><strong>Unfortunately, the curmudgeon in me realizes that this erroneous usage has become so common that it will be hard to change usage in popular literature.</strong></p>
<p><strong>But at least you now know the difference.  And you, like me, will stop when you hear some ‘expert’ (never an astronomer) mixes the terms and think about how much ignorance is being displayed.</strong></p>
</blockquote>
<hr />
<p><strong>Question:</strong> Do astronomers really <strong>never</strong> refer to any Lagrangian points as &quot;libration points&quot; as Wayne Hale's blogpost asserts?</p>

CC BY-SA 4.0
2020-04-21T08:16:16.230Z
I think libration point is used when talking about where the trojan asteroids reside. Since an object can orbit around L4 or L5, it can "balance" or "librate" around those points. But I'm not an astronomer studying trojan asteroids, so this isn't really an answer.
usernumber
CC BY-SA 4.0
2020-04-21T08:56:02.137Z
@antispinwards From time to time a short but good answer from a knowledgable user is just fine; [1](https://space.stackexchange.com/a/15110/12102), [2](https://space.stackexchange.com/a/39885/12102). I'm not sure I can predetermine and articulate "at what point" in this case, let's see how it goes and what evidence turns up
uhoh
CC BY-SA 4.0
2020-04-21T13:41:56.477Z
Wayne Hale is completely off base here. Go to scholar.google.com and search for "libration point". You'll find thousands and thousands of refereed journal articles (
"52,700 results") that use "libration point" as a synonym for "Lagrange point". I found none that use libration point to refer to the concept Hale espouses.
David Hammen
CC BY-SA 4.0
2020-04-21T14:03:06.097Z
@DavidHammen thanks, I kinda had a hunch that was so...
uhoh
CC BY-SA 4.0
2020-04-21T14:09:11.547Z
Note that you will find about 20 times as many google scholar hits referring to "Lagrangian points" as "Lagrangian points". Within astrophysical error bars 1 in 20 is about the same as never. :)
TimRias
CC BY-SA 4.0
2020-04-22T00:02:52.793Z
@mmeent I see it differently. In astrophysics thing tend to span many orders of magnitude and most things are shown on log scales often covering a half-dozen orders of magnitude or more. $\log_{10}(20)$ is only 1.3 so with an astrophysical perspective those are *nearly equal!*
uhoh
CC BY-SA 4.0
2020-04-22T21:18:48.830Z
@mmeent - Re *Note that you will find about 20 times as many google scholar hits referring to "Lagrangian points" as "Lagrangian points"* That doesn't make sense. Try again. Also note that if you go to google ngrams for a historical perspective, it shows that "libration points" apparently was the preferred terminology until fairly recently, and that "Lagrangian point" has always trailed well below both "libration point" and "Lagrange point".
David Hammen
CC BY-SA 4.0
2020-04-22T21:26:26.653Z
Also note that Farquhar (of Olympic level fame) and Martin Lo et al. (of interplanetary highway level fame) consistently referred to those points as "libration points" rather than "Lagrange points" (or even worse, "Lagrangian points"). Also note that Euler discovered the linear libration points (now denoted as L1, L2, and L3) before Lagrange discovered the equilateral libration points (L4 and L5). So if those five points are to be collectively named after people, the correct term would be "Euler-Lagrange points"
David Hammen
CC BY-SA 4.0
2020-04-22T21:39:39.417Z
@DavidHammen Wow that is a huge distortion of the ngram data. Only between 1955 anf 1972 was "libration points" more common than "Lagrangian points". For "Lagrangian point" it is only between 1960 and 1967 that "libration point" was more popular.
TimRias
CC BY-SA 4.0
2020-04-23T02:20:36.307Z
@mmeent since objects really do seem to "librate" around these points I'm gonna call keep calling them libration points from time to time as will others who do libration point orbits for a living.
uhoh
CC BY-SA 4.0
2020-04-23T09:36:15.997Z
@mmeent - My bad. I mistakenly typed Lagrangian point as lagrangian point in my ngrams search and did not click case insensitive. That said, the vast majority of the hits on Lagrangian point in a case-insensitive search have absolutely nothing to do with the five libration points that are the subject of this question. You'll find articles / books on fluid dynamics because in that field a Lagrangian point is another name for a tagged particle. You'll find articles / books on taking a Lagrangian point of view, as opposed to a Newtonian point of view or Hamiltonian point of view. And so on.
David Hammen
CC BY-SA 4.0
2020-04-23T09:41:20.500Z
If you use google scholar and search for "Lagrangian point", in quotes, the number of hits drops dramatically (by a factor of 100) -- and over half of the remaining hits still have absolutely nothing to do with the five libration points in question. This mismatch is largely due to the use of the use of "Lagrangian point" in fluid dynamics and due to "Lagrangian point of view" matching "Lagrangian point". Searching for "libration point", in quotes, also reduces the number of hits dramatically (by a factor of 10), but from a cursory search, every hit appears to be applicable.
David Hammen
CC BY-SA 4.0
2020-04-23T09:51:38.327Z
One could reasonably take the perspective that "Lagrangian point" is not nearly as good a name as is "libration point" from the perspective of performing a literature search.
David Hammen
<the-moon><orbital-mechanics><history><terminology><mathematics>
Do Astronomers really never call Lagrangian points "libration points"?
uhoh
# Do Astronomers really never call Lagrangian points "libration points"?

(Asked by: username_0 on 2020-04-21)

In [this answer](https://space.stackexchange.com/a/43568/12102) to *Who called the Lagrangian points as “Libration” points and and why was the terminology “Libration” used?* I described my feeling that Lagrangian points were also sometimes called "libration points" because for the the linearized equations of motion in the circular restricted three body problem at least some of these were equilibrium points where a small displacement would result in oscillatory motion and some of these are called halo orbits and Lissajous orbits. We know some of these are unstable even in CR3BP but for a few periods at least they are oscillatory.

Then I wrote:

**Interestingly** former NASA engineer, flight director and Space Shuttle program manager, [Wayne Hale](https://en.wikipedia.org/wiki/Wayne_Hale)'s October 2019 blog post [Definition of Terms](https://waynehale.wordpress.com/2019/10/16/definition-of-terms/) covers this very question, **and seems to disagree with this viewpoint!**

I recommend reading the full post for sure, but to summarize the post shows some "libration points" of the Moon, where [lunar libration](https://en.wikipedia.org/wiki/Libration#Lunar_libration) is maximum.

> The spot on the edge of the moon that is tilted the most toward an earthly observer is called ‘the libration point’.
>
> Have you heard that term before? I bet you have but in a different context.
>
> Joseph-Louis Lagrange (1736-1813) was an Italian mathematician who played a large part in the development of the metric measurement system (SI) in post-revolutionary France. He also studied orbital mechanics involving three bodies (e.g. sun/earth/moon) and mathematically proved there are locations around such an orbit which are gravitationally stable. These points are called Lagrange points in his honor. There are typically 5 such points and I will leave it to the student to research their locations.
>
> As you can see Lagrange points and Libration points are quite different and literally have nothing to do with each other.
>
> But if you read any number of popular media stories – and even several NASA technical papers – there appears to be confusion and the terms are used interchangeably. This is so widespread that some dictionaries have started changing the definitions to keep up with what appears to be popular usage.
>
> STOP THAT!
>
> **Unfortunately, the curmudgeon in me realizes that this erroneous usage has become so common that it will be hard to change usage in popular literature.**
>
> **But at least you now know the difference. And you, like me, will stop when you hear some ‘expert’ (never an astronomer) mixes the terms and think about how much ignorance is being displayed.**

---

**Question:** Do astronomers really **never** refer to any Lagrangian points as "libration points" as Wayne Hale's blogpost asserts?

**Tags:** the-moon, orbital-mechanics, history, terminology, mathematics

> **Comments:**
> **username_1**: I think libration point is used when talking about where the trojan asteroids reside. Since an object can orbit around L4 or L5, it can "balance" or "librate" around those points. But I'm not an astronomer studying trojan asteroids, so this isn't really an answer.  
> **username_0**: @antispinwards From time to time a short but good answer from a knowledgable user is just fine; [1](https://space.stackexchange.com/a/15110/12102), [2](https://space.stackexchange.com/a/39885/12102). I'm not sure I can predetermine and articulate "at what point" in this case, let's see how it goes and what evidence turns up  
> **username_2**: Wayne Hale is completely off base here. Go to scholar.google.com and search for "libration point". You'll find thousands and thousands of refereed journal articles ( "52,700 results") that use "libration point" as a synonym for "Lagrange point". I found none that use libration point to refer to the concept Hale espouses.  
> **username_0**: @username_2 thanks, I kinda had a hunch that was so...  
> **username_3**: Note that you will find about 20 times as many google scholar hits referring to "Lagrangian points" as "Lagrangian points". Within astrophysical error bars 1 in 20 is about the same as never. :)  
> **username_0**: @mmeent I see it differently. In astrophysics thing tend to span many orders of magnitude and most things are shown on log scales often covering a half-dozen orders of magnitude or more. $\log_{10}(20)$ is only 1.3 so with an astrophysical perspective those are *nearly equal!*  
> **username_2**: @mmeent - Re *Note that you will find about 20 times as many google scholar hits referring to "Lagrangian points" as "Lagrangian points"* That doesn't make sense. Try again. Also note that if you go to google ngrams for a historical perspective, it shows that "libration points" apparently was the preferred terminology until fairly recently, and that "Lagrangian point" has always trailed well below both "libration point" and "Lagrange point".  
> **username_2**: Also note that Farquhar (of Olympic level fame) and Martin Lo et al. (of interplanetary highway level fame) consistently referred to those points as "libration points" rather than "Lagrange points" (or even worse, "Lagrangian points"). Also note that Euler discovered the linear libration points (now denoted as L1, L2, and L3) before Lagrange discovered the equilateral libration points (L4 and L5). So if those five points are to be collectively named after people, the correct term would be "Euler-Lagrange points"  
> **username_3**: @username_2 Wow that is a huge distortion of the ngram data. Only between 1955 anf 1972 was "libration points" more common than "Lagrangian points". For "Lagrangian point" it is only between 1960 and 1967 that "libration point" was more popular.  
> **username_0**: @mmeent since objects really do seem to "librate" around these points I'm gonna call keep calling them libration points from time to time as will others who do libration point orbits for a living.  
> **username_2**: @mmeent - My bad. I mistakenly typed Lagrangian point as lagrangian point in my ngrams search and did not click case insensitive. That said, the vast majority of the hits on Lagrangian point in a case-insensitive search have absolutely nothing to do with the five libration points that are the subject of this question. You'll find articles / books on fluid dynamics because in that field a Lagrangian point is another name for a tagged particle. You'll find articles / books on taking a Lagrangian point of view, as opposed to a Newtonian point of view or Hamiltonian point of view. And so on.  
> **username_2**: If you use google scholar and search for "Lagrangian point", in quotes, the number of hits drops dramatically (by a factor of 100) -- and over half of the remaining hits still have absolutely nothing to do with the five libration points in question. This mismatch is largely due to the use of the use of "Lagrangian point" in fluid dynamics and due to "Lagrangian point of view" matching "Lagrangian point". Searching for "libration point", in quotes, also reduces the number of hits dramatically (by a factor of 10), but from a cursory search, every hit appears to be applicable.  
> **username_2**: One could reasonably take the perspective that "Lagrangian point" is not nearly as good a name as is "libration point" from the perspective of performing a literature search.  

---

## 1 answers

### Answer by username_4 on 2020-04-27. Score: 7 | Accepted answer

A full-text search using the astronomical-literature collection on the [Astrophysics Data System](https://ui.adsabs.harvard.edu) (more complete and more astronomy-specific than Google Scholar) yields 10,845 hits for "Lagrange point" and [2,302 for "libration point"](https://ui.adsabs.harvard.edu/search/filter_database_fq_database=AND&filter_database_fq_database=database%3A%22astronomy%22&fq=%7B!type%3Daqp%20v%3D%24fq_database%7D&fq_database=database%3A%22astronomy%22&q=collection%3Aastronomy%20full%3A%22libration%20point%22&sort=date%20desc%2C%20bibcode%20desc&p_=0) (not sure how long that URL will be valid, but it's easy enough to redo the search). So it's clear the former is more common than the latter.

Nonetheless, my impression from looking at article titles is that use of the "Lagrangian" sense of "libration point" significantly outnumbers the "lunar" sense that Hale prefers.

And it's clear that actual astronomers and physicists have been using "libration point" to refer "Lagrange point" since at least the beginning of the 20th Century. E.g., in [Trunpler (1923), "Search for Small Planets at the Triangle Points of Mercury and the Sun"](https://iopscience.iop.org/article/10.1086/123342), the Lagrange points are referred to interchangeably as "triangle points", "libration points", and "Lagrange's libration points." And [Plummer (1903), "On Oscillating Satellites"](https://academic.oup.com/mnras/article/63/8/436/1009014), refers to "points of libration" when discussing what are clearly the Lagrange points in the 3-body problem (e.g., "the three collinear points of libration").

So, yes, astronomers often refer to Lagrange points as "libration points", and have for at least a century; Hale is clearly wrong.

> **Comments:**
> **username_0**: Wow what a thorough investigation! I think this really sets the issue to rest once and for all. Thank you very much!  
> **username_4**: I went and added a short comment to Wayne Hale's blog post; perhaps it will appear later.  
> **username_0**: There are some NASA folk in Space SE that might be able to contact directly for you if you're interested, but I think the comment feature is the way to go; it's probably set up for review.  
> **username_4**: I also discovered that, in my one paper dealing with celestial mechanics theory ([username_4 & Sparke 1999](https://iopscience.iop.org/article/10.1086/307557/fulltext/)), I referred to "the outer (L4 and L5) Lagrangian libration points". So there's another data point on usage by astronomers ;-).  
> **username_0**: not quite as glamorous, I've just used "librate" in a question; [When will DSCOVR appear too close to the Sun for reliable downlinking?](https://space.stackexchange.com/q/43758/12102) and since you've mentioned "Resonance Definitions" these two are unanswered; [1:1 resonance of two planets around a star in close proximity - approximate perturbative mathematical treatments?](https://astronomy.stackexchange.com/q/25878/7982) and also [Just how “locked” are resonant-chains of exoplanets thought to be?](https://astronomy.stackexchange.com/q/23980/7982)  

---

