In this answer 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's October 2019 blog post 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 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.


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?

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    $\begingroup$ At what point would you accept absence of evidence as being evidence of absence? $\endgroup$
    – user24157
    Commented Apr 21, 2020 at 8:48
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    $\begingroup$ 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. $\endgroup$ Commented Apr 21, 2020 at 13:41
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    $\begingroup$ @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! $\endgroup$
    – uhoh
    Commented Apr 22, 2020 at 0:02
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    $\begingroup$ @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". $\endgroup$ Commented Apr 22, 2020 at 21:18
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    $\begingroup$ 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. $\endgroup$ Commented Apr 23, 2020 at 9:41

1 Answer 1


A full-text search using the astronomical-literature collection on the Astrophysics Data System (more complete and more astronomy-specific than Google Scholar) yields 10,845 hits for "Lagrange point" and 2,302 for "libration point" (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", the Lagrange points are referred to interchangeably as "triangle points", "libration points", and "Lagrange's libration points." And Plummer (1903), "On Oscillating Satellites", 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.


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