<p>I will try to summarize current state of comments in an answer (which I am <em>not</em> going to accept in hope someone will post a better one).</p>
<p>It seems that elevation at Moon is defined relative to a <em>sphere</em> (since Moon, unlike Earth, has negligible flattening) with <em>radius 1737.4 km</em>.</p>
<p>Its center is Moon’s <em>center of mass</em> what makes sense since the reference system defines not only elevation but also two other coordinates (selenographic latitude and longitude) and axis of rotation passes through center of mass (rather than center of figure for example).</p>
<p>I still don't understand relation between center of mass and equipotential surfaces but this is probably irelevant, since even at Earth we no longer define elevation relative to mean sea level (which is a textbook equipotential surface) but relative to ellipsoid (with center of mass as its center).</p>
<p>It seems that the most authoritative source is this pdf document:</p>
<p><a href="https://www.hq.nasa.gov/alsj/lunar_cmd_2005_jpl_d32296.pdf" rel="nofollow noreferrer">Lunar Constants and Models Document </a></p>

CC BY-SA 4.0
2023-01-30T19:58:02.837Z
Lunar surface gravity is a bit messy, due to the large mascons on the near side. Lunar data has improved considerably in the last decade or so, thanks to the gravity mapping done by the [GRAIL](https://en.wikipedia.org/wiki/GRAIL) satellites, and to continued refinements in LLR (Lunar Laser Ranging) measurements, which is on-going. Here's [a current project](https://www.oca.eu/en/294-categorie-fr-fr/laboratoires/geo-umr-geoazur/geo-recherche/geo-zoom-sur-equipe/geo-rech-astrogeo-gpm/2583-2020-2023-anr-ldlr) at The Côte d’Azur Observatory.
PM 2Ring
CC BY-SA 4.0
2023-01-30T20:10:39.890Z
Section 2.4 of [The JPL Planetary and Lunar Ephemerides DE440 and DE441](https://iopscience.iop.org/article/10.3847/1538-3881/abd414) has some details on modelling the dynamics of the lunar surface. That section refers to articles that analyse GRAIL data: [The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL Primary Mission](https://ui.adsabs.harvard.edu/abs/2013JGRE..118.1415K) & [High−degree gravity models from GRAIL primary mission data](https://ui.adsabs.harvard.edu/abs/2013JGRE..118.1676L)
PM 2Ring
CC BY-SA 4.0
2023-01-30T12:43:43.077Z
2023-01-30T18:16:35.553Z
2023-01-30T18:16:35.553Z
Leos Ondra
<p>In a recent image by Pavel Gabzdyl, the highest (+10.7 km) and lowest (-9 km) points on the Moon are marked.</p>
<p><a href="https://i.sstatic.net/b6A0M.jpg" rel="noreferrer"><img src="https://i.sstatic.net/b6A0M.jpg" alt="enter image description here" /></a></p>
<p>Detailed info about these extremal points can be found at the following links:</p>
<p><a href="http://lroc.sese.asu.edu/posts/249" rel="noreferrer">Highest Point on the Moon!</a><br />
<a href="http://lroc.sese.asu.edu/posts/898" rel="noreferrer">Great Wall!</a></p>
<p>My question is how are elevations on the Moon exactly defined? A <a href="https://ui.adsabs.harvard.edu/abs/1973LPSC....4.2811K" rel="noreferrer">1973 paper on lunar altimetry</a>  made by Apollo 15 and 16 missions defined elevation with respect to a 1738km sphere about the center-of-mass.</p>
<p>Is the same principle used today? What is the accepted radius of the sphere? How is measured (not defined) center-of-mass of the Moon, and how is that all related to equipotential surface (in analogy with sea level)?</p>

CC BY-SA 4.0
2023-01-08T19:00:56.960Z
Probably relevant https://surveyorconnect.com/wp-content/uploads/converted_files/444232=11301-LunCoordWhitePaper-10-08.pdf
James K
CC BY-SA 4.0
2023-01-08T19:16:35.567Z
From http://lroc.sese.asu.edu/posts/944 : “Since the Moon has no oceans, and thus no sea level, one can think of the mean radius as the lunar equivalent to sea level on the Earth.”
Pierre Paquette
CC BY-SA 4.0
2023-01-08T23:21:12.307Z
@PierrePaquette consider making that an answer
planetmaker
CC BY-SA 4.0
2023-01-09T02:12:49.977Z
@planetmaker: I wouldn’t find that complete enough to post as an answer—I know if it were an answer to my question, I wouldn’t “Accept” it as the best answer. In fact, it raises another question, which is basically the same as the OP’s question: What is the “mean radius” of the Moon, and how is it defined?
Pierre Paquette
CC BY-SA 4.0
2023-01-09T03:05:57.570Z
This is a great question! Related in Space Exploration SE (but I don't know if the question of the Moon's reference surface (geoid) is answered there or not: [Shape and dimensions of the Moon's reference surface for selenographic latitude/longitude?](https://space.stackexchange.com/q/27359/12102)
uhoh
CC BY-SA 4.0
2023-01-09T05:49:03.827Z
See: https://en.wikipedia.org/wiki/Selenography
Nilay Ghosh
<the-moon>
How exactly is defined elevation on the Moon?
Leos Ondra
# How exactly is defined elevation on the Moon?

(Asked by: username_0 on 2023-01-08)

In a recent image by Pavel Gabzdyl, the highest (+10.7 km) and lowest (-9 km) points on the Moon are marked.

[![enter image description here](https://i.sstatic.net/b6A0M.jpg)](https://i.sstatic.net/b6A0M.jpg)

Detailed info about these extremal points can be found at the following links:

[Highest Point on the Moon!](http://lroc.sese.asu.edu/posts/249)  
[Great Wall!](http://lroc.sese.asu.edu/posts/898)

My question is how are elevations on the Moon exactly defined? A [1973 paper on lunar altimetry](https://ui.adsabs.harvard.edu/abs/1973LPSC....4.2811K) made by Apollo 15 and 16 missions defined elevation with respect to a 1738km sphere about the center-of-mass.

Is the same principle used today? What is the accepted radius of the sphere? How is measured (not defined) center-of-mass of the Moon, and how is that all related to equipotential surface (in analogy with sea level)?

**Tags:** the-moon
> **Comments:**
> **username_1**: Probably relevant https://surveyorconnect.com/wp-content/uploads/converted_files/444232=11301-LunCoordWhitePaper-10-08.pdf  
> **username_2**: From http://lroc.sese.asu.edu/posts/944 : “Since the Moon has no oceans, and thus no sea level, one can think of the mean radius as the lunar equivalent to sea level on the Earth.”  
> **username_3**: @PierrePaquette consider making that an answer  
> **username_2**: @planetmaker: I wouldn’t find that complete enough to post as an answer—I know if it were an answer to my question, I wouldn’t “Accept” it as the best answer. In fact, it raises another question, which is basically the same as the OP’s question: What is the “mean radius” of the Moon, and how is it defined?  
> **username_4**: This is a great question! Related in Space Exploration SE (but I don't know if the question of the Moon's reference surface (geoid) is answered there or not: [Shape and dimensions of the Moon's reference surface for selenographic latitude/longitude?](https://space.stackexchange.com/q/27359/12102)  
> **username_5**: See: https://en.wikipedia.org/wiki/Selenography  

---

## 1 answers

### Answer by username_0 on 2023-01-30. Score: 2

I will try to summarize current state of comments in an answer (which I am *not* going to accept in hope someone will post a better one).

It seems that elevation at Moon is defined relative to a *sphere* (since Moon, unlike Earth, has negligible flattening) with *radius 1737.4 km*.

Its center is Moon’s *center of mass* what makes sense since the reference system defines not only elevation but also two other coordinates (selenographic latitude and longitude) and axis of rotation passes through center of mass (rather than center of figure for example).

I still don't understand relation between center of mass and equipotential surfaces but this is probably irelevant, since even at Earth we no longer define elevation relative to mean sea level (which is a textbook equipotential surface) but relative to ellipsoid (with center of mass as its center).

It seems that the most authoritative source is this pdf document:

[Lunar Constants and Models Document](https://www.hq.nasa.gov/alsj/lunar_cmd_2005_jpl_d32296.pdf)

> **Comments:**
> **username_6**: Lunar surface gravity is a bit messy, due to the large mascons on the near side. Lunar data has improved considerably in the last decade or so, thanks to the gravity mapping done by the [GRAIL](https://en.wikipedia.org/wiki/GRAIL) satellites, and to continued refinements in LLR (Lunar Laser Ranging) measurements, which is on-going. Here's [a current project](https://www.oca.eu/en/294-categorie-fr-fr/laboratoires/geo-umr-geoazur/geo-recherche/geo-zoom-sur-equipe/geo-rech-astrogeo-gpm/2583-2020-2023-anr-ldlr) at The Côte d’Azur Observatory.  
> **username_6**: Section 2.4 of [The JPL Planetary and Lunar Ephemerides DE440 and DE441](https://iopscience.iop.org/article/10.3847/1538-3881/abd414) has some details on modelling the dynamics of the lunar surface. That section refers to articles that analyse GRAIL data: [The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL Primary Mission](https://ui.adsabs.harvard.edu/abs/2013JGRE..118.1415K) & [High−degree gravity models from GRAIL primary mission data](https://ui.adsabs.harvard.edu/abs/2013JGRE..118.1676L)  

---

