<p>The short answer is, at the moment, <strong>only for the Moon</strong>. I include below a brief description of the JPL DE format to arrive to this conclusion.</p>
<p><a href="https://www.celestialprogramming.com/jpl-ephemeris-format/jpl-ephemeris-format.html" rel="nofollow noreferrer">This link</a> explains quite well the format of JPL DE ephemerides, which are available <a href="https://ssd.jpl.nasa.gov/ftp/eph/planets/ascii/de440/" rel="nofollow noreferrer">here</a>. The link is for the DE440, but a directory up we can find previous ones also.</p>
<p>In summary, we need 2 files to properly understand them: the ephemerides data themselves (split into multiple files, the ascpXXXX.440 in the previous link; the XXXX denotes the starting year for the data in that file) and the header (header.440). The header contains quite a lot of information, but the most interesting part for this discussion are the 3 lines that come after the line &quot;GROUP 1050&quot;.</p>
<p>These 3 lines contain information about the 15 types of records that are currently included in the DE (these 15 types of records are given in <a href="https://www.celestialprogramming.com/jpl-ephemeris-format/jpl-ephemeris-format.html" rel="nofollow noreferrer">Table 1 here</a>. The 2nd line specifies the number of Chebyshev coefficients given for each property of each of the records (e.g., for position records, we have 3 properties, X, Y and Z, and each of these has the number of Chebyshev coefficients given in this line). The 3rd line specifies the so-called &quot;subintervals&quot; with which each property is defined, which determines the time resolution (each complete data block of the ephemerides is an interval of 32 days, so if the number of subintervals is 1, we just get the coefficients defined for that period of 32 days; if it is 2, we get values for them for a period of 16 days and then different values for the next period of 16 days, and so on).</p>
<p>As can be seen from the linked Table 1, records 1 to 11 are positions. Record 12 are nutations of Earth (2 components), record 13 are lunar librations (3 components, the 3 angles), record 14 are lunar mantle angular velocities (also 3 components), and record 15 is the difference in seconds between TT and TDB.</p>
<p>So if we go to line 2 after the mentioned &quot;GROUP 1050&quot; line in the header, we can know how many coefficients are given for each of these properties. Properties for which values are not given have a value of 0 here. For DE440, we have 10 coefficients for Earth nutations (with 4 subintervals), and also 10 coefficients for each of the components of lunar libration (with 4 subintervals also). So we have indeed values for lunar librations! But it looks like that's about it in terms of librations, since librations for other celestial bodies are not even listed (might be worth saying, <em>yet</em>) in the list of defined records.</p>
<p>Lunar mantle angular velocity has 0 coefficients (i.e., no values given), for the time being!</p>
<p>As a side note, as you noted in comments, I thought it is interesting that more information is given about the Moon than about the Earth. A summary for each in DE440:</p>
<ul>
<li>For Moon: positions with time resolution of 4 days and 13 coefficients for each component, librations with time resolution of 8 days and 10 coefficients for each component</li>
<li>For Earth: positions with time resolution of 16 days and 14 coefficients for each component (and in fact, they are positions of the Earth-Moon barycenter! so Earth position must be derived considering the Earth-Moon mass ratio, which is also given in the header file by the way), nutations with time resolution of 8 days and 10 coefficients for each component (but we only have 2 components here compared to the 3 components for Moon librations, and there seems to be provisions for even more Moon information, i.e., mantle angular velocity)</li>
</ul>

CC BY-SA 4.0
2022-01-22T09:52:19.170Z
2022-01-22T09:52:19.170Z
Rafa
<p>Since the Earth and the Moon are so gravitationally and tidally engaged and the laser ranging data so precise, the <a href="https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris" rel="nofollow noreferrer">JPL Development Ephemerides</a> are based on extensive modeling of the Earth-Moon system including some complicated models of how their internal structures behave.</p>
<p>For purely kinematic effects, we can estimate libration of any tidally locked Moon relative to its planet from their positions in space and a vector for the Moon's axis, which might have an ephemeris of its own, or at least precession rate written somewhere.</p>
<p>But I'd like to ask:</p>
<p><strong>Question:</strong> For how many solar system bodies do recent JPL Development Ephemerides include libration?</p>
<p>For the purposes of my question, I think that this would be interpolated data in the ephemeris that exists explicitly for the attitude or orientation of a rigid body Moon, not something that could be derived from positions and other parameters as mentioned above.</p>

CC BY-SA 4.0
2022-01-22T01:58:29.463Z
companion question: [What are all the contributions to libration; is there a self-consistent formalism?](https://astronomy.stackexchange.com/q/48263/7982)
uhoh
CC BY-SA 4.0
2022-01-22T02:02:22.923Z
Also, asked in Space SE: [Just how locked is Titan? Does it exhibit libration due to eccentricity? Have residual oscillations not yet damped out been detected or ruled out?](https://space.stackexchange.com/q/57527/12102) and [Roughly, how much of our Moon's apparent libration amplitude seen from the Geocenter is due to different effects?](https://space.stackexchange.com/q/45366/12102) (currently unanswered) and [How "locked" are Pluto and Charon? How much does each librate as seen from the other?](https://space.stackexchange.com/q/45342/12102)
uhoh
CC BY-SA 4.0
2022-01-22T02:04:24.087Z
and here in Astronomy SE [Explanation about the resonance, mean motion resonance and libration](https://astronomy.stackexchange.com/q/35604/7982)
uhoh
CC BY-SA 4.0
2022-01-22T07:11:00.740Z
Maybe I misunderstood, but if you mean which librations are explicitly included in the JPL DE files in the form of Chebyshev coefficients, as far as I know, only Moon librations are included. See here https://ssd.jpl.nasa.gov/planets/eph_export.html, and maybe more explicitly explained https://www.celestialprogramming.com/jpl-ephemeris-format/jpl-ephemeris-format.html (the most recent here is DE432, but I have verified the same columns are present with the same number of coefficients in the most recent DE440 and DE441)
Rafa
CC BY-SA 4.0
2022-01-22T07:13:59.583Z
The header file here https://ssd.jpl.nasa.gov/ftp/eph/planets/ascii/de440/ (header.440), in particular the 3 lines after the line "GROUP 1050", denote it. It can be better understood in combination with file ascii_format.txt here https://ssd.jpl.nasa.gov/ftp/eph/planets/ascii/
Rafa
CC BY-SA 4.0
2022-01-22T07:36:42.957Z
@Rafa It seems you understand my question correctly. I did not ask (but wish I did) if the rotational vectors were available for interpolation. It would be interesting to find that the DE’s provide more complex information for the Moon than they do for Earth!
uhoh
CC BY-SA 4.0
2022-01-22T08:00:32.340Z
In fact I wondered the same recently! For lunar librations, coefficients for interpolating the three angles (phi, theta, psi) are given. There is also provision for providing coefficients for the three components (x, y, z) of lunar mantle angular velocity, but they are not currently given, as indicated by the fact that the second-to-last numbers in the second and third line in the header file after the "GROUP 1050" line are 0. On the other hand, for Earth there is provision for giving coefficients for the 2 components of nutations (in longitude and obliquity), but are currently not given ...
Rafa
CC BY-SA 4.0
2022-01-22T08:02:37.600Z
... (4th-to-last values of the same lines). Interestingly, they were given in the older DE405, but not in modern ones. Also considering that coefficients for the X, Y and Z position of both bodies are given, it seems indeed that more information about the Moon is provided! I guess they expect that Earth orientation parameters are available elsewhere...? Which I guess is true, but still a bit surprising to see that more information is given for the Moon than for Earth. To add to it, the time resolution of coefficients for Moon position is 4 days, while for Earth is 16 days!
Rafa
CC BY-SA 4.0
2022-01-22T09:14:13.370Z
@Rafa comments are considered temporary; they can (potentially) be deleted in the future, and things in chat rooms scroll up into oblivion. Since you are fully of really useful, helpful and interesting information and offer it freely, I recommend that you start putting these gems into answer posts where they can take on some level of long-term stability and can more easily be searched for and found again in the future.
uhoh
CC BY-SA 4.0
2022-01-22T09:57:42.553Z
Sounds good! I'm by no means an expert, but hopefully I can contribute to some details! :)
Rafa
<planetary-science><ephemeris><nasa><lunar-libration>
For how many solar system bodies do recent JPL Development Ephemerides include libration?
uhoh
# For how many solar system bodies do recent JPL Development Ephemerides include libration?

(Asked by: username_0 on 2022-01-22)

Since the Earth and the Moon are so gravitationally and tidally engaged and the laser ranging data so precise, the [JPL Development Ephemerides](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris) are based on extensive modeling of the Earth-Moon system including some complicated models of how their internal structures behave.

For purely kinematic effects, we can estimate libration of any tidally locked Moon relative to its planet from their positions in space and a vector for the Moon's axis, which might have an ephemeris of its own, or at least precession rate written somewhere.

But I'd like to ask:

**Question:** For how many solar system bodies do recent JPL Development Ephemerides include libration?

For the purposes of my question, I think that this would be interpolated data in the ephemeris that exists explicitly for the attitude or orientation of a rigid body Moon, not something that could be derived from positions and other parameters as mentioned above.

**Tags:** planetary-science, ephemeris, nasa, lunar-libration

> **Comments:**
> **username_0**: companion question: [What are all the contributions to libration; is there a self-consistent formalism?](https://astronomy.stackexchange.com/q/48263/7982)  
> **username_0**: Also, asked in Space SE: [Just how locked is Titan? Does it exhibit libration due to eccentricity? Have residual oscillations not yet damped out been detected or ruled out?](https://space.stackexchange.com/q/57527/12102) and [Roughly, how much of our Moon's apparent libration amplitude seen from the Geocenter is due to different effects?](https://space.stackexchange.com/q/45366/12102) (currently unanswered) and [How "locked" are Pluto and Charon? How much does each librate as seen from the other?](https://space.stackexchange.com/q/45342/12102)  
> **username_0**: and here in Astronomy SE [Explanation about the resonance, mean motion resonance and libration](https://astronomy.stackexchange.com/q/35604/7982)  
> **username_1**: Maybe I misunderstood, but if you mean which librations are explicitly included in the JPL DE files in the form of Chebyshev coefficients, as far as I know, only Moon librations are included. See here https://ssd.jpl.nasa.gov/planets/eph_export.html, and maybe more explicitly explained https://www.celestialprogramming.com/jpl-ephemeris-format/jpl-ephemeris-format.html (the most recent here is DE432, but I have verified the same columns are present with the same number of coefficients in the most recent DE440 and DE441)  
> **username_1**: The header file here https://ssd.jpl.nasa.gov/ftp/eph/planets/ascii/de440/ (header.440), in particular the 3 lines after the line "GROUP 1050", denote it. It can be better understood in combination with file ascii_format.txt here https://ssd.jpl.nasa.gov/ftp/eph/planets/ascii/  
> **username_0**: @username_1 It seems you understand my question correctly. I did not ask (but wish I did) if the rotational vectors were available for interpolation. It would be interesting to find that the DE’s provide more complex information for the Moon than they do for Earth!  
> **username_1**: In fact I wondered the same recently! For lunar librations, coefficients for interpolating the three angles (phi, theta, psi) are given. There is also provision for providing coefficients for the three components (x, y, z) of lunar mantle angular velocity, but they are not currently given, as indicated by the fact that the second-to-last numbers in the second and third line in the header file after the "GROUP 1050" line are 0. On the other hand, for Earth there is provision for giving coefficients for the 2 components of nutations (in longitude and obliquity), but are currently not given ...  
> **username_1**: ... (4th-to-last values of the same lines). Interestingly, they were given in the older DE405, but not in modern ones. Also considering that coefficients for the X, Y and Z position of both bodies are given, it seems indeed that more information about the Moon is provided! I guess they expect that Earth orientation parameters are available elsewhere...? Which I guess is true, but still a bit surprising to see that more information is given for the Moon than for Earth. To add to it, the time resolution of coefficients for Moon position is 4 days, while for Earth is 16 days!  
> **username_0**: @username_1 comments are considered temporary; they can (potentially) be deleted in the future, and things in chat rooms scroll up into oblivion. Since you are fully of really useful, helpful and interesting information and offer it freely, I recommend that you start putting these gems into answer posts where they can take on some level of long-term stability and can more easily be searched for and found again in the future.  
> **username_1**: Sounds good! I'm by no means an expert, but hopefully I can contribute to some details! :)  

---

## 1 answers

### Answer by username_1 on 2022-01-22. Score: 4 | Accepted answer

The short answer is, at the moment, **only for the Moon**. I include below a brief description of the JPL DE format to arrive to this conclusion.

[This link](https://www.celestialprogramming.com/jpl-ephemeris-format/jpl-ephemeris-format.html) explains quite well the format of JPL DE ephemerides, which are available [here](https://ssd.jpl.nasa.gov/ftp/eph/planets/ascii/de440/). The link is for the DE440, but a directory up we can find previous ones also.

In summary, we need 2 files to properly understand them: the ephemerides data themselves (split into multiple files, the ascpXXXX.440 in the previous link; the XXXX denotes the starting year for the data in that file) and the header (header.440). The header contains quite a lot of information, but the most interesting part for this discussion are the 3 lines that come after the line "GROUP 1050".

These 3 lines contain information about the 15 types of records that are currently included in the DE (these 15 types of records are given in [Table 1 here](https://www.celestialprogramming.com/jpl-ephemeris-format/jpl-ephemeris-format.html). The 2nd line specifies the number of Chebyshev coefficients given for each property of each of the records (e.g., for position records, we have 3 properties, X, Y and Z, and each of these has the number of Chebyshev coefficients given in this line). The 3rd line specifies the so-called "subintervals" with which each property is defined, which determines the time resolution (each complete data block of the ephemerides is an interval of 32 days, so if the number of subintervals is 1, we just get the coefficients defined for that period of 32 days; if it is 2, we get values for them for a period of 16 days and then different values for the next period of 16 days, and so on).

As can be seen from the linked Table 1, records 1 to 11 are positions. Record 12 are nutations of Earth (2 components), record 13 are lunar librations (3 components, the 3 angles), record 14 are lunar mantle angular velocities (also 3 components), and record 15 is the difference in seconds between TT and TDB.

So if we go to line 2 after the mentioned "GROUP 1050" line in the header, we can know how many coefficients are given for each of these properties. Properties for which values are not given have a value of 0 here. For DE440, we have 10 coefficients for Earth nutations (with 4 subintervals), and also 10 coefficients for each of the components of lunar libration (with 4 subintervals also). So we have indeed values for lunar librations! But it looks like that's about it in terms of librations, since librations for other celestial bodies are not even listed (might be worth saying, *yet*) in the list of defined records.

Lunar mantle angular velocity has 0 coefficients (i.e., no values given), for the time being!

As a side note, as you noted in comments, I thought it is interesting that more information is given about the Moon than about the Earth. A summary for each in DE440:

* For Moon: positions with time resolution of 4 days and 13 coefficients for each component, librations with time resolution of 8 days and 10 coefficients for each component
* For Earth: positions with time resolution of 16 days and 14 coefficients for each component (and in fact, they are positions of the Earth-Moon barycenter! so Earth position must be derived considering the Earth-Moon mass ratio, which is also given in the header file by the way), nutations with time resolution of 8 days and 10 coefficients for each component (but we only have 2 components here compared to the 3 components for Moon librations, and there seems to be provisions for even more Moon information, i.e., mantle angular velocity)


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