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Lunar libration cycles question

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#1 cpsTN

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Posted 14 July 2019 - 06:35 PM

I know that libration is cyclical but is it precisely predictable? I've been observing the Moon for more than 30 years but with schedules and sickness and clouds, etc, I'm not able to observe it continuously enough to have ever noticed whether the same libration angle comes around every three months or so many days or on the same date or whatever. I am wondering if there is a predictable pattern and what that would be. Surely, by now we know enough about the Earth-Moon system to know when we can see what and for how long. We can predict when we can see the Lunar X and other "transient" features, so I presume libration can be pinpointed precisely as well. Can anyone point me to a site or other information that would open this to me?



#2 Tom Glenn

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Posted 14 July 2019 - 07:19 PM

Lunar ephemeris calculators include libration, and these values are accurate into the future.  You can probably Google search for online calculators that are easy to use.  The ones I prefer to use are NASA's JPL Horizons program, and the website Calsky.  The links are below.  These sites offer tremendous amounts of data, but they are often not the most user friendly if you are looking for quick answers, which is why I say you might just search for a quicker website that will spit out lunar ephemeris.  With these sites below you will kind of have to figure out how to navigate for yourself, but they do offer extreme amounts of data and you can customize your observer location.  

 

https://ssd.jpl.nasa.gov/horizons.cgi

https://www.calsky.com

 

Libration in latitude is caused by the Moon's elevation above or below the ecliptic plane.  Therefore, the periods of maximum libration in any one direction (N or S) cycle according to the draconic month, or 27.21 days (from max N to max N, or S to S).  Maximum libration in longitude is related to the Moon's velocity in orbit, which is related to its relationship with orbital apogee or perigee, and therefore this cycles with the anomalistic month, or 27.55 days.  Note that both of these numbers are less than the synodic month of 29.53 days.  This means that the change in libration is uncoupled from lunar phase, but each is independently predictable.  However, not all librations are equally strong in absolute value.  This is especially true for libration in longitude, which I assume has to do with the relative position of the Earth-Moon-Sun and how this affects the velocity of lunar orbit.  For example, the maximum libration in longitude is sometimes over 8 degrees, but other times less than 8.  

 

On a related note, does anyone know of any software that can quickly and easily generate graphs that show the libration cycles over a period of time?  That would be useful.  Of course this could be done by looking up the individual data points and plotting the graph, but I didn't' know if any software already had this built in for the Moon.  


Edited by Tom Glenn, 14 July 2019 - 07:22 PM.


#3 Tom Glenn

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Posted 14 July 2019 - 07:32 PM

To add to my above comment, if you use the JPL website, you will select the Moon as the target body, set your observer location, date, and then you will need to go to the table settings.  For libration, you will need to check the box labeled "Observer sub-lon & sub-lat".  This will then give you the sub-Earth coordinates on the Moon for your given location, which corresponds to the libration.  These numbers will vary slightly depending on your location on Earth (usually by a few tenths of a degree unless you were very near the poles).  Generalized ephemeris tables will usually report a sub-Earth point that is based upon the center of the Earth rather than a set of topographic coordinates.  



#4 frank5817

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Posted 14 July 2019 - 08:29 PM

To gain an understanding of the lunar libration components and how they are calculated you will see that it is not a simple trigonometric formulation that gives you your answer. Here

It is best to find a program that calculates this as Tom recommends above.

Also keep in mind the Moon's orbit is elliptical and it moves faster and slower in that orbit via Kepler's laws.

The lunar orbit also precesses, there is diurnal libration to consider and so on, not a trivial calculation.


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#5 Tom Glenn

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Posted 15 July 2019 - 12:49 AM

Frank, that is a very interesting paper.  Thanks for providing.  I think it highlights very well how this is not a trivial calculation.  Thankfully we have access to ephemeris programs that can provide this information to us!  



#6 beggarly

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Posted 15 July 2019 - 03:29 AM

Theory and practice: http://users.telenet...ibratieboek.pdf

 

... any software that can quickly and easily generate graphs that show the libration cycles over a period of time?

 

https://github.com/f...i/LTVT Download

LTVT can generate libration data:

 

Librations calculated for a geocentric observer
Center Dist(ance) and Sun Angle calculated for feature at 0.0000°E  0.0000°N
  Feature is 0.0000° from disk center at zero libration.
  "Libr(ation)" is how much closer feature is to disk center at time of observation.
  "%Illum" is percent illumination of the full lunar disk.

Times being searched at interval of 1440 minutes subject to constraints:
  *  Sun angle at feature >0.0° and <90.0°
  *  Distance of feature from apparent lunar disk center <90.00°

                      Center                      Sun Angle       Librations
   Date      Time UT   Dist.   Libr.  %Illum  Altitude Azimuth   Long.    Lat.
1/07/2019  00:00:00   6.687  -6.687    4.29 -71.8866  269.155  -5.579   3.692
2/07/2019  00:00:00   5.280  -5.280    0.89 -84.1366  267.685  -4.805   2.191
3/07/2019  00:00:00   3.769  -3.769    0.05 -83.6011   91.875  -3.732   0.523
4/07/2019  00:00:00   2.714  -2.714    2.00 -71.3500   90.564  -2.432  -1.205
5/07/2019  00:00:00   3.034  -3.034    6.72 -59.0990   90.294  -0.991  -2.867
6/07/2019  00:00:00   4.371  -4.371   13.93 -46.8513   90.178   0.492  -4.343
7/07/2019  00:00:00   5.851  -5.851   23.13 -34.6086   90.111   1.923  -5.527
8/07/2019  00:00:00   7.111  -7.111   33.70 -22.3720   90.066   3.217  -6.345
9/07/2019  00:00:00   8.007  -8.007   44.95 -10.1419   90.031   4.307  -6.757
10/07/2019  00:00:00   8.486  -8.486   56.25   2.0814   89.999   5.146  -6.757
11/07/2019  00:00:00   8.544  -8.544   67.00  14.2980   89.967   5.709  -6.367
12/07/2019  00:00:00   8.213  -8.213   76.73  26.5085   89.928   5.987  -5.633
13/07/2019  00:00:00   7.551  -7.551   85.05  38.7136   89.877   5.987  -4.610
14/07/2019  00:00:00   6.638  -6.638   91.68  50.9143   89.797   5.723  -3.369
15/07/2019  00:00:00   5.580  -5.580   96.43  63.1115   89.647   5.218  -1.979
16/07/2019  00:00:00   4.526  -4.526   99.21  75.3060   89.249   4.496  -0.516
17/07/2019  00:00:00   3.709  -3.709   99.99  87.4918   84.960   3.586   0.950
18/07/2019  00:00:00   3.447  -3.447   98.84  80.3009  271.476   2.518   2.355
19/07/2019  00:00:00   3.875  -3.875   95.87  68.1067  270.739   1.326   3.641
20/07/2019  00:00:00   4.758  -4.758   91.26  55.9093  270.536   0.050   4.758
21/07/2019  00:00:00   5.805  -5.805   85.20  43.7086  270.448  -1.267   5.666
22/07/2019  00:00:00   6.833  -6.833   77.88  31.5039  270.405  -2.575   6.331
23/07/2019  00:00:00   7.733  -7.733   69.53  19.2947  270.388  -3.819   6.729
24/07/2019  00:00:00   8.427  -8.427   60.38   7.0804  270.388  -4.936   6.838
25/07/2019  00:00:00   8.851  -8.851   50.67  -5.1394  270.406  -5.862   6.643
26/07/2019  00:00:00   8.951  -8.951   40.69 -17.3647  270.443  -6.531   6.134
27/07/2019  00:00:00   8.683  -8.683   30.81 -29.5957  270.509  -6.879   5.312
28/07/2019  00:00:00   8.026  -8.026   21.44 -41.8321  270.621  -6.853   4.189
29/07/2019  00:00:00   6.998  -6.998   13.11 -54.0731  270.824  -6.417   2.799
30/07/2019  00:00:00   5.689  -5.689    6.39 -66.3173  271.261  -5.561   1.202

               *** search completed ***

 

http://www.ngc7000.c...oelix/index.htm

Graphical output from Coelix Apex:

Attached Thumbnails

  • Librations1.jpg
  • Favorable.jpg

Edited by beggarly, 15 July 2019 - 03:46 AM.

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#7 John_Moore

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Posted 15 July 2019 - 05:30 AM

Of course, the NASA Scientific Visualization Studio animations out-putted every year are a nice introduction to the complexities of librations. 

 

John Moore



#8 beggarly

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Posted 15 July 2019 - 10:24 AM

According to this document ( http://users.telenet...ibratieboek.pdf ) conditions of illumination and libration repeat after one Saros.

The simulation in LTVT shows nearly the same result.

Attached Thumbnails

  • Almost One Saros Apart.jpg


#9 catalogman

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Posted 15 July 2019 - 11:40 AM

<snip>

 

On a related note, does anyone know of any software that can quickly and easily generate graphs that show the libration cycles over a period of time?  That would be useful.  Of course this could be done by looking up the individual data points and plotting the graph, but I didn't' know if any software already had this built in for the Moon.  

There's a monthly libration graph in MoonCalc (see the .gif at the bottom of the
download page for the software):

 

https://mooncalc.moonsighting.org.uk/

 

If it doesn't ask for your location, then it doesn't include the diurnal libration

(which can be as much as 1 degree).

 

--catalogman

 

EDIT: It looks like the observer's coordinates are on the .gif, so MoonCalc includes all of

          the important librations.


Edited by catalogman, 15 July 2019 - 02:08 PM.


#10 catalogman

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Posted 15 July 2019 - 11:42 AM

To gain an understanding of the lunar libration components and how they are calculated you will see that it is not a simple trigonometric formulation that gives you your answer. Here

It is best to find a program that calculates this as Tom recommends above.

Also keep in mind the Moon's orbit is elliptical and it moves faster and slower in that orbit via Kepler's laws.

The lunar orbit also precesses, there is diurnal libration to consider and so on, not a trivial calculation.

There is also a physical (or dynamical) libration caused by the Earth's
attraction to the closest part of the slightly ellipsoidal Moon. Its value
is very small (maximum value about 3.5'); its periodicity is the superposition
of the free and forced oscillations.

 

There's a numerical example for the optical, diurnal, and physical librations
on p. 323 of the ES. (See the article in your post, which rederives
the optical libration in the ES but makes no mention of the others.)

 

--catalogman



#11 Tom Glenn

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Posted 15 July 2019 - 05:47 PM

Theory and practice: http://users.telenet...ibratieboek.pdf

 

... any software that can quickly and easily generate graphs that show the libration cycles over a period of time?

 

https://github.com/f...i/LTVT Download

LTVT can generate libration data:

 

 

Thanks for the links.  That pdf is full of a lot of good illustrations.  I've yet to try LTVT, mostly due to time constraints, coupled with previous posts I've seen complaining about the program being cumbersome to install/use, but the file description doesn't sound so bad, so I'll give it a try sometime soon.  Those graphs you show are exactly the type I'm talking about.  It's useful to see the libration plotted that way.  



#12 Tom Glenn

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Posted 15 July 2019 - 05:53 PM

There's a monthly libration graph in MoonCalc (see the .gif at the bottom of the
download page for the software):

 

https://mooncalc.moonsighting.org.uk/

 

If it doesn't ask for your location, then it doesn't include the diurnal libration

(which can be as much as 1 degree).

 

--catalogman

 

EDIT: It looks like the observer's coordinates are on the .gif, so MoonCalc includes all of

          the important librations.

Thanks for the link.  That program would be useful, but unfortunately, I don't know how easy it will be to get it up and running on my computer.  It's pretty old (2001) and needs to run in DOS mode, and I'm already running Windows in a virtual machine on a Mac, so it will probably require some additional steps to make this work.  But I can look into it.  



#13 Tom Glenn

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Posted 15 July 2019 - 06:02 PM

According to this document ( http://users.telenet...ibratieboek.pdf ) conditions of illumination and libration repeat after one Saros.

The simulation in LTVT shows nearly the same result.

As you say, there is some slight differences in the exact numbers, but the libration and phase are nearly the same, as is the sub-solar point.  Because the Saros cycle is not an exact multiple of days, but has an extra 8 hours, then it's likely that you wouldn't be able to observe at the exact moment both times, as the Moon would potentially be below the horizon for one of them.  


Edited by Tom Glenn, 15 July 2019 - 06:02 PM.


#14 catalogman

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Posted 17 July 2019 - 07:23 AM

Attached is a screenshot of MoonCalc running in DOSEmu (Linux),
so DOSBox (Win) should work.

 

The user has a choice of geocentric or topocentric values.

 

 

There's also an online calculator:

 

https://www.cloudyni...bration-graphs/

 

https://www.curtrenz.com/moon.html

 

Lunar Libration - July:    https://www.curtrenz.com/moon11.html

 

Lunar Libration - August:  https://www.curtrenz.com/moon12.html

 

Lunar Libration in 2 Dimensions Combined:  https://www.curtrenz.com/moon10.html

 

All values are geocentric, not topocentric.

 

--catalogman

Attached Thumbnails

  • MoonCalc_in_DOSEmu.JPG


#15 catalogman

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Posted 17 July 2019 - 07:26 AM

For the OP, here's an easy proof of the periodicity: it shows that maximum optical libration in
longitude occurs on the orbit where r = a(1 - e2)1/4.

 

http://scienceworld....nLongitude.html

 

 

--catalogman


Edited by catalogman, 17 July 2019 - 07:26 AM.


#16 Tom Glenn

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Posted 17 July 2019 - 04:13 PM

Catalogman, thanks for those links.  In particular, Curt Renz's website looks very useful, and I had never been there before.  The only thing that could be confusing to someone looking at his graphs is that they report the shift in the mean center of the Moon (0,0) versus the apparent center, which means that the values reported are the opposite to the libration values that would be given in an ephemeris table, which reports the coordinates of the sub-Earth point.  But that's why reading the legend is important!  It looks as though Curt used to post on CN, but unfortunately is no longer a member?  I was also able to find a post from three years ago that made me do a double-take, because it's nearly identical to the one here, and by the same OP!  Deja vu?

 

https://www.cloudyni...ion-occurances/

 

In general, I've noticed that the Lunar Observing forum, which doesn't get much traffic anyways compared to the other forums here on CN, also has unfortunately experienced a decline in participation over the past several years, with many knowledgable members no longer posting.  That's too bad.  


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