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The lunar motion can be predicted with basic celestial mechanics, but the perigee and apogee are not always the same, basically because the attraction of the Sun makes some oscilations in the semi-axis of the orbit (https://en.wikipedia.org/wiki/Perturbation_(astronomy)).

My question is: how do they know when the full moon will get as close as it got in the recent supermoon? For example, the Dailypost article Biggest Supermoon in 68 years will light up the November sky claims that the full moon won't come this close to Earth until November 25th, 2034.
How do they kow that? Are they using the perturbation theory equations to predict this? If so, can anybody give me some source or explanation of how it's done analytically?

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    $\begingroup$ The most accurate answer to your question is that NASA or someone similar announces it and they reprint it. How does NASA do it? They use the CSPICE libraries: naif.jpl.nasa.gov/naif/tutorials.html If you're insanely interested, feel free to contact me, I've written some CSPICE programs and may be able to help if you want to write your own. $\endgroup$ – barrycarter Nov 13 '16 at 19:18
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A slightly more useful answer than my comment above:

Using http://wgc.jpl.nasa.gov:8080/webgeocalc/#NewCalculation "Angular Separation Finder" feature, we can determine when the angle between the Sun and the Moon is at a local maximum. It turns out this isn't quite the definition of Full Moon, but it's very close. I couldn't find a way to make webgeocalc compute full moon times exactly, though I'm sure there is a way, and, of course, there are plenty of tables of full moons online.

Starting at http://wgc.jpl.nasa.gov:8080/webgeocalc/#AngularSeparationFinder we fill out the form as so:

enter image description here enter image description here enter image description here

and click the "Calculate" button.

This yields a list of all "full" moons. Scroll down and click on the "Save All Intervals" button:

enter image description here

We now want to find the moon's distance at all of the times we just saved (ie, the times of the "full" moons). To do this, start at http://wgc.jpl.nasa.gov:8080/webgeocalc/#StateVector and fill out as follows:

enter image description here enter image description here enter image description here

NOTE: to get the list of intervals above, drag from the saved intervals result window into the list of intervals window.

The results, which you can also download, tell you the moon's distance from the Earth at the times of the "full" moons we computed earlier:

enter image description here

I downloaded the results in Excel format, imported them into gnumeric and sorted by radius (distance from Earth to Moon) and did a little additional cleanup to get:

enter image description here

(the full spreadsheet is available at https://github.com/barrycarter/bcapps/blob/master/STACK/StateVectorResults.xls)

So, yes, tonight's full moon (yellow) is the closest we'll have until 2034-11-25 (red). It's also the 6th closest moon we'll have this century.

To see other examples of geocalc in action, see my:

For more about how NASA calculates these values in the first place: Where can I find a set of data of the initial conditions of our solar system? which is also now linked to the general "how to compute positions" wiki answer: Where can I find/visualize planets/stars/moons/etc positions?

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    $\begingroup$ Downvoted, for two reasons. One is that this answer is absolutely useless to those who cannot see. The alt text for each of the nine images in this answer is "enter image description here". This answer is not accessible. The other reason is that this answer does not answer the question. Those SPICE kernels are not handed to JPL by the Flying Spaghetti Monster. A correct answer would explain how those SPICE kernels (and how the DE4xxx ephemerides) are created. $\endgroup$ – David Hammen Nov 14 '16 at 12:31
  • $\begingroup$ @DavidHammen I've added links to how NASA computes these files. Re those who can't see: I'm not sure what text would be helpful -- I always upload images and leave the default text there. Ultimately, I don't think the webgeocalc site itself is that accessible. $\endgroup$ – barrycarter Nov 14 '16 at 13:06
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    $\begingroup$ @DavidHammen you appear to be overly sensitive to a very narrow issue (that of text-to-speech). $\endgroup$ – Carl Witthoft Nov 14 '16 at 13:41
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    $\begingroup$ My downvote is basically, "TL;DV" (didn't view) WIthout a careful explanation of how those images are used and why one needs all those steps, it's just a pile of screenies. $\endgroup$ – Carl Witthoft Nov 14 '16 at 13:42
  • $\begingroup$ @CarlWitthoft I would think the screens are self-explanatory (though I do explain them better in one of the two "geowebcalc" links to my other answers), but, then again, I think my code is self-explanatory too, even though I don't understand it 6 months after I've written it, so you're probably right, and, not that it's relevant, this is a run-on sentence. $\endgroup$ – barrycarter Nov 14 '16 at 14:39

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