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Venus and Saturn will be approximately two finger widths apart in the constellation Sagittarius on December 11, 2019. I was wondering: how often do Venus and Saturn come together in the sky like this? I would assume it wouldn't be that frequent. Is it quite frequent? Is there a formula to predict something like this?

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  • $\begingroup$ The frequency will depend on your definition of "close on the sky" for the conjunction. According to this link, 2 fingers is about 2.5 degrees (depending on which fingers you used and presumably variation in finger width...) - is this your definition of "close together" ? $\endgroup$ – astrosnapper Oct 7 at 16:19
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To answer How to calculate conjunctions of 2 planets earlier, I computed all planetary conjunctions from -13200 to 17190 and you can search the results at:

http://search.astro.barrycarter.info/index.pl

Prefilled with the values you want (assuming two fingerwidths is 2.5 degrees):

http://search.astro.barrycarter.info/index.pl?p1=Venus&p2=Saturn&lowyear=-13200&highyear=17190&sep=2.5&sunsep=0&submit=SEARCH

and a direct link to the results (with the "LIMIT 200" removed, so you can see all 26,671 results):

http://ae2bcbd33ae927c8e17c62ff155325f3.astro.db.mysql.94y.info/

Note that there are 26,671 2.5 degree conjunctions in 30,390 years, which works out to about 0.88 conjunctions per year.

The http://search.astro.barrycarter.info/index.pl page also provides information on bulk downloading the data, and you may also want to visit:

https://github.com/barrycarter/bcapps/tree/master/ASTRO/CONJUNCTIONS/

Read the README first, but the file you need is the 26.out.bz2 files, since Venus is the second planet and Saturn is the 6th planet.

As always, I'm not perfect, so please don't rely on my results, but do tell me if you find errors, thank you.

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How often do Venus and Saturn come together in the sky like this?

Sagittarius is between November 22 and December 22 (2019, UT1).

The "List of conjunctions (astronomy)" (2015-2020) says that they have had conjunctions on:

Date           Time UTC Planet Angle distance  Planet Elongation to Sun
January 9, 2016   03:57:19  Venus 5' north of      Saturn 36.3° West
October 30, 2016  08:25:30 Venus 3°02' south of  Saturn 36.9° East
December 25, 2017 17:49:20 Venus 1°08' south of  Saturn 3.5° West
February 18, 2019 13:54:15 Venus 1°05' north of  Saturn 42.7° West
December 11, 2019 04:42:34 Venus 1°49' south of  Saturn 30° East

So the answer is one year, plus or minus two months, but 3 years for the same elongation.

Saturn completes one orbit around the Sun every 29.4571 years, or 10,759.22 days.

Venus completes one orbit around the Sun every 0.615198 years or 224.701 days.

Since 10,759.22 / 224.701 = 47.8823859262, Venus will be in conjunction 47.9 times per orbit of Saturn, needless to say that each time won't be in Sagittarius (and that requirement might make this an Astrological question). 47.8823859262 / 12 comes up 3.99019883 times, so 10,759.22 / 3.99019883 = 2696.412 (in days) or 7.38743013698 (in years)

So the answer to: "Venus-Saturn conjunction in Sagittarius on Dec 11, 2019 - How often does this happen?" is 7.38743013698 times per orbit of Saturn.

Is there a formula to predict something like this?

Yes. I'll look and see if I can find either a formula (which is likely a complex computer program, requiring you to enter some information), or a longer list. An initial attempt to answer your second question didn't turn up anything.

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    $\begingroup$ Minor point, but because the Earth moves, the 47.9 times per Saturn's orbit isn't quite right because for conjunction you need Earth-Venus-Saturn to line up in that order. Venus-Earth-Saturn doesn't work cause they're on different sides of Earth, and Earths movement around the sun significantly changes the angle between Earth and Venus. I think, for a bad estimate, we can say Saturn is fixed, and estimate how often Venus passes that part of the sky from Earth's view. 3 body calculations confuse me, so I'm not sure how to make a good estimate. $\endgroup$ – userLTK Oct 8 at 2:19
  • $\begingroup$ @userLTK - I did struggle a bit to explain it better but then user MikeG came by with an edit and not only unnecessarily reduced the precision but used the edit to slightly change the meaning of what was written (by days, by years) to days and years, when that's not the final unit of measurement. So I left answering for the edit to the more knowledgeable one whom made it, my other choices are rollback and re-edit; the second I've not got back to (considering the overall limited interest). I appreciate both your visits, and those whom merely came to look. Better if Mike wrote the exact answer. $\endgroup$ – Rob Oct 8 at 3:10
  • $\begingroup$ @Rob Sorry my edit bothered you. It's still your answer. See Wikipedia: Significance arithmetic. $\endgroup$ – Mike G Oct 8 at 12:59
  • $\begingroup$ @MikeG It's not a case of "bothered". You used that "sufficiently fair reason" to make other changes. Since you didn't also correct the "answer" too it indicates to user userLTK (and others) that either there are two people whom take issue with their comment or you didn't complete your edit. I'm leaving you two to discuss this amongst yourselves for that reason. I may come back to improve the answer, especially if it earns a few 100 votes; otherwise I simply remind myself that I retired ~10 months ago, when I hit 20K rep. $\endgroup$ – Rob Oct 8 at 14:32
  • $\begingroup$ "Other changes" already retracted. If you'd rather generate 200 words of protest than resolve userLTK's concern, that's on you. $\endgroup$ – Mike G Oct 8 at 19:26

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