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?
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:
Prefilled with the values you want (assuming two fingerwidths is 2.5 degrees):
and a direct link to the results (with the "LIMIT 200" removed, so you can see all 26,671 results):
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:
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.
How often do Venus and Saturn come together in the sky like this?
Sagittarius is between November 22 and December 22 (2019, UT1).
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.