A new visualization reveals the pattern of closer-than-usual approaches between Jupiter and Saturn over the centuries.

We have known for thousands of years that the sky is full of harmonies and rhythms. Pythagoras called it the “music of the spheres.”

Great conjunctions of Jupiter and Saturn follow a number of such rhythms. The most obvious is the roughly 20-year gap between each conjunction, when the two giants appear close together on the sky. During this period, Saturn completes two-thirds of its 30-year orbit, while Jupiter completes one lap of its 12-year orbit plus two-thirds of its next one. The odd two-thirds of an orbit mean that successive conjunctions are separated in the sky by about 240 degrees. In 1606, Johannes Kepler showed how three successive conjunctions form a near-perfect triangle when plotted on the zodiacal circle.

Longer timescales reveal other patterns, too: One of the notable points about the Great Conjunction of 2020 is that it is the closest one since 1623. Our team of programmers, astronomers, and enthusiasts at timeanddate.com wanted to visualize the roughly 400-year rhythm of super-close conjunctions between Jupiter and Saturn.

For fun, we created an algorithm to run through a mathematical model of Jupiter's and Saturn's movements over a 16,000-year period, starting from the year AD 1. (We used the JPL DE431 ephemeris, a high-precision model of the solar system developed by NASA's Jet Propulsion Laboratory.)

There are a number of ways to determine that a conjunction is occurring: the two celestial objects might have the same right ascension, same declination, or they might simply have some minimum separation on the sky. We looked for the moments when Jupiter and Saturn have the same right ascension, then measured the difference in their declination to show how far apart the two bodies are at conjunction. (The declination difference can be positive or negative, depending on whether Jupiter is above or below Saturn in the sky.)

For triple conjunctions — in which retrograde motion causes Jupiter to appear to pass Saturn on the sky three times in a zigzag fashion — we've used the single closest event for our calculation.

When we plotted a chart with the year along the x-axis, and the declination difference along the y-axis, we obtained a wave-like pattern. Close Great Conjunctions occur around the points where the waves cross the horizontal grid line showing a declination difference of zero.

The Great Conjunction of 2020 (which has a declination difference: +0.10°) is highlighted in red. The next close conjunction, highlighted in yellow, is in 2080 (declination difference: -0.10°).

Going back 400 years, we can see the two previous closer-than-usual conjunctions of Jupiter and Saturn in 1623 (green, declination difference: +0.09°) and 1563 (light blue, declination difference: -0.12°).

After 2080, the next close Great Conjunctions will occur in 2417 and 2477.

At some point, there will inevitably be “perfect” conjunctions of Jupiter and Saturn. These events are called transits when Jupiter partially obscures Saturn, or occultations when Jupiter completely covers Saturn. These events are few and far between. The next one is in 7541, 5,500-some years from now: A transit in February will be followed by an occultation in June, part of a triple conjunction. After that, there will be a transit in 8674, and occultations in 13340 and 13738.

Whatever else happens over the coming millennia, the music of the spheres will play on.

Michael Peterson

December 18, 2020 at 12:52 pm

This is a great article. My only complaint is that if it had only gone back to 7 BC instead of AD 1, it would have included the triple conjunction of 7 BC.

Graham_Jones

December 21, 2020 at 4:46 pm

Thanks Michael! (One of the reasons we didn't go back further than AD 1 is that we hadn't thoroughly tested our algorithm with negative numbers.)

Glenn

December 18, 2020 at 6:13 pm

Better to say that Saturn is N or S of Jupiter using the protocol of the dimmer object with respect to the brighter. Also above or below is hemisphere dependent so from say London on Dec 21st Saturn will be above Jupiter but from Sydney Aust it will be below, but in both instances it is 0.1* N of Jupiter. Got to see the triple in 1981.
Heavens Above has the planets at RA 8h 59 m on July 18th 1623 but the sun at 8h 10m so only 8.25* away.

Glenn

December 18, 2020 at 6:17 pm

And March 1226 better with planets 45* west of sun in morning sky.

Anthony Barreiro

December 18, 2020 at 9:56 pm

This is very interesting. Thank you.

I imagine that over time random perturbations in the orbits of Jupiter, Saturn, and Earth would create error bars that are wider than the apparent width of Jupiter, thus preventing confident predictions of transits and occultations. Any idea how far out into the future we can be reasonably certain exactly where the planets will be in the sky?

Graham_Jones

December 21, 2020 at 4:48 pm

Thanks Anthony, that's a good question — the long-term accuracy of ephemerides is a fascinating area of investigation.

Anthony Barreiro

December 22, 2020 at 6:44 pm

Thanks Graham. Could you give us a rule of thumb? When do you start taking predictions of very rare astronomical events with a grain of salt? Thousand of years from now? Tens of thousands of year? Hundreds of thousands?

Graham_Jones

December 30, 2020 at 3:04 am

Thanks again Anthony. According to a JPL paper: "The DE431 time span from the year –13,200 to the year 17,191 extends far beyond historical times and caveats are offered. For the planets, uncertainties in the initial conditions of the orbits will cause errors in the along-track directions that increase at least linearly with time away from the present. Resonances including, but not limited to, those between Jupiter and Saturn, and between Uranus, Neptune, and Pluto, may complicate the propagation of errors." https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf

misha17

December 18, 2020 at 10:42 pm

The Jupiter and Saturn may be in the same constellation in 2080, but the conjunction will occur in March, when they will be low in the sky before dawn. They will still be near each other in December 2080, when Venus passes by them in low in the evening sky while Mars is nearby in Aquarius

https://heavens-above.com/SkyChartPDF.ashx?time=3502059120000&showEquator=false&showEcliptic=true&showStarNames=true&showConsNames=true&showConstellationLines=true&showConstellationBoundaries=false

misha17

December 18, 2020 at 10:47 pm

Oops, the link shows the December sky for 2020, not 2080

Andrew James

December 18, 2020 at 10:51 pm

"There are a number of ways to determine that a conjunction is occurring: the two celestial objects might have the same right ascension, same declination, or they might simply have some minimum separation on the sky. "

Aren't conjunctions measured by ecliptic longitude (lambda), with minimal distance based on the time as same longitude as its separation.. e.g. elliptical latitude (beta)? Same right ascension or same declination would also need a position angle to have any meaning.

Also., "These events are called transits when Jupiter partially obscures Saturn, or occultations when Jupiter completely covers Saturn." They are actually called mutual planetary occultation or mutual planetary occultation transit, and have four contact points - ingress and egress. Only eighteen (18) are calculated between 1700 and 2200AD. The last was 3rd January 1818 AD by Venus and Jupiter. The next 22nd July 2065 AD by Venus and Jupiter. [Venus and Jupiter after that on 14 Sep 2123. Only two has been witnessed / recorded, being Mars and Jupiter on 12th September 1170 AD and Venus and Mercury by John Bevis on 28th May 1737.

Mercury and Venus events are more common, with the possibility of Venus transiting across Mercury or vice versa. All other events have the nearer planet doing the transiting.

Andrew James

December 18, 2020 at 10:59 pm

Oops. I meant" "They are actually called mutual planetary occultation or mutual planetary transit...." It is meant to distinguish from lunar occultations.

misha17

December 19, 2020 at 3:10 pm

I'm pretty sure that almanacs list the time of a conjunction. and the amount of separation, at the instance when they share the same Right Ascension, not ecliptic longitude. Same for lunar phases (New Moon, Full Moon, etc.).

You are right that they might approach closer when they share the same ecliptic longitude. During a lunar eclipse the instance of opposition or "Full Moon" (180 degrees difference in RA between the Sun and Moon), might several minutes different from the instance of "Greatest Eclipse" (the moon closest to the center of the Earth's shadow, and closest to the anti-solar point). During the Nov 30th penumbral lunar eclipse, Full Moon occurred at 9:31UT, and Maximum Eclipse occurred at 9:43 UT

Andrew James

December 19, 2020 at 6:37 pm

Quote: "A planet is said to be at conjuction when it is at the same ecliptic longitude as the Sun [or planet], and so approximately in line with it." Penguin Dictionary of Astronomy Jacqueline Mitton (1991)

However, the Astronomical Almanac list of conjunctions are low precision to 0.1 degrees, whereas the difference in RAs and ecliptic coordinates of two objects are minor. This was done in the old days this way to save time by not making an addition set of calculations and moreover when they adjudging planetary positions by timing transits in transit telescopes. Lunar events are more complex, e.g. lunar parallax needs to be compensated for.

My point was "...minimal distance based on the time as same longitude as its separation." can only be made when two ecliptic longitudes are the same, where ecliptic latitude equals minimum separation.

It is assumed the model used here based on JPL DE431 ephemeris needs to only be low precision to calculate when conjunctions occur to nearest year or month.

Monica Young

December 21, 2020 at 10:44 am

Hi Andrew, You are correct regarding the definition of conjunction, but the authors used a simpler measurement to simplify the code for these calculations. They inform me that it does not significantly alter the dates that they calculate for the conjunctions.

Graham_Jones

December 21, 2020 at 4:52 pm

Thanks Andrew, misha17 and Monica. Different sources define a conjunction in different ways — for this exercise, it made little difference which one we used. (As Monica said, we chose the simplest approach.)

Andrew James

December 21, 2020 at 6:39 pm

Monica
Much of this is described in the 'Explanation Supplement of the Astronomical Ephemeris' (1961) pg.210. The interpolation is made from just three daily positions, and is expressed to the nearest hour UT. Accuracy is not needed because observers on different longitudes will visually see small differences as the bodies slide pass each other. Knowing closest approach is mostly trivial, especially when the window to view most conjunctions are limited by proximity to the Sun, intervening daylight, etc.
Few would lose sleep in missing the exact time majority of conjunctions (or oppositions.)
Saying "There are a number of ways to determine conjunctions...." might be true when calculating the time of conjunctions, but it is is imprecise to state astronomical conjunctions are defined by differences in Right Ascension.

To be precise: Observer ecliptic lon. & lat. can be obtained using JPL's 'Horizons' [Uses source DE431mx + jup357_merged + sat427l_merged_DE438.] Closest approach of Jupiter/Saturn in RA is 2020-Dec-21 15:53 UT while closest approach in ecliptic coordinate is RA is 2020-Dec-21 18:01 UT (A difference of 02h 08m.) Minimum separation is 6.106 arcmin in PA 16 degrees, and when RAs are aligned 6.107 arcmin in PA 0 degrees.

Andrew James

December 21, 2020 at 7:23 pm

Just looked in daylight at ~ 21:56 UT very near closest approach using 20cm with 26mm Plössl in Sydney, Australia. Easily spotted Jupiter, but Saturn's low surface brightness was a bit more difficult than expected.

SophiSolus

December 21, 2020 at 6:22 am

Today is the great conjunction of Saturn and Jupiter. You can see a fabulous 3D representation of this event here https://solarsystem.one/greatconjunction.html?event=jupitersaturn

Rich

December 21, 2020 at 8:19 pm

There's a tiny typo in the plot "2,100 years of Jupiter-Saturn Conjunctions".
On the x-axis, the first "1,500" should be "500". 🙂

Monica Young

January 5, 2021 at 9:53 pm

Thanks for the sharp eye, Rich, the typo was ours and we've fixed it now.

Steve Bilanow

December 24, 2020 at 11:15 am

The reason for this pattern in close conjunction times is similar to the reason for patterns in transits of Venus and for solar and lunar eclipse times; when the time of conjunctions progress to times when their orbital location line up with their orbit nodes, they are closest. For Jupiter and Saturn conjunctions, each of the vertices of the trigon pattern get closer or further from the relative nodes of their orbits. As defined relative to the Earth orbit plane, the inclination of Jupiter is 1.303 and the inclination of Saturn is 2.485 and thus their orbits have a relative inclination 1.182 degrees. I think the amplitude of waves in your long term declination differences are a bit larger mainly because you are showing declination differences rather than ecliptic latitude. The Earth's orbit moving above and below the plane of Saturn's orbit adds some variation and spread in the declination differences.

Neil-Mottinger

December 30, 2020 at 5:19 pm

Yes, a great article which I will forward to my 300+ space enthusiasts. I'm wondering why there is no mention of the 1226 conjunction? There are numerous references to it in other sources, but none here. I appreciated your reference to the JPL planetary ephemeris you used.

Graham_Jones

January 2, 2021 at 12:20 am

Many thanks for this, Neil. The 2,100-year chart shows that the 1226 conjunction (declination difference -0.04°) was one of the two closest conjunctions during this period. The other was in the year 372 (declination difference +0.03).

timeanddate.com fan

August 24, 2022 at 11:30 pm

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