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Table 1: Appulses of Jupiter and Saturn between 1000 BCE and CE 3000 with a separation < 10′.

Date Separ. Elong. -998 May30 9′ 19′′ 39 E -939 Sep04 3′ 29′′ 42 W -482 Mar06 6′ 23′′ 55 W -423 Dec28 1′ 29′′ 17 E -85 Aug11 3′ 44′′ 20 W 372 Mar06 1′ 52′′ 53 W 431 Dec31 6′ 16′′ 17 E 709 Sep13 8′ 22′′ 61 W 769 Jul23 4′ 17′′ 2,4 W 1166 Dec11 9′ 48′′ 25 E 1226 Mar05 2′ 09′′ 49 W 1563 Aug25 6′ 47′′ 42 W 1623 Jul16 5′ 10′′ 13 E ′ ′′ 2020 Dec21 6 17 30 E Figure 1: Displacement of a Trigon after 60 years. 2080 Mar15 6′ 19′′ 44 W 2417 Aug24 5′ 25′′ 26 W 2477 Jul06 6′ 20′′ 27 W 2815 Feb23 9′ 58′′ 30 W 2874 Dec25 2′ 21′′ 36 E 2934 Mar19 9′ 43′′ 38 W will have already left behind the ascending node (Fig. 2). The 8◦-shift of the Trigon leads to the effect that appulses are precluded for the subsequent centuries. Only when one of its legs approaches a node, there will be tight encounter: thereafter in 2417 and 2477 at the opposite (descending) node. Figure 2: Separation of Jupiter and Saturn at the instant of their conjunction. Negative values indicate Jupiter passing Planetary southward. The three sinusoidal curves represent one leg of the Trigon. A brief remark in an article by Johan Stein [4] informs us about an observation by the astrologer Francesco Giuntini (1523–1590): Jupiter almost occulted Saturn on 24 August the planets are slowly varying with time by reason of secu- 1563. In fact, the planets passed by each other similarly lar variations of their orbits [3]. For very distant times any close as in 2020. In the pre-telescopic era the shining ob- prediction of an accuracy smaller than the apparent diamet- jects seemed merging. The resolution of the normal eye- ′ ers of the planetscannot be made, as long as we lack secure sight is at 1 , but this turns out a matter of contrast and fixpoints from observation to be utilised in a wider baseline individual training of the observer. for extrapolation purposes. The characteristics considered Mutual occultations of any two planets in the Solar to be stable for millions of years regard only the orbital System do exist within the time span of our historic era dur- parameters, not to be confused with the . A com- ing ±3000 years, but there is none for Jupiter and Saturn. parison of various software deploying different integrators This oddity was already noticed by Salvo de Meis [1]. We would be desirable though. made an effort to look a bit further for an overlap of their Still, there is a chance to spot a line-up of Jupiter and planetary discs. A promising case is found for 16 February Saturn: that special view emerges extraterrestrically from 7541 using the ephemeris of the DE431 theory of - Neptune on 29 April 2046 (Fig. 3). Gazing from this fur- ary motions. Near misses are going to happen in 4523 and thermost planet, Saturn is on the superior arc of its orbit in 6687. a distance of 38.7 AU from Neptune while Jupiter is head- However, extrapolationsof this kind can hardly be veri- ing to its inferior conjunction with the being 26.7 AU fied, as they put astronomical calculations to extremes. All away. The planets meet in an optical line 8◦ to the east motions in the are extrapolated from our nar- of the sun. It will be the sole occultation event for these row window of precise measurements. The movements are two giants visible from any planet during the entire 21st prone to gravitational perturbances, and even the slightest century. deviation might cause a delay. Moreover, the diameters of

2 Gripp & Khalisi (2021): Appulses of Jupiter and Saturn

Figure 3: Occultation of Saturn and Jupiter on 29 April 2046 viewed from Neptune.

Besides the case of Jupiter and Saturn, there is also no occultation for the remote and Neptune to be seen from Earth. That seems intelligible as their conjunctions take place only at 170 years on average and their orbits are inclined by 10◦. An overlap of their discs will probably not occur within 1 million years. In regard to the Jovian planets, it is actually Saturn who refuses to meet its giant colleagues. While Uranus and Nep- tune are hit by Jupiter once or twice during our historical time, Saturn resists any such visit with the outer planets. As viewed from Earth, it is only occulted by the inner plan- ets. The next occultation will be performed by on 12 August 2243.

Acknowledgements

This paper is a summary of two articles in the German journal for Sternzeit 46, issue no. 1 + 2/2021, p18–23 and p69–71.

References

[1] Salvo de Meis. Some mutual planetary occultations. Journal of the British Astronomical Association, 103: 185–187, 1993. [2] Donald V. Etz. Conjunctions of Jupiter and Saturn. Journal of the Astronomical Society of Canada, 94: 174–178, 2000. [3] Jean Meeus. Mutual occultations of planets. Journal of the British Astronomical Association, 80:282–287, 1970. [4] Johan Stein. The Triple Conjunctions of Jupiter and Saturn. Popular Astronomy, 57:182–184, 1949. [5] Robert B. Weitzel. Jupiter and Saturn at solar opposi- tion. Popular Astronomy, 53:27–29, 1945.

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