Has the conjunction between Venus, Jupiter, and Regulus only occurred twice in 2,000 years?

  • I recently heard the claim that mid-July, the "Star of Bethlehem" formed for the first time in 2,000 years, where the Star of Bethlehem is a three-way conjunction between Venus, Jupiter, and Regulus. The Wikipedia page I just linked mentions one such conjunction occurring in 2 BC, and other sources (like EarthSky) mention the conjunction that happened last month, in 2015 AD. Has this three-way conjunction never happened in the intervening 2016 years?



    (For the purpose of this question, I'll say that it counts as a conjunction when each pair of bodies is separated by no more than 10 degrees, as suggested by this CosmoQuest forum thread on the subject.)


    Also, I would have added the tags [tag:regulus] and [tag:conjunction], but I don't have enough rep. Yet.

    Does the conjunction have to be visible to count? Jupiter conjuncts Regulus every 12 years or so, and Venus moves around quite a bit, so you'd expect more frequent conjunctions. I found one on 21 Aug 2003 (roughly), but the Sun is right there as well, so the conjunction wouldn't be visible. Since Venus stays fairly near the Sun all the time, this might be a problem more frequently as well. Same thing Aug 1991 as well.

    Visible conjunctions preferred, but you could point out that non-visible conjunctions happen too.

    10 degrees either way might be a bit much. On average, Jupiter spends 8 months within 10 degrees of Regulus, which is longer than it takes Venus to make a complete tour of the Zodiac. So, you're pretty much guaranteeing a conjunction every 12 years or so.

    Hmm. Looking at the forum thread again, one person said that the maximum separation for all pairs was 5.5 degrees on July 16. So, perhaps that would be a better restriction?

    Yeah. 10 degrees is quite a bit, really.

    The Moon is 0.5 degrees in diameter. Anything much bigger than that would not count as a very spectacular conjunction. A few degrees at most, let's say 5, but it would really have to be more like 2 degrees or 1 to look particularly interesting.

    The actual date was around June 29 or 30. Not mid July, just FYI.

    Still working on a "good" answer, but 9 Sep 1659 has a much closer conjunction of the three (all fit within 3 degrees), and I've found several other close conjunctions, though this one is the most impressive I've found so far.

  • barrycarter

    barrycarter Correct answer

    6 years ago

    The 2 BCE conjunction had Regulus, Jupiter, and Venus within 5.346
    degres, and the Sun was 19.371 degrees distant.



    The 2015 conjunction had the three within 5.488 degrees, with the Sun
    30.930 degrees away.



    There are 81 conjunctions between those two dates where Regulus,
    Jupiter, and Venus are less than 5.488 degrees apart, although, in
    some cases, the Sun would be too close to see these conjunctions.



    I list all of these conjunctions below, and also include conjunctions
    as far back as 999 BCE and as far forward as 2999 CE.



    The first two columns are the date and time.



    The third column is the maximum pairwise separation (in degrees) of
    Regulus, Jupiter, and Venus.



    The fourth column is the smallest angular distance from the Sun (in
    degrees) of the three.



    Additional notes follow the list:




    -998-08-13 17:47:22 4.460 17.341
    -986-06-14 19:33:17 5.078 31.064
    -962-06-13 20:42:13 1.599 37.154
    -939-08-24 16:05:37 0.960 32.337
    -903-06-23 23:23:31 4.166 23.499
    -879-06-22 18:41:22 2.388 28.906
    -856-09-02 02:38:31 0.900 40.426
    -820-07-03 18:56:04 3.059 15.483
    -796-07-02 11:36:42 3.326 19.880
    -773-09-09 05:10:53 2.068 46.122
    -737-07-14 22:02:17 1.914 7.202
    -713-07-13 13:16:57 4.432 10.473
    -654-07-25 04:03:45 0.919 0.676
    -618-06-16 16:24:53 2.111 36.170
    -571-08-04 08:00:55 0.890 9.482
    -535-06-08 09:43:32 1.519 43.497
    -512-08-15 20:18:35 4.304 21.310
    -488-08-14 11:02:13 2.216 17.658
    -452-06-14 20:40:52 1.507 38.039
    -429-08-26 12:36:08 3.022 30.516
    -405-08-25 05:36:22 3.500 25.655
    -369-06-24 14:26:28 1.383 30.683
    -346-09-04 07:24:03 2.055 38.915
    -322-09-03 07:20:58 4.678 33.128
    -310-07-05 12:23:59 4.755 15.643
    -286-07-04 05:57:12 1.723 21.719
    -263-09-10 01:35:27 1.743 44.339
    -239-09-10 16:58:48 5.467 39.382
    -227-07-15 14:17:13 3.299 7.717
    -203-07-14 05:55:31 3.137 12.390
    -156-09-12 06:11:05 5.008 41.107
    -144-07-25 20:01:44 1.779 0.850
    -132-06-30 22:00:27 4.887 21.625
    -120-07-24 10:48:43 4.594 2.846
    -61-08-06 01:53:32 0.781 8.312
    -25-06-11 09:01:53 2.012 43.414
    -2-08-17 13:43:06 5.346 19.371 (conjunction in 2 BCE)

    -1-06-11 09:00:23 4.978 45.464
    22-08-16 03:46:55 1.066 16.885
    58-06-16 21:31:59 1.924 38.499
    81-08-27 08:28:28 4.344 28.668
    82-06-16 01:28:35 4.809 41.268
    105-08-26 00:47:42 2.203 25.078
    141-06-25 09:01:41 1.347 31.319
    164-09-05 10:04:04 3.548 37.319
    165-06-24 06:31:05 5.379 33.701
    188-09-04 07:11:50 3.049 33.055
    224-07-04 23:17:54 1.226 23.421
    247-09-13 15:10:43 3.233 44.173
    271-09-13 05:17:58 3.587 40.061
    283-07-17 06:44:26 5.353 7.568
    307-07-15 23:33:14 1.106 14.268
    330-09-10 21:05:11 4.715 41.177
    354-09-17 08:06:60 3.418 44.034
    366-07-27 11:51:60 3.985 0.992
    390-07-26 03:05:29 2.339 4.782
    449-08-06 18:09:31 2.584 6.358
    473-08-05 08:52:09 3.774 1.408
    485-06-13 23:13:34 3.793 41.669
    509-06-14 10:03:10 3.248 45.079
    532-08-16 22:56:25 1.136 15.985
    556-08-15 13:18:21 5.306 9.232
    568-06-18 04:59:43 3.729 37.949
    592-06-17 10:00:36 3.097 42.534
    615-08-27 17:07:18 0.513 24.909
    651-06-27 07:39:52 2.799 31.415
    674-09-07 10:08:57 5.021 35.627
    675-06-26 05:23:47 3.875 35.349
    698-09-06 05:27:18 1.613 32.746
    734-07-06 15:41:56 1.585 24.008
    757-09-15 06:00:16 4.344 43.078
    758-07-05 10:40:10 4.927 26.804
    781-09-14 13:11:04 2.606 39.663
    817-07-16 15:15:47 1.096 16.042
    840-09-17 11:49:26 4.635 45.023
    864-09-19 23:02:46 2.770 44.576
    876-07-28 03:47:10 5.109 0.757
    900-07-26 19:38:38 1.354 6.699
    959-08-08 09:59:38 3.685 4.399
    983-08-07 01:00:51 2.596 0.922
    995-06-18 07:09:17 4.556 40.276
    1019-06-19 20:30:29 2.698 43.446
    1042-08-18 14:56:17 2.469 14.017
    1066-08-17 05:54:20 3.837 8.756
    1078-06-20 14:43:27 5.059 37.822
    1102-06-19 21:49:33 1.707 43.667
    1125-08-28 15:18:36 1.383 23.486
    1149-08-27 06:37:45 4.987 17.075
    1161-06-28 07:08:46 4.549 31.267
    1185-06-27 05:43:18 2.039 36.937
    1208-09-07 05:59:08 0.502 32.528
    1244-07-07 11:31:14 3.647 23.669
    1268-07-06 06:22:18 2.826 28.583
    1291-09-17 00:48:31 0.553 40.580
    1327-07-18 07:04:40 2.460 15.742
    1351-07-17 00:10:09 3.975 19.529
    1374-09-23 07:58:08 1.568 46.055
    1410-07-28 09:20:39 1.073 7.770
    1434-07-27 02:11:36 5.317 10.122
    1493-08-07 16:51:42 0.882 0.938
    1529-06-29 06:47:15 2.990 37.035
    1552-08-19 07:13:29 4.307 12.057
    1576-08-17 22:28:03 2.198 8.457
    1612-07-01 16:15:13 0.936 44.541
    1635-09-09 08:38:22 2.760 21.568
    1659-09-08 00:14:25 3.635 16.511
    1695-07-09 07:11:03 1.123 38.488
    1718-09-20 00:58:55 1.552 30.735
    1742-09-18 17:58:01 4.959 24.413
    1754-07-20 07:11:04 4.686 24.403
    1778-07-19 02:46:21 1.812 30.338
    1801-09-29 19:39:12 0.682 39.105
    1837-07-31 00:36:14 3.503 16.558
    1861-07-29 17:54:30 2.897 21.392
    1884-10-06 07:55:46 1.204 45.253
    1920-08-11 02:21:34 2.259 8.435
    1944-08-09 18:40:08 4.058 12.042
    2003-08-22 07:15:20 1.041 0.825

    2015-07-16 11:48:33 5.488 30.930 (conjunction in 2015 CE)
    2027-08-20 23:44:27 5.261 2.523
    2086-09-01 14:32:37 0.790 8.374
    2122-07-08 16:51:26 1.516 43.744
    2145-09-14 01:53:17 4.836 19.637
    2146-07-08 12:23:30 5.417 45.470
    2169-09-12 17:38:23 1.559 16.679
    2205-07-15 09:10:00 1.372 38.734
    2228-09-24 20:25:03 3.776 28.900
    2229-07-14 10:39:27 5.357 41.055
    2252-09-23 13:21:48 2.792 24.725
    2288-07-23 23:00:59 1.054 31.616
    2311-10-05 21:49:18 2.753 37.499
    2335-10-04 18:19:54 3.841 32.416
    2371-08-04 11:28:25 1.029 23.258
    2394-10-13 02:17:26 2.210 44.307
    2418-10-12 12:48:16 4.632 38.993
    2430-08-15 18:58:06 4.175 8.408
    2454-08-14 11:37:59 2.188 13.939
    2477-10-10 03:40:59 3.897 41.142
    2501-10-16 12:47:51 4.549 41.762
    2513-08-26 23:54:34 2.667 0.875
    2537-08-25 15:50:58 3.690 4.447
    2596-09-06 05:26:08 1.151 6.635
    2620-09-05 21:40:43 5.240 0.897
    2632-07-15 02:33:17 2.386 43.108
    2656-07-15 11:20:55 4.650 45.236
    2679-09-18 10:25:21 0.705 15.875
    2715-07-21 15:26:25 2.319 39.102
    2738-09-30 15:29:27 4.810 27.036
    2739-07-20 18:15:52 4.425 42.356
    2762-09-29 08:12:17 1.644 24.014
    2798-07-29 19:09:49 1.599 32.315
    2821-10-09 21:38:10 3.932 35.818
    2822-07-28 16:03:44 4.946 35.075
    2845-10-08 17:02:38 2.697 31.836
    2881-08-08 05:45:37 0.984 24.514
    2904-10-18 16:53:19 3.435 43.217
    2928-10-17 21:25:11 3.325 38.965
    2964-08-19 03:36:41 0.956 15.872
    2987-10-21 20:20:21 4.041 45.058


    Notes:




    • You can (and should) check these numbers against a reliable source, such as Stellarium or HORIZONS (http://ssd.jpl.nasa.gov/?horizons)


    • These numbers are imperfect for several reasons:




      • Like most planetarium programs, I neglect light travel
        time (Stellarium neglects light travel time by default, but you
        can change this in the settings). This is probably the largest
        error in the numbers above.


      • NASA solves differential equations from known constants to
        publish planetary positions. The constants aren't necessarily
        accurate (they are updated occasionally), and NASA publishes only
        approximations to the differential equations solutions. The
        approximations are usually good within a few meters, but if the
        constants were/are drastically different in the past/future
        (and/or are erroneous), these results would not apply.



    • My methodology:




      • I used the SPICE kernels
        (http://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/kernel.html)
        to find the positions of Jupiter and Venus (in the ICRF J2000
        frame) daily from 999 BCE to 2999 CE.


      • I assumed the position of Regulus was constant in the ICRF J2000
        frame. Since ICRF J2000 is a non-precessing frame, this is
        essentially accurate, but neglects Regulus' small proper motion.


      • I computed the daily maximal angular separation between Jupiter,
        Venus, and Regulus.


      • I found local minima among the daily separations, and used the
        ternary method to find the instant of the actual local minimum.


      • I looked at the separations for 2 BCE and 2015 CE, and filtered
        the results to only show conjunctions with separations less than
        the maximum of these two separations.


      • I computed the position of the Sun on the filtered list, and
        included the separation between the Sun and the closest of the
        Jupiter, Regulus, and Venus.


      • I did most of the work in Mathematica, but used the Unix program
        j2d to convert Julian dates to calendar dates, because Mathematica
        uses the proleptic Gregorian calendar, which most people do not
        use.


      • You can see what I did (in extremely cluttered form) at:





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




    • I wanted to present the results in a sortable HTML table, but
      stackexchange doesn't allow tables of any sort.


    • Here are Stellarium screenshots of some of these
      conjunctions. Regulus is the light blue star, Venus is bright
      yellow, and Jupiter is the one with the moons. The object I've
      selected (if any) is not necessarily relevant to the conjunction.




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


License under CC-BY-SA with attribution


Content dated before 7/24/2021 11:53 AM

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