Signs and Seasons, Days and Years

Appendix B


Visibility of Venus/Jupiter conjunctions

Looking at the exceptionally close cases, of less than a minute (.0167 degree) separation

Range of years: -620 to 35 (621 BC to 35 AD)

Observer position: Jerusalem
Here I’ll mostly be using the astronomical numbering system for years, in which 1AD = 1, 1BC = 0, 2BC = -1, 3BC = -2, 621BC = -620, etc. For this first time span all cases are shown, whether or not the point of closest conjunction was visible from Jerusalem. Data is from Solex, except for time and altitude of the two cases with negative altitudes far below the horizon. When in the mode that views the sky from the perspective of a particular geographical location, Solex doesn’t include events more than 30 degrees below the horizon. So these four data points, marked by outlined boxes, are from Stellarium. This might result in small inconsistencies, but the time is likely within 5 minutes and the altitude within 1 degree of what Solex would have calculated. The point in the Sabbath and Jubilee cycles of each conjunction is marked by brown shading for the first year, or purple shading for the last year of the cycle. Note that during the Babylonian captivity there is a 12-year shift in the Sabbath/Jubilee cycle which affects the years -573 and earlier. The unmarked column next to the Sabbath cycle column is the year number used for Sabbath calculations. This is the Julian year in which the fall-oriented Hebrew year begins.

Visibility of the point of closest conjunction

For all but three cases, the point of closest conjunction was not visible from Jerusalem because it occurred during daylight hours, between about 06:00 and 18:00. The three cases which are potentially visible in terms of this daylight factor are shaded in pink. For two of these remaining three cases, the point of closest conjunction was not visible from Jerusalem because it occurred far below the horizon, leaving only one case whose point of closest conjunction was visible from Jerusalem. The cases which were above the horizon are shaded in blue, so the one visible case is the one shaded in both pink and blue, in the year ‑2 (3/2 BC). This has been additionally marked by brown shading.

Brightness of the conjunctions

The brightness of the conjunctions is largely determined by the magnitude of the brighter of the two planets, Venus. The more negative values of magnitude are the brighter magnitudes. From this we see the two brightest cases to have been in the years -463 and -2. These have been shaded in yellow. But as previously noted, the conjunction of -463 couldn’t be seen at its closest point because it occurred below the horizon.

Appendix B table

In the years -620 to 35 then, the Venus/Jupiter conjunction of the year -2 (3/2 BC) stood out from all the similar conjunctions as being one of the two brightest cases, and as the only case whose closest point of conjunction was visible from Jerusalem. How rare is this then, for such a conjunction to actually be observable from Jerusalem? If we expand the range of years, will we find other cases where the point of closest conjunction was observable?

Range of years: -5000 to 2100

This is a lot of years to look at, so I’ll limit the data this time to showing only the visible cases. After eliminating the cases in which the point of closest conjunction occurred during daylight hours or below the horizon, only the following 12 cases remain:
Appendix B table2


Looking at these occurrences in Stellarium for comparison, it does a fairly decent job of matching these results back to around ‑4000. Further back than that, the separation is off by not just seconds but by many minutes of arc from the Solex results. I take this to probably be a general breakdown of Stellarium’s precision when going back this far. For the dates more recent than ‑4000, Stellarium agrees at least that all these conjunctions fit the category of closer than 1 minute separation. Given some other known inaccuracies of Stellarium for ancient dates, I put much more confidence in Solex’s estimate of closest approach. As for time differences between Stellarium and Solex, they are within 30 minutes of each other back to the year -3000, and within 2 hours of each other back to -4000. Part of this difference could just be a matter of what Delta T correction is being used.

Brightness of the conjunctions

This time we find the conjunction of the year -2 (3/2 BC) to be the clear winner for brightness. Looking at just these cases whose point of closest conjunction was visible from Jerusalem, none of the other contenders come close.

During the Babylonian captivity there’s a discontinuity in the Sabbath/Jubilee cycle which amounts to shifting or delaying the cycle by 12 or 61 years. More study is needed to determine precisely where to place the transition point. It’s clear that the old cycle applies to the years ‑623 and earlier, and the new cycle to the years ‑513 and later. The best transition point may be at Ezekiel’s Jubilee in the year ‑574, delaying that Jubilee to the year ‑562. For now that’s how I’m handling it. In the first table this discontinuity affects only the first data point, for the year ‑618, making it the 5th year of a Sabbath cycle where otherwise it would have been a Sabbath year. In the second table the discontinuity affects all data points prior to the year ‑2, with the result that none of them are the first or last year of a Sabbath or Jubilee cycle, with the exception of just the year ‑2884. It would be interesting to try to identify whether this date has any significance, but trying to make any historical connections will likely be very challenging. It’s a very old date, possibly from the early years of Noah’s life, over 500 years before the flood – an era for which we have only very sketchy records.

For now the significant observation to make is just that after the year ‑2884, back sometime before Noah’s flood, there isn’t another Sabbath-year-oriented occurrence until the year ‑2. So even with this expanded range of years, the Venus/Jupiter conjunction of the year ‑2 (3/2 BC) stands out as quite a special event.


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