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Exploring conjunctions of Mercury with Venus

***6/3/2015 – Unfinished***
***Check back in a few weeks for the latest on this piece of research***

Table of conjunctions between Mercury and Venus

Some of Mercury’s activities are difficult to see because of its closeness to the Sun. It can’t be seen at all when it’s closer than about 10 degrees – and its separation from the Sun is never more than 27-29 degrees. When it’s visible just before dawn this can be as much as 28 degrees, and on rare occasions close to 28.5, which Solex rounds up to 29. When it’s visible just after sunset the separation can be as much as 27 degrees, and on rare occasions close to 27.5, which Solex rounds up to 28. At these separations from the Sun, Mercury’s close approaches to Venus are clearly visible. This chart of conjunctions is the result of an investigation to find out more about when and how often this happens.

Whether these conjunctions are visible in the morning just before sunrise, or in the evening just after sunset, depends on which side of the Sun Mercury and Venus are on at the time. Focusing for now on just the evening conjunctions, this table shows the dates of the most easily visible occurrences identified by Solex for the period from 5200 BC to 4200 AD. We’ll look first at the occurrences found to have the maximum separation of 27-28 degrees from the Sun. This involves only a minimal number of datapoints – only 41 occurrences over the whole time span, and it provides us with a solid basic framework on which the patterns of the other occurrences can be understood.

 

The information highlighted in blue is the date, followed by the separation in degrees between Mercury and Venus, then followed by the separation in degrees between Mercury/Venus and the Sun.

  • The dates follow the astronomical standard of using negative numbers for BC dates, where the year 0 is 1 BC, the year -10 is 11 BC, the year -100 is 101 BC, and so on.
  • The separation between Mercury and Venus is always something less than 2, simply because that’s the limit that was specified for generation of the data, with the Solex program identifying all cases where Mercury and Venus pass within 2 degrees of each other. This is only an arbitrary constraint on how much data to pay attention to, and could be adjusted to be less restrictive if the data patterns suggest that something of interest may yet be evading our observation.
  • The separation between Mercury/Venus and the Sun (I’m using Mercury/Venus as a shorthand to refer to a close approach or conjunction between the two planets) is the measure of visibility. This is 27 degrees for most of the datapoints in this first table, though in two cases it’s 28. When the data is broadened in the next table to include a wider range of separations from the Sun, the changes in this separation will be pointed out by changes in the color of the highlighting. For this first table the distinction in color is being used only to a small degree, highlighting the two 28’s in purple while all the rest are in blue.

As for the placement in the table of these highlighted dates with respect to each other – when we examine these 41 datapoints, two time periods stand out as providing the basic framework on which the pattern of conjunctions can be understood. We find that a given occurrence is often followed 40 years later by a similar occurrence close to the same time of year – for Julian dates, falling just 8 to 13 days earlier in the year at the next occurrence. And then zooming out to a larger timescale, we find that a given occurrence is often followed 980 years later by a similar occurrence even closer to the same time of year – for Julian dates, falling between 2 days earlier and 2 days later at the next occurrence. The yellowish-colored numbers show this basic framework as calculated by the spreadsheet, with these numbers marking years, and with each number being 40 years after the one just above it, and 980 years after the one just to the left of it in the previous column. And then the actual data from Solex, the exact dates and separation values marked by blue or purple highlighting, has been placed in this framework, replacing the yellowish-colored numbers with real data at each of these points.

For this first table, paying attention to just the most highly-visible close approaches of Mercury to Venus, we find that by organizing the data into five separate series’ of conjunctions, every datapoint is given a place in the 40 by 980 year framework. What you’ll initially see on the screen is only about half of the table, from the year -5200 up to roughly the year 500. Actually the majority of the 27+ degree datapoints fall in this earlier half of the table, with separations of as much as 27 degrees between Mercury/Venus and the Sun being much more rare in our present day. But they do occasionally still happen, as you can see if you find the scroll bar at the bottom of the chart and drag it to the right. There on the right side you’ll find the four remaining datapoints, occurring  in just the last two series’ of conjunctions, with the most recent occurrence having been in the year 1511, and the next one in 2451.

Examining these five series’ we find that they all have a tendency to drift upward as time goes on, with both 980 years and 940 years being common intervals. It’s the 940-year span that causes the upward drift, and the 980-year span that’s marked by holding steady horizontally on the chart. A 40 by 940 year framework would reduce the amount of drift with respect to the year of the occurrences, replacing the upward drift with a gradual downward drift. But with respect to the specific dates of the occurrences on the Julian calendar, the 980-year span wins out, having a much closer match than the 940-year span.

The numbers just to the left of the year show the orientation of these occurrences with respect to the 49-year Jubilee cycle, indicating in which year of the Jubilee cycle each one occurred, with the number   1   being the first and 50th year of the cycle, a Jubilee year, and the number  49  being the last year of the cycle, a Sabbatical year. Since the 980-year span has a length of exactly 20 x 49 years, or 20 Jubilees, this Jubilee orientation holds steady horizontally across the chart up until the probable break in counting of Jubilees in the mid-500’s BC. The correct alignment of Jubilee periods to the historical timeline is still debated, though for the pre-exile time span at least it’s been fairly solidly established by scholars. This table allows the Jubilee alignment to be readily adjusted by just changing the values of two parameters on the top row of the chart. The first parameter controls the overall alignment of Jubilees across the whole historical timeline. Its value is “0” by default, giving us the probable correct alignment for the pre-exile period. But this can be changed to reflect any of the 48 other possible alignments, by replacing “0” with any number from 1 to 49.

The second parameter controls the alignment of Jubilees in just the post-exile period, by specifying the length of the gap in counting of Jubilees. A value of “0” here eliminates the gap, making the Jubilee alignment hold steady across the chart from beginning to end. The default value of “12” or “61” provides the alignment of a 61-year gap, which a previous astronomical study (Restoring the Timetable of Sabbath and Jubilee Years) has identified as providing the most meaningful alignment to a number of astronomical observations. But just as with the first parameter, the value of the second parameter can be changed in order to explore other Jubilee alignment theories. Though any gap length can be used here, note that the overall effect of a number greater than 49 is identical to the effect of that number minus 49. So for example, if you plug in the numbers 61 and 12, you’ll find that they produce exactly the same post-exile Jubilee alignment. For those interested in exploring various alignments that have been proposed, second parameter settings of 6, 13, 20, 27, 34, 41, and 48 will all give results consistent with Wacholder’s post-exile Sabbatical year alignment, while settings of 5, 12, 19, 26, 33, 40, and 47 give results consistent with Zuckermann’s post-exile Sabbatical year alignment, and with what the nation of Israel currently follows.

The thin black line running down the approximate mid-point of the table just to the left of the Jubilee alignment numbers, indicates where the transition is made from pre-exile to post-exile Jubilee calculations. In most cases the choice is easy – but two of the five series’, the first and the fourth, are more interesting because they were both producing visible conjunctions in the 500’s BC, around the time when the gap must have occurred. I take Ezekiel’s Jubilee in 574/573 BC or the year -573/-572 to probably be the last known Biblical event with a pre-exile Jubilee orientation, so this is where I’ve placed the boundary line, right after this Jubilee year. Though by the pre-exile Jubilee schedule this was indeed a Jubilee year, it’s worth noting that this event actually occurred well into the period of exile, between 24 and 25 years from the point at which the exile of Ezekiel and King Jehoiachin had begun. So the question of where exactly to mark the “end” of the pre-exile period isn’t necessarily straightforward. The counting of years for Jubilee purposes probably actually came to an end 25 years before this when Ezekiel was first exiled.

Now just to clarify, indicating the year as “-573/-572” doesn’t mean that we’re undecided about which of these years is correct. It’s actually meant to provide greater precision. Since a Hebrew lunar year doesn’t start on Jan 1 as a Julian year does, the Julian year when a Hebrew year begins and when it ends are always different. If we refer to one of these years as just 573 BC, or -572, it leaves the unanswered question, “Do you mean the year which began in -572, or the year which ended in -572? And then another potential ambiguity is the fact that there is more than one starting point for Hebrew years. For some purposes the year begins in the springtime with month 1, the month of Passover. But then for other purposes, in particular for the reckoning of Sabbatical and Jubilee years, the year begins in the fall with month 7, at Rosh Hashanah, the Hebrew New Year. For my purposes here, it’s the Sabbatical and Jubilee years that I want to account for. So what “-573/-572” actually means here is “the fall-to-fall Hebrew year which began in Julian year -573 and ended in Julian year -572.

Looking at the chart, we see one particularly interesting datapoint in connection to the Jubilee cycle. Of these 41 occurrences of maximally visible close encounters between Mercury and Venus, there is one – just one – which is aligned with the cycle of Jubilees. This is the occurrence on May 27 of 573 BC, happening in a Jubilee year. Given the historical significance of this year, with its beginning being the last known event linked to the pre-exile schedule of Sabbatical and Jubilee years, it feels quite likely that this correlation was more than just an accident – that it was likely intentionally placed there to communicate something to the prophets of the time, maybe to Ezekiel himself, about the events that were taking place.

It’s worth noting too that the one other occurrence on this chart which falls during the period of exile also comes at a historically significant time, on -586/06/18. This is known to be near the time of the final siege of Jerusalem by Babylon. Whether it was before or after the conclusion of the siege I’m not sure – I need to study the timing of that event some more – but it’s likely within a year of the time when Jerusalem and the Temple were destroyed, so probably had an intended meaning in connection with that event. Just taking a tentative look for now, in Ezekiel 40:1, the prophet writes “In the twenty-fifth year of our exile, at the beginning of the year, on the tenth of the month, in the fourteenth year after the fall of the city—on that very day the hand of the LORD was upon me and he took me there.” In saying in the fourteenth year after the fall of the city”, this seems to indicate that between these events thirteen years had passed and a fourteenth year was still in progress, partially completed, or in other words, the elapsed time between the two events was between 13 and 14 years. Based on the work of other scholars I take the second event, Ezekiel’s Jubilee, to have happened in the fall of -573 (574 BC). Counting back 14 years from this point then places us in the fall of -587 (588 BC) as the earliest possible time for the first event. And knowing already from history that the fall of Jerusalem happened in summertime, on day 9 of month 4, it then seems most probable that it happened the summer following the fall of -587 (588 BC), which would be the summer of -586 (587 BC). The two positions held by scholars for dating of the fall of Jerusalem are to place it in the summer of either 587 or 586 BC, so we’re at least in the ballpark. This successfully lands us on one of these two positions, on day 9 of month 4 in the Julian year 587 BC.

[Note: Day 9 of month 4? Where did I get this? Is it not day 9 of month 5, the ninth of Av?]

[Ok, this came from Finegan – and he got it from a legitimate source. Month 4 day 9 is a specific event recorded in Jer 52:6 and 2 Kings 25:3, which could indeed be viewed as the date of the fall of Jerusalem. However, this is followed by a second event a month later, recorded in 2 Kings 25:8-10 and Jer 52:12-14, in which the Temple and Jerusalem are burned, and the walls of the city are broken down. The text of these two passages is almost identical, except for the date given in 2 Kings 25:8 (month 5, day 7) and Jer 52:12 (month 5, day 10). So this is interesting. It seems clear that the text of one of these sources was adjusted, after originally having been copied varbatim from the other. So which one is the original? And was the later adjustment a legitimate correction, or the introduction of an error?]

 

 

Ok, so now I have to know – how exactly does this relate to the conjunction? Because if the reasoning is on track up to this point, then the conjunction and the fall of Jerusalem happened in the same summer. Well, TorahCalendar tells me that -586/06/18, or Jun 18 587 BC, was day 27 of month 3 in the Julian year 587 BC – and that day 9 of month 4 was just 11 days later, on June 29.

That feels close enough to be meaningful.

In fact, if I go to Stellarium to see what Mercury and Venus actually looked like on these dates, I find that they are indeed at their closest the evening of June 18, but that they continue to be visible for a number of days afterwards as they separate from each other, with the last evening on which both might still have been visible being either June 29 or June 30, depending on the exact viewing conditions at the time. This is either the very day of the fall of Jerusalem, or the day after. So here we see a meaningful correlation between the fading of this most excellent specimen of a Mercury/Venus conjunction, and the final end of this era of Israel’s history. Wow.

[Note: As for visibility, yes – Alcyone confirms that Venus was visible up to June 30, and Mercury two days later, up to July 2. And June 29, when they both were still visible, was indeed month 4 day 9. But note that this is the first of two dates a month apart, both of which could be considered “the fall of Jerusalem”. What the fading of Mercury and Venus as evening stars is marking is not the burning of the city and Temple, but the other event a month earlier.]

Now broadening the scope of the investigation to include all occurrences with a separation of 24-27 degrees from the Sun:

 

The basic structure of the data is the same as in the first table. What’s changed is that the five existing series’ have been filled out with more datapoints providing a more complete picture of each one, and also that six additional series’ have been added into the chart in order to account for every datapoint that Solex has identified. Carefully examining each of these series’, for some of them I find the dates from one occurrence to the next one 980 years later to be gradually getting later by 1-3 days each time. These are the last two series’, the ones which show the strongest tendency to drift upwards as time goes on and favor a 940-year cycle length. But yet even these two show the 980-year cycle length to be fairly strong, with both having some long spans of 6 or 7 occurrences in a row with each one following the previous one by 980 years, spanning 100 or 120 Jubilees before drifting out of alignment.

For the other series’ I find the dates from one occurrence to the next one 980 years later to be gradually getting earlier by 0-3 days each time, with some of them having spans of 2-4 occurrences in length holding steady at the same Julian date. Most of these still show some tendency to drift upwards, but less so than for the last two series’.

But the very first series in the chart seems to be especially well-formed and tuned to the 980-year cycle. For this one the tendency to drift upward has somehow been largely nullified and balanced. Two features that stand out when examining this series are 1) It has the longest continuous series of datapoints each separated from the last one by 980 years. The other series’ occasionally show as many as 7 or 8 in a row, but this one has two cases of 9 in a row, from -4506 to 3334, and from -4466 to 3374, with each of these spans being 160 Jubilees in length. 2) It also has the longest series of datapoints which hold steady at the same Julian date. The longest such spans for any of the other series’ are spans of 4 occurrences, which happens once in the third series and once in the ninth series. This first series has a span of 4 occurrences as well, and also one span of 5 occurrences. This most stable, steady series of them all stretches from -4346 to -426, a span of 80 Jubilees in length, holding steady from beginning to end at the Julian date of May 6. And then we notice that the first four occurrences of this most stable series are also aligned in a significant way with the Jubilees – occurring in year 49, in the final Sabbatical year of every 20th Jubilee cycle. This certainly looks like it should mean something – having been so carefully fine tuned to provide such a stable series of conjunctions, and then also being so nicely aligned with the Jubilee cycle.

So what should it mean? Looking at just the first chart it wasn’t so clear, but having filled in the data more completely now, two numbers stand out as very likely to be significant. These are -1446 and -1406. According to the best scholarship currently available on Biblical chronology, the date of the Exodus of the nation of Israel from Egypt was at Passover of 1446 BC (-1445), and the date of their entrance into the Promised Land was 40 years later, not long before Passover of 1406 BC (-1405). Here we see the same forty-year span that these conjunctions have been marking down through the ages coming close to aligning with the forty years of the Israelites in the wilderness. This 40-year correlation seems rather compelling. But these two conjunctions – they didn’t happen at Passover. So where exactly did they fall in relation to these events?

Again this will take some more investigation, but it appears that they both occurred in the year prior to the event that they seem to be marking, though less than a year before the event. By the reckoning of TorahCalendar.com, for both of these signs the date on which they reached their peak was sometime in month 2, during the Omer count between that year’s Passover and that year’s Feast of First Fruits or Pentecost. If we first look at these two events in Stellarium, we can identify the date on which Mercury and Venus as actually seen at Sunset were at their closest to each other, and make any needed minor adjustments to the date, giving us this:

  • -1446/05/17 (Solex) becomes -1446/05/16 (Stellarium), or 16 May, 1447 BC (TorahCalendar), the evening beginning a Sabbath day, month 2, day 27, day 41 of the Omer count, 13 days after Second Passover. Range of dates on which both Mercury and Venus are visible – Apr 21/22 (month 2, day 2/3, Omer 16/17) up through May 28/29 (month 3, day 9/10, 3/4 days after Pentecost). This is the more striking of the two conjunctions, being quite close when visible in the evening, and clearly setting apart one particular day, May 16, as most clearly marked, with Mercury and Venus at a separation of just 0.6 degree.
  • -1406/05/06 (Solex) becomes -1406/05/05 (Stellarium), or 5 May, 1407 BC (TorahCalendar), the evening beginning a Wednesday, month 2, day 7, day 22 of the Omer count, one week before Second Passover. Range of dates on which both Mercury and Venus are visible – Apr 12/13 (month 1, day 14/15, Passover/Day 1 of Unleavened Bread) up through May 17/18 (month 2, day 19/20, Omer 34/35). This is the less striking of the two conjunctions, being a bit more distant, and not so clearly selecting one particular day, with Mercury and Venus at a separation of 1.3 degree on May 5, and 1.5 degree on May 6.

What both were marking may have been the significant event that would happen at or near the following Passover – first the Exodus in 1446 BC, and then the crossing of the Jordan in 1406 BC – perhaps signs from the Lord regarding what He would soon accomplish for the people of Israel.

But because of an ambiguity in how to interpret the relationship between the crossing of the Jordan and the beginning of the Jubilee year, an alternative interpretation also seems to be possible. It does seem to be solidly established that year 1 for the nation of Israel’s presence in the land of Canaan was the fall-to-fall Jubilee year of -1406/-1405, or 1407/1406 BC. But the Passover just after the crossing of the Jordan – did this occur in that Jubilee year, in -1405, or did it occur in the preceding Sabbatical year, in -1406, with the Jubilee year beginning 6 months later? Here’s an outline of the two possible interpretations:

Plan A

  • 2nd month of -1446 (1447 BC)  Mercury/Venus sign marking that something significant will happen the following Passover
  • Passover of -1445 (1446 BC)  Exodus from Egypt
  • 2nd month of -1406 (1407 BC)  Mercury/Venus sign marking that something significant will happen the following Passover
  • 7th month of -1406 (1407 BC)  Begin Jubilee year
  • Passover of -1405 (1406 BC)  Crossing the Jordan (in the Jubilee year)

Plan B

  • Passover of -1446 (1447 BC)  Exodus from Egypt
  • 2nd month of -1446 (1447 BC)  Mercury/Venus sign marking what had just happened at Passover, visible from near the beginning of month 2 up through Pentecost, with greatest astronomical significance at the end of Omer day 40.
  • Passover of -1406 (1407 BC)  Crossing the Jordan (in Sabbatical year just before the Jubilee year)
  • 2nd month of -1406 (1407 BC)  Mercury/Venus sign marking what had just happened at Passover, visible from just after Passover up through about day 35 of the Omer count, with greatest astronomical significance at the end of Omer day 21.
  • 7th month of -1406 (1407 BC)  Begin Jubilee year

Though both interpretations seem possible, “Plan A” seems better from several perspectives. Probably the most noticeable difference between the two interpretations is that Plan B shifts the Jordan crossing and Exodus dates back by one year, which would conflict with the current best interpretations of other scholars. In order to permit this interpretation we would need to either reinterpret the 480 years from the Exodus to Solomon’s Temple as meaning a full 480 years rather than an inclusive count, or revisit the chronology of the Hebrew kings and see if Solomon’s Temple could be placed one year earlier. The one thing which suggests “Plan B” as maybe worth further exploration is the timing of the two Mercury/Venus conjunctions with respect to the Passovers. Seeing that they both occur during the time period from Passover to Pentecost gives them the potential to have been meant for some instructive purposes in relation to the Passovers which had just happened – first the actual Exodus, and then its first commemoration in Canaan just after crossing the Jordan.

There’s one more astronomical sign which has continued to nudge me in the direction of these events possibly having had a slightly earlier timing – and if “Plan B” is a genuine possibility, it might not take too much more adjustment of our understanding to be able to also admit this one as a valid possibility. This sign is a lunar eclipse right at Passover of the year -1447 (1448 BC). Of course lunar eclipses in general aren’t a rare thing, and we have no specific mention in Scripture of anything regarding the moon having actually happened on the night that the death angel passed over Egypt. But yet astronomically there is a rarity to this particular case which makes it rather compelling. First, this lunar eclipse was a total eclipse, which makes it a bit less common. Second, it was a Passover eclipse, meaning that it happened to the full moon which occurs in the middle of month 1 of the lunar year, within a few days of Passover. But this one wasn’t just “within a few days” of Passover. It was a rarer case which happened right on the night of Passover, at the beginning of day 14 of month 1 of the lunar calendar. Then last is the exact timing of this total Passover eclipse. The total phase of the eclipse lasted from about 11:51 pm to 1:28 am, April 15-16, 1448 by Julian reckoning, which tells us that if the Exodus did happen in 1448 BC, there was a blood moon in the night sky when the death angel passed over at midnight. The moon was totally eclipsed at this point.

But can this date be reconciled with the existing Exodus scenario of present-day scholars and with our other astronomical observations? Here’s an initial attempt at envisioning what this would look like, and what pressures it would put on our existing theories:

Plan C

  • Passover of -1447 (1448 BC)  Exodus from Egypt
  • 2nd month of -1446 (1447 BC)  Mercury/Venus sign marking the first Passover commemoration of the Exodus while camped at Mt. Sinai, visible from near the beginning of month 2 up through Pentecost, with greatest astronomical significance at the end of Omer day 40.
  • Passover of -1406 (1407 BC)  Crossing the Jordan (in Sabbatical year just before the Jubilee year)
  • 2nd month of -1406 (1407 BC)  Mercury/Venus sign marking the first Passover commemoration in the Promised Land, visible from just after Passover up through about day 35 of the Omer count, with greatest astronomical significance at the end of Omer day 21.
  • 7th month of -1406 (1407 BC)  Begin Jubilee year

Issues
1) Rather than being required to “either reinterpret the 480 years from the Exodus to Solomon’s Temple as meaning a full 480 years rather than an inclusive count, or revisit the chronology of the Hebrew kings and see if Solomon’s Temple could be placed one year earlier,” we would now need both of these adjustments in order to reach back as far as 1448 BC as the year of the Exodus.
2) For the Mercury/Venus sign of -1446, it actually feels like an improvement, placing this sign at a time when the people were receiving a lot of instruction on how to celebrate the feasts.
3) This places the crossing of the Jordan 41 years after the Exodus. This does seem like a possibility if we take the 40 years in the wilderness to have begun at the peoples refusal to go up and take the land rather than at the Exodus itself. But it will require some study to see whether this really is a plausible and consistent interpretation of what Scripture says.
4) This requires the same adjustment as Plan B as far as the relationship of the crossing of the Jordan to the start of year 1 in the land – entering the land before year 1 begins, with year 1 and the first actual planting in the land beginning in the fall 6 months after the crossing of the Jordan.


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