Searching for the Star of Bethlehem (updated)

A popular explanation for the Star of Bethlehem is that it was actually a conjunction of Jupiter and Venus that presumably occurred on June 17, 2BC  (see bethlehemstar.net).  In other words, in the evening hours of that day, Jupiter and Venus appeared so close together in the sky to observers in the middle east that they were visually indistinguishable.  To a casual observer this object would look like a single object, brighter than both Venus and Jupiter separately.

Venus/Jupiter Conjunction in the year 2 BC

By itself, Venus is a spectacularly bright celestial object—only the Sun and Moon shine brighter.  Jupiter is also bright, but it pales in comparison to Venus.  On the date in question, Venus was about six times brighter than Jupiter.  Hence, a Venus/Jupiter combo would be only a little bit (16%) brighter than Venus by itself.  Would Jupiter really brighten the pair up enough that this conjunction would stand out as a singular event in the early evening sky? I suspect not.

Also, would the Magi really have been confused by this conjunction.  In ancient times, people lived and slept under the stars.  They were very well aware of the planets and their unusual wanderings relative to the stars.  The conjunction of Venus and Jupiter comes up slowly over the course of a week or so.  Could the Magi, and everyone else, really have failed to notice Venus and Jupiter in the evenings leading up to the conjunction or, more obviously, in those following the conjunction?

Such conjunctions occur once every few years but, according to widely-available modern planetarium programs (e.g., The SkyX, Starry Night, Cartes du Ciel, etc.), this particular conjunction was an especially close encounter.  Specifically, these planetarium programs tell us that the separation between Venus and Jupiter appeared to be only about 38 arcseconds at the time of the conjunction.  This is a very small separation.  For comparison, the full Moon is about 1800 arcseconds in diameter and so the diameter of the full Moon is about 50 times the separation of Venus and Jupiter at this conjunction.  The average person cannot distinguish two points of light separated by less than about 100 arcseconds.

But, here are two important questions.  How rare is such a close conjunction and can we trust our planetarium programs when making queries thousands of years into the past (or future)?  For me, answering the first question is fairly easy because some years ago I wrote my own simulator of our Solar System.  My simulator takes as given, the positions and velocities of all the major bodies in our Solar System and uses Newton’s Law of Gravity to simulate the evolution of the entire system over time. It was easy for me to add some “closeness” tests, run time backwards in my simulator, and print out every close encounter event between Jupiter and Venus.

Using my software, it turns out that there were 849 Venus/Jupiter conjunctions between 100BC and now (Dec, 2011) in which the angular separation was less than 1800 arcseconds (the diameter of the full Moon).  Of these, 38 of them found Venus and Jupiter within 100 arcseconds of each other, i.e.,indistinguishable to the human eye.   On average, that’s one such indistinguishability event every 60 years or so—relatively rare but not profoundly, miraculously, rare.

All Venus/Jupiter Conjunctions from 100 BC to present
All Venus/Jupiter Conjunctions from 100 BC to present

But, what about the second question:  can we trust the planetarium programs?  Well, again, the fact that I’ve written my own simulator sheds some light on this question.  I compared the conjunctions produced by my simulator with the predictions made by one of my planetarium programs.  Looking back in time, the two methods give nearly identical results—at least for the first several hundred years.  But, as time moves further from the present epoch, the predictions begin to diverge from each other—not in big ways, just in the details.  For example, my simulator does predict the conjunction in 2BC but it, according to the simulator, was not an especially close encounter.

Okay, who’s wrong?  My simulator should be subject to the most suspicion because it was written by me and not tested or verified by anyone else.  That is true.  But, in my defense, I developed this code over a number of years taking great care to get it right.  But, still, it might be wrong.  What about the planetarium programs?  There are several popular ones.   I have at least two of them on my personal computer.  They give the same prediction.  Isn’t that strong evidence that they are right and my program is wrong?  Not necessarily.  Planetarium programs use the same formulas describing the orbits of the various celestial objects.  Hence, they should agree with each other.  But, these formulas are just approximations.

The real problem is hard.  The nine planets not only get tugged by the Sun, but they also interact with each other.  Jupiter, being the most massive, has a significant gravitational effect on the other planets, including Venus.  The formulas used in planetarium programs are very good, but they are not perfect.  My simulator, on the other hand, is not based on a simple formula.  To find out where things were 2000 years ago, I have to run the simulator from now back to then one small step at a time.  Using a very small time step, this computation takes several minutes.  But, the answer should be very precise.   I suspect it is better than the answer given by the planetarium programs.

So, it seems to me, that the Venus/Jupiter conjunction of 2BC was probably not a very spectacular event.  It’s hard to imagine that it would have triggered the dramatic events recorded in the Bible and attributed to the Star of Bethlehem.

Addendum (added 12/29/2011): Roger Sinnott contacted me and explained that he was the person who first suggested the June 17, 2BC, Venus-Jupiter conjunction as a possible explanation for the Star of Bethlehem in a Sky&Telescope article that appeared in December 1968 (pages 384-386).  At the time, his analysis was based on Keplerian orbits (with perturbations).  After he published a second article on the subject in 1986, James DeYoung and James Hilton at the U.S. Naval Observatory reported (S&T, April 1987, page 357) that they compared the state-of-the-art numerical integrator (JPL’s DE102) against Bretagnon’s state-of-the-art Keplerian analytical method (VSOP82) and got results consistent with each other and with Sinnott’s earlier report.

The modern version of JPL’s numerical integrator is known as DE406.  Tabulated and interpolated results are accessible via JPL’s Horizons website (http://ssd.jpl.nasa.gov/horizons.cgi).  DE406 is the ultimate modern tool for validating the earlier claims.  Using the web interface, I downloaded positional information for Venus and Jupiter on June 17, 2BC.  According to DE406, the conjunction on this date had a minimal separation of 26.2 arcseconds, which is further evidence that this was indeed a very close conjunction.  Of course, there is some uncertainty in any measurement and therefore in any prediction.  It would be interesting to determine error estimates.

Anyway, these developments suggest that there is some subtle issue with my integrator.  I am looking into it.

 

Human Journey

Robert J. Vanderbei is chair of the Operations Research and Financial Engineering department at Princeton University and co-author of the National Geographic book Sizing Up the Universe. Vanderbei has been an astrophotographer since 1999, and he regularly posts new images on his astro gallery website.