The (Purported) Star of Bethlehem

An astronomical phenomenon has grabbed media attention lately -- the "overlap" of Jupiter and Saturn in the night sky, creating a bright spot some call the "Star of Bethlehem".  Some articles also point out that the planets are "closest" on December 21, 2020 than they have been in centuries!

Saturn, left, and Jupiter, right, are seen after sunset from near Mine Falls Park (42.7603, -71.4908), Tuesday, Dec. 22, 2020, in Nashua, New Hampshire.  (50mm, F/1.8, 6", ISO100)  Credits: Geo Field Report

Zooming in shows the two planets separated by a small angular distance; the distinctive ring structure around Saturn (left) is visible in this picture.  (250mm, F/5.6, 6", ISO800)  Credits: Geo Field Report

The more scientific way to describe this overlap is "conjunction", it is an apparent closeness between objects due to perspective, even though the objects may not actually be physically close.  When earth, Jupiter, and Saturn "line up", we have this year's Bethlehem Star conjunction; when earth, moon, and the Sun "line up", we have a conjunction called solar eclipse.

Conjunctions are not rare in our solar system.  This is because the orbits of the planets lie closely on a disc, known as the "invariable plane", give or take several degrees of tilt.  So Saturn and Jupiter, and really any pair of planets, must conjunct with a period roughly equal to the inverse of their relative angular velocity, similar to how race cars overtake each other on the race track.  Jupiter's orbital period is 12 years and Saturn, 29 years, so the next conjunction should happen in 1/(1/12-1/29) = 20.5 years... yep, the next one is in October 2040, our napkin calculation was pretty close!  The slight difference comes from the fact that the orbits are not exact circles but ellipses and the planets' velocities differ slightly depending on their distance to the sun (see: Kepler's Second Law).

This invariable plane has been of great interest to human kind for millennia.  Since the sun is at the center, and all planets orbit on the plane, from our perspective on earth, it is as if the sun and the planets all travel on the same "track".  This track is known as the ecliptic, and the zodiac signs are the constellations along this track.

So where should you look in the night sky to find the Star of Bethlehem?  News articles helped us with a good hint that Saturn and Jupiter are close to the horizon to the southwest if you are in the northern hemisphere.  Careful readers could deduce that since the Saturn-Jupiter conjunction lies on the ecliptic with the sun, one must be able to find them near where the sun sets!


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