The Moon

Today in class we studied the Moon.  The Moon plays an odd role in the history of astronomy.  The regular, repeating progression of the Moon's phases must have been one of the first signs of order that ancient humans found in the night sky.  This "law of nature" was likely discovered even before the seasonal variations of the Sun, although perhaps after the regularity of the daily motion of the sky.  In any case, it is surely something that the first humans to pay attention to the sky would have picked up on quickly.

The explanation for the phases, in terms of the Moon reflecting Sunlight, may have taken longer since there is some basic geometry involved.  But even this is not a great challenge and certainly the Ancient Greeks had a complete handle on how the Moon's phases worked (even though they were not entirely sure that the Moon shone by reflecting sunlight).  My students learn how the phases work by playing with my EJS Phases of the Moon program.

But the Moon's motion relative to the stars is tricky.  At first glance it seems simple: the Moon drifts eastward relative to the stars just like the Sun does, only faster (13 degrees per day, compared to the Sun's one degree per day).  My students find this for themselves using Stellarium.  But whereas the Sun follows a repetitive circular path through the Celestial Sphere (the Ecliptic), the Moon never quite repeats its motion.  It moves roughly along the Ecliptic, but not exactly.  Sometimes it is above, sometimes below.  So while the rough outline of the Moon's motion is pretty easy, the details of its motion are hard.

Really hard.  Ptolemy was heavily criticized for his theory of the Moon, because in order to explain the quirky motion of the Moon across the Celestial Sphere Ptolemy had used a model in which the distance of the Moon from Earth changed by a factor of 2 from minimum to maximum.  This would mean that the Moon's apparent diameter should sometimes be twice what it is at other times - and this just doesn't happen (the apparent diameter does vary, but only by a tiny bit).  Copernicus came up with a new and improved theory of the Moon (with not one, but TWO epicycles) and in some ways his theory of the Moon was the most popular part of his De Revolutionibus.  Tycho developed a new lunar theory, etc, etc. 

With most aspects of solar system astronomy, this trend of improving theories ends with Newton.  But not so with the Moon.  Newton got the physics right, but the problem of the Moon being simultaneously attracted by Earth and Sun was too difficult for even the great Newton to solve.  He could only give a rough approximation to the solution.  This approximation was later refined by Euler, Clairault, and d'Alembert.  Eventually all of this culminated in the Hill-Brown theory of the early 20th century.  Even that has been superseded in recent times by calculations using computers.  So in some sense, the quest to predict the Moon's motion is still ongoing.

For my class, we content ourselves with the rough view: understanding the phases, defining sidereal and synodic months, determining the Moon's average rate of motion relative to the stars and to the Sun, determining approximate rising/setting times for various Moon phases, and such.  But for ancient and early modern astronomers this was not enough, for one very particular reason: they wanted to be able to predict lunar and solar eclipses.  To do this one needed an accurate theory of the Moon's motion, and as we have seen this was a long time coming.  The problem was that even a small error could make the difference between an eclipse occurring or not occurring.  Still, those astronomers were able to do well enough to get it right most of the time.  And they certainly understood why we don't get a lunar eclipse at every full moon (or a solar eclipse at every new moon), which is something my class is learning too!  (To learn about this we use Mario Belloni's EJS Solar and Lunar Eclipse program.)