In-between calculations

In the twilight land of Spherical Astronomy. . .

Recently one of our astronomer’s colleagues confessed to a bit of confusion about a detail of observational work: the time of sunset.  Not that it varied through the year and why, nor how to make use of it (for instance) when planning an observing run, but details of its computation.  This colleague had taught basic astronomy for years and was well-versed in the higher-level work of his research (analyzing spectra with certain computer programs), but accurately figuring out when the sun would set fell sort of in the middle.

In a very similar way, our navigator and astronomer fall on two sides of the subject known as Spherical Astronomy.  The navigator took predictions from the Nautical Almanac and did calculations of his position using tables of numbers produced for that purpose.  If the astronomer needed to work out the position of an object in the sky to point a telescope at it, he would use a computer subroutine someone else had written.  Although the solving of spherical triangles was the heart of what each was doing, neither actually did it.  Nor did either know how.

It was different only a generation or so before.  It used to be part of an Astronomy degree to master Spherical Astronomy to the point of being able to figure many things, from sunrise and sunset to the orbits of stars and planets.  This was required even if the astronomer’s research lay in a different direction and he or she never actually did any of these for real.  During his undergraduate teaching time our astronomer picked up copies of relevant textbooks from retiring colleagues who were pruning their libraries.

Going farther back, in the nineteenth century Astronomy was chiefly about making the observations and calculations leading to (for instance) good predictions of sunset and sunrise as well as orbits.  A bit earlier, it was a matter of applying one’s Spherical Trigonometry to come up with the most convenient formulas to do so.

Now, as far as we can tell, Spherical Astronomy is no longer taught.  Part of the reason lies in the fact that everything can be calculated by machines, entirely out of sight, so it’s no longer necessary.  Mostly, it’s because there is so much more for an astronomer to learn that there simply isn’t time even to mention the subject.  As long as forty years ago an astrophysicist lamented that there wasn’t time to teach all the Physics an astronomer needed, and produced two full volumes of material to prove it.  (We’re not sure how many astronomers went on to absorb the contents.)

Well, those Spherical Astronomy textbooks remain in our astronomer’s library.  And he has in fact looked into the sunrise/sunset section so he can explain things in detail to his colleague.  He may yet get around to manipulating some spherical triangles by hand.  He’s done more complicated mathematics, after all.