Chiron and Me: Hacking Astronomy

by Eve S. Gregory

High school was boring, so I quit in my junior year and married The (real) Most Interesting Man in the World.

Even if school had offered courses in astronomy, which they hadn't, I'd have missed them anyway.

But I didn't recognize my astronomical educational deficiency until 1983, when I was asked by New York astrologer Al H. Morrison to compute an ephemeris for Chiron.  I'd never found anything I couldn't learn to do, if I really wanted to, so why not?

Now, how do you compute an ephemeris?  Social engineering, hard work, and hacking, of course!  (If I'd have been a better social engineer, I wouldn't have had to work so hard.)

Going to college and eventually acquiring a degree in astronomy was not practical.

Besides, I didn't want to become an astronomer.  I just wanted to compute an ephemeris.  I had my first computer, a Timex-Sinclair ZX81, which cost $100.  It was a little black box about eight inches square and about two inches thick.  Its keyboard was printed on its black plastic membrane cover.  It had a whole 16 kB of memory, BASIC, and a small thermal printer.  With a black-and-white TV for a monitor, what else did I need?

Well first of all, I needed to know something about planetary orbits.

I had a vague general idea, but computer programs require specifics.  So I went to the state library and ordered down all of their college astronomy textbooks.  There were a lot of them.  Most were entirely too abstruse for a neophyte, but Essentials of Astronomy from Columbia University Press (1977) was a good fit, so I went to the bookstore and ordered a copy.  It didn't answer all of my questions, but it proved invaluable for my purposes.

There were, of course, no World Wide Web, Wikipedia, or smartphones available to me, so I wrote lots of letters.

Some were not answered, but many were.

One person sent me three laboriously handwritten pages of advice, because I knew and had written the correct plural form of ephemeris.  (It's ephemerides.)  Then someone recommended Jean Meeus's Astronomical Formulae for Calculators.  I bought it.  It had all of the necessary computations in it, but not in the order or form in which they were required in the program I was writing.

The great thing about Meeus, though, is that each little computation set has an example with the correct answer, so I could test each program module before proceeding.

My good friend Richard had a Pascal Engine (with two big floppies!) and a lot of computing experience.  He was my go-to guy and advised me to write the program in separate modules, testing each one individually - and it was good advice.  Spaghetti is great on the plate, but not in the program.

Ah, but there were a few missing elements, osculating elements, that is, for the orbit of Chiron, the asteroid that later was found to be a comet.

The label didn't matter but the elements did.

Further inquiries revealed that Daniel Green, assistant to Dr. Marsden at the Smithsonian Astrophysical Observatory, had computed them.  Orbital elements are computed from observations.  Chiron was still quite far away, though headed our way, but observations of it were relatively few at that time.  Green had computed a ten-day-interval twentieth century ephemeris from those elements, and Dr. Marsden agreed to sell them to Morrison.  In December 1983, we were able to get a new set of elements computed by Dr. Marsden.

By June 1984, I had acquired a more powerful computer, a Timex-Sinclair 2068 with a whole 48K of memory.

It was a small silver box about eight by twelve inches by a couple of inches thick.  Most of the exterior was keyboard.  A small TV served as a monitor.  And this computer could generate color!  I wrote a program to make a pixelated little man limp across the screen.  But much more important, I could save programs and output on a cassette tape.  It was fussy about volume settings, but it allowed tedious work to be saved.  What an improvement!

The ephemeris computations were made in astronomical units (one AU = 149,597,870,700 meters), the approximate average distance from the Earth to the Sun, so the maximum number of decimal places possible had to be used.

The new elements arrived as a paper printout, so they had to be input by hand and saved to a cassette tape.  There were 100 of them and they had to be 100 percent correct.  Having worked in land surveying before computers were involved, I understood the rigorous methods necessary.  After the elements were input, they were used to compute other constants needed by the main program.

I found differences between Green's earlier elements and Marsden's later ones.

While the computations were made in radians, the ephemeris printouts had to be in degrees, minutes, and seconds.

But an odd sort of bump showed up in the orbit.  Some of the positions were negative numbers and my little computer rounded them.  It rounded "1.1" to "1".  It rounded "-1.1" to "-2"!  That one took a while to find.

There was also some trouble converting right ascension and declination to longitude and latitude, but I got that figured out by October.

To confirm that they were converted correctly, I plotted longitude and latitude and right ascension and declination as X/Y-coordinates by hand on graph paper.  They both plotted the same pattern, so I knew they were correct.  By the end of October 1984, I began printing program output in 420 day overlapping sections.  Each section took two and a half hours to compute and another half hour to print.

The first half of the ephemeris printout was mailed to Morrison on January 14, 1985.  I mailed the rest soon after.  When Morrison had all of the printouts, he found the spacing was wrong for his format requirements.  So I sent replacement printouts in February.

Then I bought a new printer and a 16-bit Sanyo MBC 555-2 computer with two five and a quarter inch floppy drives and a good double precision BASIC.  (Hard drive?  What's that?)  It came with its own CRT monitor.  This was high technology!  Saving programs and output on a cassette tape had been a real pain.

By March 14, 1985, I had typed the ephemeris program onto a Sanyo floppy disc, made some test runs, and found it was working correctly.

Morrison, however, had come up with more features he wanted computed.  Soon, I was running the program on the Sanyo and printing declinations that he requested.  He got the declinations in early April, but then he wanted nodes.  So I revised the program to compute them from the Marsden elements.

Through his company, CAO Times, Al Morrison published the Daily Position Ephemeris of Chiron, 1891-2000, with an article by Zane Stein about the meaning of Chiron in birth charts, in New York in November 1985.  Morrison also negotiated a deal with Chiron Verlag to publish a translated version in Germany in 1989.  (Used copies were available at Amazon.com last time I looked.)

But that is not the end of this story.

In March 1986, one of Morrison's astrologer friends spotted an error in the ephemeris.

Yikes!

I checked it out and found that the separate printing program had inexplicably removed some numbers from two pages.  I never did figure out why, but I reprinted the corrected pages and sent them to him in May 1986.  He replaced them and life went on.

Eventually, I even got paid a little something for it.

Am I glad I did it?  Yes.

Would I do it again?  Hell no!