Computing the Heavens

© 2003 by Robert C. Moler

The sky and planet charts that have appeared in the Stellar Sentinel since its inception have been supplied by yours truly. The first planet charts produced were on a tiny computer called a Sinclair ZX81. It predates all commercial astronomical software I know of.

A long time ago in a city far, far, away an interviewer on the radio seemed somewhat puzzled that a person who worked with and programmed computers could possibly be interested in astronomy.

I reminded him that astronomers had computers before computers were invented. While that sounds impossible, it’s true. Back BC, Before Computers at least of the electronic variety, observatories had a room full of human computers, mostly women, working with tables of logarithms, and mechanical calculators to calculate orbits, the distances of stars or even what time it really was. I’m not sure of the image he had of astronomer. Perhaps it was that of a lone observer peering through a telescope, notebook in hand, drawing and describing what was seen.

Yes, observation and description are essential parts of astronomy, but much of the description is mathematical. From the ancient Greek philosophers we got the idea that planetary orbits were circular about a stationary earth. Not from observation did this deduction come, but from the idea that the heavens were perfect, thus must move in perfect uniform circular motion.

The problem with this is that this motion does not fit actual observation, so it was tinkered with. Planets just didn’t move on circles, but they rode on circles that rode on other circles. The smaller circles were called epicycles, while the main one for each planet was called the deferent. The Greek astronomer Claudius Ptolemaeus (Ptolemy) about 140 A.D. compiled the book Almagest (The Greatest) in which he codified these ideas. It served as the astronomy authority until the 16th century.

Mikolaj Kopernik, better known as Nicholas Copernicus (1473-1543 )in his book On the Revolution of the Celestial Spheres removed the largest of the epicycles of the planet’s orbits placing the sun in the center of the solar system, but kept the uniform circular motion. He actually came up with more epicycles than the old Ptolemaic model. What was needed was accurate observations of the planets.

It came soon enough, with the observations of the astronomer with the funniest nose, Tycho Brahe (1546-1601). Tycho lost his nose in a duel, and had a nose made of tin fashioned as a replacement. In any case, he built an observatory called Uraniborg on the island of Haveen in Denmark and made the most accurate observations of star and planet positions prior to the invention of the telescope.

Lusting after those observations was one Johannes Kepler (1571-1630), whose mother was once tried as a witch. A mathematical genius, Kepler made a living tutoring students in mathematics, writing almanacs, and writing horoscopes for the local duke, or whatever, but his passion was the motions and distances of the planets. In this regard Kepler ingratiated himself to Tycho, who jealously guarded his observational data, and dribbled it out in bits and pieces to Kepler. Kepler was most interested in the orbit of Mars, whose motion was the least satisfactorily described by the deferent-epicycle system. After Tycho’s death Kepler did finally get access to the whole body of the old observer’s work, and was able to formulate his three laws of planetary motion:

  1. Planets orbit the sun in ellipses with the sun at one foci.

  2. Planets sweep out equal areas of the ellipse in equal times.

  3. The squares of the periods of the planets are proportional to the cubes of their mean distance from the sun.

Isaac Newton (1643-1727) derived his three laws of motion, and then went on to develop the Law of Universal Gravitation. Which explained why Kepler’s laws work In order to do it and explain the motion of the moon Newton had to invent calculus, which was my downfall in college.

The laws of Kepler and Newton are the foundations of the programs I use to illustrate the Stellar Sentinel. They started with planet charts written in Basic for that old ZX81. Then I wrote a planetarium type program called the Floppy Universe and a planet display and animation program called Floppy Solar System which I used for the Star Chart and Planet pages respectively. Once I had a hard drive I changed the name of the former to the Calculated Sky. All were written in Microsoft Basic.

When I got a C language compiler and a new PC in the early 90’s I wrote a new program called Looking Up (LU) which combined the best functions of Calculated Sky and Floppy Solar System. It remained a DOS program.

When I got a computer using Windows XP operating system, I found that the screen displays that I used for the charts could not be saved to the clipboard and printed. So I converted the programs again, this time to the only Windows compiler I had and had experience with called Clarion. Its strengths is as a rapid application developer, but it’s not so great in the graphics department, particularly in animation. The new program is called Looking Up for Windows (LUW), and as of this writing is about 70% complete. I still use the DOS version for the Ephemeris of Sky Events.

What’s next? Well to complete LUW. Then, I might look into the graphical interfaces and compilers of the Linux operating system. The price is right!

Questions? Send Email to me at

Updated 02/24/03