Planetary Motions

Planetary Motions

Planetarium Sky

We see the planets from a moving earth. Their earth-centered or geocentric movements are therefore a combination of their own individual motions through space and the motion of the earth about the sun. In addition, the planes of their orbits are inclined at comparatively small angles to the plane of the earth’s orbit. Relative to the fixed stars, therefore, the planets are seen to trace quite complex paths. They advance in right ascension, become stationary, and then regress, moving in pendulations and loops which lie near the ecliptic.

All these geocentric movements can be seen in any planetarium. They are made possible in principle by mounting each pair of planet projectors on two concentric gear plates. One plate is mechanically coupled to the sun projector and represents the orbit of the earth. The other moves at a different rate and represents the orbit of the planet. Pins on the gear plates represent the relative positions of the earth and the planet. By connecting the pins with an adjustable rod arranged parallel with the projectors, the latter can be made to reproduce the geocentric aspect of the planet in the planetarium sky. For showing the motion of Venus only two gear plates are required. The other planets, owing to the more eccentric or oval form of their orbits, require three.

The planetarium sun can be made to circuit the ecliptic once in any time with the range 15 seconds to 10 minutes. When this “annual motion” is used it is automatically coupled with that for precession but is quite free from the diurnal motion. When the diurnal motion is used it is automatically coupled with the annual and precessional motions. On the other hand, the precessional motion can be operated on its own. In view of these accomplishments it is small wonder that Bauersfeld, when he designed the first fixed latitude instrument, covered 600 folio sheets with basic astronomical and technical calculations!

Added refinements

If a modern planetarium instrument is to merit the name “universal” it must be able to project more than just the sun, moon, planets, and stars. A planetarium sky would not be complete without a representation of the Milky Way. Star identification is helped by being able to project constellation figures, and various circles of the celestial sphere are important features. These and many other additions can be found in modern planetariums.

The Milky Way is formed by two drum-type projectors, one at the side of each star globe. A drawing based on photometric measurements of the Milky Way was photographed to form two diapositives, each of which was wrapped round a glass cylinder. Inside the cylinder is a lamp surrounded by a glass tube. The latter has a hollow wall half full of mercury which effectively screens off that part of the Milky Way beneath the horizon. Lenses are deliberately left out since the Milky Way is essentially an irregular band of faint, diffuse light.

At the extreme end of the dumb-bell, attached to each star globe, is a smaller sphere for forming constellation figures and a precession circle. The sphere has 16 projectors, each fitted with a gravity-controlled shutter. Also attached to the star globes are individual optical projectors which reproduce the light changes of three well-known variable stars – Delta Cephei; Beta Persei, or Algol; Omicron Ceti, or Mira. Further projectors on or near the dumb-bell reproduce the appearance and motion of Comet Donati 1858, moving clouds, the celestial meridian, celestial equator, part of the declination system, the ecliptic, nautical triangle, mean sun, horizon circles, compass points, and a geographical latitude map.

In addition to the main instrument, many planetariums contain a number of auxiliary projectors to show eclipses of the sun and moon, the total eclipses of the sun being accompanied by views of prominences and the corona, f.i. Others produce the artificial skyline, a shower of shooting stars, the main types of aurorae, and an earth satellite capable of motion along any prescribed path. One projector takes the form of an optical orrery and shows the solar system as seen from a viewpoint well outside the orbit of Saturn. When this is used spectators can watch the relative heliocentric motions of the planets and, by means of a “light line” which connects the earth and any other circling planet, see how these motions give rise to the geocentric paths of the planets.

A giant planet. The planets appear to describe loop-shaped paths against the background of stars. Illustration: © Elena

At the Console

During a planetarium show, the lecturer has remote control over each and every projector. Sitting at the console near the northern face of the dome, he acts as a guide for spectators seated in the theatre. Whether he is pointing out interesting objects in the night sky, illustrating the ways of the planets, or describing objects in deep space, the story he tells is dictated by the changes which he alone initiates in the planetarium sky. He seldom refers to notes and scarcely even reads from a script. He requires no light to find the controls. Like a car driver at night his hand reaches out unerringly to touch the required knob or switch. As in driving, full coordination comes with experience, but as the lectures drives the machinery in the planetarium he must maintain a running commentary of what is being shown. This means that before he gives a presentation he must memorize the proposed schedule of events, translate them into operations, and plan the general content, scope and level of his discourse.

The voice of the lecture, alive and compelling, is an integral part of planetarium experience. The lecturer identifies himself with his audience. He provides the interpretation, answers silent questions and anticipates new ones, appreciates the requirements and limitations of his audience, and never once loses sight of his main objective – to give an increasing number of people from all walks of life some insight into the nature, structure and extent of the astronomical universe. So although planetariums have projectors for their heart, their spirit is astronomy, and their life comes from the people who operate beneath their domes.

Courage of Kepler and Galileo

The courage of Galileo and Kepler in promoting the heliocentric hypothesis was not evident in the actions of others, even those residing in less fanatically doctrinal parts of Europe. For example, in a letter dated April 1634, René Descartes, then living in Holland, wrote: Doubtless you know that Galileo was recently censored by the Inquisitors of the Faith, and that his views about the movement of the Earth were condemned as heretical. I must tell you that all the things I explained in my treatise, which included the doctrine of the movement of the Earth, were so interdependent that it is enough to discover that one of them is false to know that all the arguments I was using are unsound. Though I thought they were based o very certain and evident proofs, I would not wish, for anything in the world, to maintain them against the authority of the Church… I desire to live in peace and to continue the life I have begun under the motto To live Well you must live unseen.

The connection between Holland as an exploratory power and Holland as an intellectual and cultural center was very strong. The improvement of sailing ships encouraged technology of all kinds. People enjoyed working with their hands. Inventions were prized. Technological advance required the freest possible pursuit of knowledge, so Holland became the leading publisher and bookseller in Europe, translating works written in other languages and permitting the publication of works proscribed elsewhere.

Adventures into exotic lands and encounters with strange societies shook complacency, challenged thinkers to reconsider the prevailing wisdom and showed that ideas that had been accepted for thousands of years – for example, on geography, – were fundamentally in error.

In a time when kings and emperors ruled much of the world, the Dutch Republic was governed, more than any other nation, by the people. The openness of the society and its encouragement of the life of the mind, its material well-being and its commitment to the exploration and utilisation of new worlds generated a joyful confidence in the human enterprise. This exploratory tradition may account for the fact that Holland has, to this day, produced far more that its per capita share of distinguished astronomers, among them Gerard Peter Kuiper, who in the 1940’s and 1950’s was the world’s only full-time planetary astrophysicist. The subject was then considered by most professional astronomers to be at least slightly disreputable, tainted with Lowellian excesses. Carl Sagan was grateful to have been Kuiper’student.