Wayward Comet:. Martin Beech

written their somewhat bizarre story lines would have been deemed entirely plausible, or at least not impossible.

      Comets have long been the celestial mirrors to reflect human hopes and fears. They have brought-out individual weaknesses, and they have inspired intellectual triumphs. The story of discovery, however, is far from complete and much yet remains to be unraveled with respect to the physical origins and evolution of the wayward slips of light called comets. And, while many volumes have been written about the history of comets, it is not my intention to overly dwell upon that long-explored material here. Yes, comets are special and they certainly have a prominent place in human history – indeed, their unexpected appearance, on occasion, has literally changed the course of history – but here it is the taming of the comet that I wish to study. What, indeed, are the wayward paths followed by comets? More than straightforward geometry, however, it is also the history and development of one specific machine, the cometarium, which will be explored in this text. Indeed, the cometarium is the tamed comet; it is the comet placed in clockwork with its path and appearance constrained to the rhythmical turn of a mechanical crank. As an artifact of that great, if not innate, human desire to build models, both physical and mental, the cometarium is a tactile expression of a comet’s curving path – we can literally hold the dynamics of a comet within our hands - rotate it before our eyes and change our perspective view like some omnipotent observer. Indeed, the cometarium brings the unimaginable scale of a comet’s orbit down to Earth, making it human-sized and perceptible as a single entity. The cometarium turns the complex physics that underlies a comet’s motion in space into the indomitable and certain roll of meshed gearing – it literally cuts to the chase. For all this, however, the tameness portrayed by the cometarium, as we shall see, turns out to be a chimera; the comet is a beast that moves beyond the certainty encoded within finely interlocking gears. But all is not lost, and nor were the skills and labor of the instrument-maker deployed in vain; the cometarium, as part of the great panoply of planetary models, is an enduring art form, and a work reflective of great human intellect.

      While the original cometaria were constructed using a non-standard set of twin elliptical pulleys, the more contemporary models are made of cardstock, thin wire, and on occasion glass and wood. These latter day cometaria capture, in freeze-frame format, the entire cometary path – the time and position variation of the comet being traced out upon a gently curving arc. Less elegant, perhaps, than their engineered forebears, modern card cometaria are no less useful in showing, even to the simplest tyro, how comets move through the inner solar system. The craftsmanship may well have gone, but the message endures. And, indeed, it is through such simple card models that the general public and the non-specialist have come to know the ways of the comet. Largely replaced now by animation sequences displayed on a computer screen, the card cometarium still has contemporary pedagogical relevance, and building, by ones own hand, such a display provides, even in our computer dominated age, a personal, tactile and tangible link to the world of the comet.

      At its core the cometarium is a demonstration device – built to illustrate the highly elliptical nature of cometary orbits, and to mimic the phenomenon of changing orbital speeds. Indeed, the cometarium is the mechanical embodiment of the first two laws of planetary motion as outlined by Johannes Kepler in his great thesis Astronomy Nova published in 1609. The cometarium, as traditionally designed, however, fails in one of its prescribed tasks. The failure is only slight, indeed, not readily noticeable to the eye, and the failure in no manner distracts from the cometarium’s intended demonstration function. The sticking point, for those that wish to quibble, is Kepler’s second law. While the cometarium illustrates this second law, revealing the characteristic speeding up of a comet’s motion as it rounds the Sun, it does not actually solve-for the full requirements of Kepler’s second law. The cometarium is not an analog computer. For all this, however, specialist mechanical-cousins to the cometarium were constructed during the early to mid 20th Century in order to solve the equations associated with Kepler’s Problem. As we shall see later on, while Kepler’s three laws of planetary motion tell us about the orbital shape and characteristic motion of an object (a planet, comet, asteroid, or spacecraft) moving under the influence of a central force, they do not actually tell us where the object will be in its orbit at some specified time. It is this latter question that constitutes Kepler’s Problem. In the modern era the equations behind Kepler’s Problem are easily and rapidly solved for on a PC, but before the time of electronic computation much pencil-work was required to extract a solution. Necessity, as ever, being the mother of invention, resulted in the design and construction of several remarkable mechanical devices to help speed-up the astronomers’ number-crunching. These analog devices, which have no specific group name, were very much scientific instruments; built with the aim of extracting an actual number from a set of variable input parameters. Ingenious, complex, delightful and now entirely obsolete, these devices, just like the original cometarium, had a relatively short ascendancy, but it is their remarkable story that will be revealed in the following chapters.

      A few final introductory comments about units and notation are now probably called for. Astronomers notoriously mix and match their units in almost any fashion; in general, however, the SI system will be used through this text, with astronomical distances being given in astronomical units (AU), light years (ly) or parsecs (pc). The astronomical unit corresponds to the Earth’s orbital semi-major axis and is equivalent to some 149.6 million kilometers. The light year and the parsec build upon the AU scale, with 1 ly = 63,240 AU and 1 pc = 3.262 ly. Comet designations have a somewhat complex history and format, and not every text applies them consistently. Most comets don’t have a specific common name, but all comets have a designation number that is now provided for by the Minor Planet Center (MPC) at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts. The current designation system is based upon the year of discovery and a letter plus number pair indicating the month and order of discovery. A comet with an orbital period less than 200 years which has been observed to pass perihelion at least twice is given a P/ designation – so Halley’s Comet, for example, is known as comet 1P/ Halley since it was the first known periodic comet, and its orbital period was determined by Edmund Halley to be about 75 years. Halley’s Comet is also cataloged according to each of its recorded returns, and is additionally designated, for example, as 1P/1982 U1 (the U1 indicating that it was the first comet to be detected in the first half of the month of October). A non-periodic comet or a comet observed just once is given a C/ designation – so, for example, the recently observed comet Hale-Bopp (discovered by Alan Hale and Thomas Bopp) is designated C/1995 O1 (with the O1 indicating that it was first detected in the second half of the month of July). A lost and/or destroyed comet is given a D/ designation: comet D/1894 F1 (Denning), for example, was discovered by the famed amateur astronomer William Frederick Denning in March of 1894, and although the observational data at that time indicated an elliptical orbit and an orbital period of about 7.5 years, the comet has not been seen since Denning first swept it up. And, finally, in terms of applying names to comets, the current rules set by the MPC dictate that up to three independent discoverer names can be applied to any one comet.

      CHAPTER 1

      THE COMET CONSTRAINED

The education of Euphrosyne

      Obscure in the modern-era, the heyday of the cometarium was set in the first half of the 19th Century. It is a device that was built upon the intellectual certainty of Newtonianism and the observational triumphs of 18th Century astronomy. Before exploring the details of all these multifaceted connections, however, let us first see how famed instrument maker and jubilant author Benjamin Martin (1714 - 1782) introduced the cometarium in his imagined dialogue between a young natural philosopher, Cleonicus, and his eager and able pupil, Euphrosyne (figure 1.1). The year of the work is 1772, and Halley’s Comet had but 13 years earlier appeared in the night sky to vindicate Edmund Halley’s 1705 prediction and thereby sealing the hegemony of Newton’s theory of gravitational attraction as applied to celestial bodies. The dialogue proceeds thus:

      Figure 1.1: The Young Gentleman and Lady’s Philosophy – Dialogue XVL by Benjamin Martin (1772)

      Euphrosyne: Since