Wayward Comet:. Martin Beech

filled my head with such odd kinds of ideas, and I scarcely known whether I hope or fear most to see a comet; but dear Cleonicus, since that is shortly to be the case, and a comet we must behold, if your astronomical prediction is to be regarded, I think I may as well take courage, and resolve to attend the important event undauntedly.

      Cleonicus: Fortitude, my Euphrosyne, is an excellent virtue; and hence I must admonish you to speak with more reverence of astronomical predictions.

      Euphrosyne: If I remember right, you once told me, that you could make the manner of the comet’s motion intelligible by a proper instrument, as well as those of the planets.

      Cleonicus: I did so; the instrument I mean is called the cometarium, and which I shall now spend one quarter of an hour in explaining to you – Here is the machine.

      Euphrosyne: And a beautiful one it is; I can almost tell the use of it by its very appearance.

      Cleonicus: Observer, when I turn the winch, the brazen comet moves, and with a very unequal pace in its elliptical orbit, about the focal Sun.

      This wonderful dialogue, in just a few short refrains, sets the scene for the appearance and application of the cometarium, invented, in fact, some forty-years before Martin was writing, and it also brings out the new order that had been imposed – or more correctly revealed – in relation to cometary orbits. Indeed, the final stanza of the discussion presented points towards serious astronomy and the visual illustration of the first two of Kepler’s laws of planetary motion. In contrast, however, the first stanza reveals an initial sense of doubt on behalf of Euphrosyne. The fact that the prediction is to be regarded as correct, as emphasized by Cleonicus rests upon Newton’s laws and the (mostly) correct predictions by Edmund Halley in 1705 (to be described below).

      But what was this device that Cleonicus showed to Euphrosyne? The answer to this lies partly within an earlier work by Martin. Businessman that he was, Martin knew that the predicted return of Halley’s Comet in 1758 was bound to cause a ripple of public interest in matters astronomical. To this end he published in 1757 a small pamphlet entitled The Theory of Comets Illustrated, and to go with this work he re-invented and re-named a device previously called the equal-area machine; a demonstration device made known through the popular public lectures of Scottish astronomer James Ferguson. It was Martin, in 1757, who first coined the name cometarium, and for the tidy sum of just 5-Guineas such a device could be purchased to further enhance ones viewing of the spectacle soon to be portrayed in the heavens above.

      From the very outset the appearance of the cometarium is somewhat odd and perhaps even intimidating (figure 1.2). Its working face displays a number of graduated dials and pointers, and set within a large ring is an elliptical track-way. Certainly it has the appearance of a serious demonstration device - there are no frills or extraneous details. But what exactly is the device trying to tell the user?

      Figure 1.2: The cometarium as improved by Benjamin Martin. The text around the elliptical track reads: “the come of the year 1682”.

      The cometarium is not exactly like the planetarium and orrery, whose function is essentially evident at first glance; they are devises to show the relative motion of the planets around a central Sun (see Chapter 2). This being said, some features of the cometarium, as Euphrosyne so eloquently observed, are readily understandable. Having already been told that comets move along elliptical orbits about the Sun, it is clear that the central elliptical track must represent the path of the comet. Indeed, inscribed around the edge of the inner elliptical plate are the words “the Comet of the year 1682”. This track, therefore, represents the orbit of Halley’s Comet, and indeed, the year corresponds to the very time at which Halley observed the comet and began to wonder about its origins and past history (see Appendix 1).

      Given that the elliptical track corresponds to the orbit of the comet the rotation point of the comet-driving radial arm must correspond to the location of the Sun - and, indeed this rotation point is distinguished by a spiked coronal motif. From this offset position of the Sun, it is immediately seen that there are two points in any comets orbit where it is at its closest and most distant locations. These are the perihelion and aphelion points respectively, and it takes the comet exactly half of its orbital period to move from one to the other. It is the rotation of the radial arm extending form the Sun focus point that drives the comet ball around the elliptical track, and the large circular ring, centered on the Sun, corresponds to the great circle of the comet path projected onto the celestial sphere. The lower circular dial of the cometarium indicates the time elapsed since perihelion passage, and its scale is divided into 75 divisions, corresponding to an orbital period of 75 years.

      It is now well known that the period of Halley’s Comet is not exactly 75 years, and that from one perihelion passage to the next its orbital eccentricity and orientation can change. The cometarium is not intended to represent, therefore, any specific orbit as it might have been observed at some specific return of Halley’s Comet, nor does it act as a predictive instrument to tell the user where the comet is going to be in the sky. Indeed, although Martin labeled his cometarium as corresponding to that of the comet for 1682, this designation is entirely irrelevant, and in reality any orbital period can be modeled. The only relevant point is that one 360-degree rotation of the time dial corresponds to the orbital period of the comet. The only way that different orbital eccentricities can be accommodated is by literally changing the eccentricity of the track in which the comet ball is constrained to move. This being said, Halley’s Comet was the very first verified periodic comet, and in 1755 it was still the only comet known to have returned more than once to the inner solar system.

      Figure 1.3: The interior wheel-work to Benjamin Martin’s cometarium.

      To make the cometarium work the demonstrator turns the small crank K (as seen in the lower left hand corner of figure 1.3). Connected to a continuous worm gear, the crank directly engages with the first circular gear c. The center of gear c is connected to the lower time dial located on the front of the cometarium. The crank K, therefore, is the time input of the machine; the more turns being given to crank K, so the greater the time interval being recreated along the comet’s orbital path. Gear C is directly meshed to a second circular gear Q whose center is located at one of the focal points of the elliptical track. The spindle at Q is further fixed to a rigid elliptical former LM. If we now imagine that the demonstrator turns the crank K at a constant rate, the gearing - so far described - is such that the elliptical former will be driven about its focal point at a constant rate. This constant rate of rotation is transformed into a non-constant rate of rotation by letting the elliptical former LM drive a second elliptical former NO about its focal point P. This drive is achieved via a figure of eight catgut string constrained to move along a v-grove cut into the edges of the elliptical formers. A spindle attached at P to the elliptical former NO will now rotate at a non-constant rate. By attaching a drive arm to the spindle at P on the front face of the cometarium, the comet ball will be driven around its track with varying speed. Spindle P represents the Sun-occupied focal point of the comet’s orbit, and the drive rate of the comet ball will be at its fastest when near to the Sun and at its slowest when far away from the Sun. Further details of the motion of the comet ball will be presented later in Chapter 2 and in Appendix II. In the mean time, we now regain contact with the dialogue of Cleonicus and begin to understand his final quoted words which tell us that the “brazen comet moves, and with a very unequal pace in its elliptical orbit about the focal Sun”. The cometarium being described by Cleonicus is clearly, given the focal point location of the Sun, a product of the Copernican hypothesis and it is the development of this idea that we shall briefly consider next.

The workings of the solar system: a brief history

      Although the night sky is animated