Wayward Comet:. Martin Beech

13th Century, when, for example, they were used to enable the calculation of holy days within the Christian calendar, or to demonstrated the many uses of the astrolabe6. Volvelle, or wheel charts, are typically designed to act as some form of analogy computer – indeed; they are distant relatives of the circular slide rule. The modern day descendent of the astrolabe is the planisphere, which in turn is a two component volvelle-like device. Made-up of two circular disks that rotate about the same center (corresponding to the celestial pole on the sky) the planisphere is a 2-dimensional model of the celestial sphere. The lower disk contains a projection of the stars and constellations that will be visible from a given location (specified by latitude) on Earth’s surface during the course of one year. The front disk is opaque except for a cutout window that enables the user to see the star disk situated below. By rotating the two disks so that they are aligned at a specified hour and day of the month, the window in the upper disk will reveal the stars that will be visible above the observer’s horizon. The planisphere is a wonderfully simple, but incredibly useful device, enabling the determination of approximate rise and set times for stars and constellations, and, of course, if the predicted path of a comet through the sky is printed on the lower dial, then the rise and set times, as well as sky location of the comet on a specific day can be determined. Planispheres showing the path of Halley’s Comet were certainly sold during its 1986 return (figure 1.20), and at other times planispheres showing the progress of other comets across the sky have been manufactured and sold to the public (see later with respect to the 1832 return of comet Biela).

      Figure 1.20. Planisphere window view for the path of Halley’s Comet across the sky from December 1985 to March 1986. Note the change in direction of the tail on the sky as the comet approaches perihelion on 9 February 1986.

      In celebration of its imminent return in 1986, renowned astronomy writers Patrick Moore and Heather Couper (with illustrations by Paul Doherty) produced a pop-up book on Halley’s Comet. The text featured pull-out tabs to show the expected appearance of the comet’s tail, in specific months, as it approached and rounded perihelion; it also contained a 3D-pop-up representation of the comet’s orbit, showing the location of the comet at specific times between 1948 and 2024 (the latter two dates being times when the comet was and will next be at aphelion). While the book by Moore and Couper was written for a juvenile audience its interactive and explorative nature makes it a delightful read – the story and the science jump right out of the page.

      The first print to reveal the 3-dimensional geometry of cometary orbits was published by Dutch polymath Nicolaas Struyck in volume 2 (1753) of his Vervolg van de beschryving der staartsterren. The image (figure 1.21) is a 2-dimensional hybrid of a pop-up book – indeed, one can easily imagine opening-out a plush, semi-circular binder with the orbits rising up, hydra-like, from the inside of the cover pages. The cometarium by Stuyck is highly detailed and shows near-to-perihelion, and above the ecliptic, portions of the orbits to some 14 comets (table 1.3) as recorded between 1533 and 1748. No specific scale for the cometarium is indicated, but its design incorporates the Sun at the center of a circular base plate, with a circle band representing the Earth’s orbit. Although not clear from the diagram, the model Earth, which is located at the center of two circular protractors, is probably moveable and can be set to a particular day and month of the year location. A string is attached to the Earth model and this, stretched to any one of the cometary tracks, would enable an estimate of its ecliptic coordinates to be made. Furthermore, by stretching the string from the Earth model, to the comet location and then onto the Sun, the comets phase angle and solar elongation could be determined. The orbit tracks are clearly marked with one-day interval striations and they are orientated correctly with respect to inclination, argument of perihelion and longitude of the ascending node – the (i, ω, Ω) co-ordinates in figure 1.13. The location of the comet is set by sliding a small ball, complete with cometary tail, to the appropriate data as indicated along the orbital track. While the image of Struyck’s cometarium is highly detailed, and could certainly have functioned as a demonstration device, there is no specific evidence to indicate that the cometarium was ever physically made and/or used for lecturing purposes.

      Figure 1.21. The cometarium of Nicolaas Struyck. The diagram is from volume 2 of the Vervolg van de beschryving der staartsterren (1753). See table 1.3 for details.

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label	Comet	Designation	P(yr)	e	i (°)	notes
A	1748	C/1748 H1	---	1.00	94.54
B	1742	C/1742 C1	---	1.00	112.95
C	1744	C/1743 X1	---	1.00	47.14	(1)
D	1533	C/1533 X1	---	1.00	149.59
E	1748	C/1748 K1	---	1.00	67.08
F	1706	C/1706 F1	---	1.00	55.27
G	1678	6P/d’Arrest	6.62	0.67	2.81	(2)
H	1707	C/1707 W1	---	1.00	88.65
I	1743	C/1743 C1	---	1.00	2.28
K	1702	C/1702 H1	---	1.00	3.38
L	1699	C/1699 D1	---	1.00	109.42
M	1739	C/1739 K1	---	1.00	124.26	(3)
N