true paths became paramount.
Figure 1.16. Descartes vortices, with a star located at each center (Y, f, F, S, L, D). The meandering path of a comet (starting at point N in the lower center and continuing to the upper right) works its way from one outer vortex boundary region to another.
Hevelius continued to study comets and eventually published his magnum opus on the subject Cometographia in 1668. Within this tome he attempted to describe and classify cometary tails, and posited that comets move along paths corresponding to conic sections (recall figure 1.10) with the Sun located at a focal point (although he did vacillate somewhat on this latter condition). Since comets were still believed to be ephemeral, one-off displays, Hevelius suggested they were some kind of spurious planet, formed from material exhalations derived from either one of the outermost planets Jupiter or Saturn – the planet of origin being determined by the comet’s color. The frontispiece to Cometographia reveals the Hevelius viewpoint on comet orbits and origins (see figure 1.17). The image shows Hevelius flanked by the ghost of two philosophers past: Aristotle and Kepler. To his right is Aristotle, ignored and pointing somewhat vaguely to a diagram showing comets as atmospheric phenomena constrained to the sublunar region, their tails pointing in any and all directions. To the left of Hevelius, in more earnest stance is Johannes Kepler, who holds his diagram revealing the rectilinear motion of cometary paths; their tails streaming away from the Sun. Hevelius, however, cannot hold the eye of Kepler, and with a gentle, staying wave of his left hand points emphatically with his right to the new interpretation. Comets move along gently curving paths (parabolic or hyperbolic – but not elliptical). Hevelius essentially truncated the long and gently curving (interstellar) pathways depicted by Descartes (figure 1.16); downgrading comets thereby from vortex skimming stars of unknown origin, to locally birthed planet-born progeny.
While justly famed for his lunar and star mapping work, Hevelius, in later life, was overwhelmed by the scientific and instrumental advancements that had developed around him. The beginning of the end for Hevelius began, in fact, with his observations relating to the comet of 1664, for which he presented sky positions that were at odds with all other observers. Then in 1674 Robert Hooke, in his Animadversions, launched into a long critique of Helvelius’s Machina Coelestis (published in 1673) – chastising Hevelius for relying on the eye to make positional observations when telescopic sights offered a much more precise means of measurement. Further misfortune followed in September of 1679 when his observatory in Danzig, Stellaburgum, burnt to the ground. And finally, with the appearance of the comet of 1680, and Newton’s 1687 triumphant description of its orbit as a parabola, with the Sun at the focal point (recall figure 1.5), Helvelius’s notion of comets moving along gentle curving paths was laid to rest. Hevelius died in 1687, the last of the great Tychonic School of naked-eye observers, being spared the news of Newton’s work and the 1705 publication of A Synopsis of the Astronomy of Comets by Edmund Halley in which the periodic nature of the comet of 1682 was revealed.
Figure 1.17. The title page from Hevelius’s Cometographia (1668). To the left in the image is Aristotle, centrally seated is Hevelius and to the right is Kepler. In the center background a crowd of onlookers, some with arms raised to the sky, contemplate the approaching comet. Meanwhile, lofted above the superstitious plebeians, are seen the “astronomers” at work. Three large sextants (characteristic of the design promoted by Tycho Brahe) can be seen in the image, along with an observer viewing the comet through a telescope. The dividers placed on the table next to Helvelius’s right hand are a sign of authority and exactness.
Kepler, Galileo, and Helvelius (and indeed all astronomers prior to their time) accepted that comets were large ephemeral objects, quasi-planets perhaps, but objects with a limited lifetime. This notion began to change, however, with the realization, through Edmund Halley’s investigations, that at least some comets moved along elliptical paths and were in principle at least long-lived and subject to repeated returns to the inner solar system. Newton’s thoughts on the topic were discussed in his Principia (1687) and in his second magnum opus, Opticks (first published in 1704). In these works Newton suggested that while comets had a solid and durable nucleus, they were additionally surrounded by a tenuous atmosphere. Newton additionally suggested an alchemical link with respect to the utility of the vapors emanating from cometary tails, arguing that planets needed to accrete such matter in order to replenish the fluids vital to the process of vegetation and putrefaction [6]. Indeed, in his Opticks Newton asked, “to what end are comets?” - answering in effect that it was only by the accretion of cometary material that sustained life on Earth was possible. With Newton, the swirling vortices of Descartes were laid to rest. “The motions of the Comets”, Newton writes in his Principia, “are exceedingly regular, are governed by the same laws with the motions of the planets, and can by no means be accounted for by the hypothesis of vortices. For comets are carried with very eccentric motion through all parts of the heavens indifferently, with a freedom that is incompatible with the notion of a vortex”. While Newton freed comets from the random buffetings supplied by Descartes swirling tourbillions, he none-the-less entrapped them within the ever searching web of gravity. By this act, Newton placed comets within the realm of direct calculation; their paths, at least in principle, being described by mathematical formula and direct computation.
With the mathematical techniques put in place by Isaac Newton, the 18th Century saw ever more calculations of cometary orbits being made. With, in principle, their orbits now being understood and numerated, the issue as to their origins and purpose became a matter of greater interest. It was now clear that comets, for at least some of the time, moved in a realm beyond the planets. Indeed, Halley’s Comet, at aphelion, is located three times further from the Sun than Saturn, the outermost of the known planets until the discovery of Uranus, by William Herschel, in 1781. One of the first diagrams to clearly illustrate cometary orbits and contrast them against those of the planets was that constructed by Thomas Wright of Durham. Writing in his text Clavis Cœlestis: being the explanation of a diagram entitled a Synopsis of the Universe (published 1742). Wright notes that, “Besides the Planets, which all move round the Sun from West to East near the Plain of the Ecliptic; there are other surprising Bodies in the System call’d Comets, whose Motions are perform’d in very different Plains, and in all manner of Directions, both direct and retrograde”. Lavishly illustrated, and massive in scale, Wright shows in the supplementary diagrams that accompanied Clavis Cœlestis the paths deduced for Halley’s three ‘periodic’ comets near to the Sun (figure 1.18), but leaves as a mystery their more distant peregrinations. Other diagrams of the time simple stop once the cometary distance extends beyond that of the orbit of Saturn (figure 1.19) – in many ways, rather than invoking the terrestrial map maker’s “here be dragons”, the astronomers responded with the notion that in the realm beyond Saturn, “there be comets”.
Figure 1.18. A small section of Thomas Wright of Durham’s A Synopsis of the Universe, published in 1742, showing the orbits deduced for the comets of 1661, 1680 and 1682 interior to the orbit of Mars. These three comets were highlighted by Edmund Halley as being periodic – that of 1661 being, in fact, Halley’s Comet.
At the time of publishing Clavis Cœlestis Wright was actively engaged in the study of comet C/1742 C1, describing his observations in the February, March, and April issues of The Gentleman’s Magazine. Wright ultimately submitted his derived orbit for the comet to the Royal Society. Employing these same mathematical skills a few years later, Wright speculated upon a possible extension of Kepler’s laws of planetary motion with respect
