The Curved and the Straight: Cometary Theory from Kepler to Hevelius

This study is a recasting and extension of a theme in my doctoral dissertation, “The Background and Early Development of Newton's Theory of Comets”, Indiana University, 1966.

For an excellent analysis of the use of some of the ideas treated in this study by Ismael Boulliau in his investigations of planetary motions, see Wilson C. A. , “From Kepler s Laws, So-called, to Universal Gravitation: Empirical Factors”, Archive for history of exact sciences, vi, no. 2 (1970).

Galileo , Dialogue concerning the two chief world systems, trans. Drake S. (Berkeley, Calif., 1953), 45.

Gandillac Maurice , La philosophie de Nicolas de Cues (Paris, 1941), 221–8.

Cf. Galileo , II Saggiatore (Rome, 1625): “As for me, never having read the pedigrees and patents of nobility of shapes, I do not know which of them are more and which less noble, or which more and which less perfect. I believe that all of them are, in a way, ancient and noble; or, to put it better, that there are none which are noble and perfect or any that are ignoble and imperfect, except in so far as for building walls the square shape is more perfect than the circular, while for rolling or for moving wagons I deem the circular more perfect than the triangular.” Quoted from Drake Stillman and O'Malley C. D. , The controversy on the comets of 1618 (Philadelphia, 1960), 279.

Kepler Johannis , Mysterium cosmographicum (Tubingae, 1596); in Gesammelte Werke, i (Munich, 1938), 23: “Hac enim vna re diuinus mihi Cvsanvs, alijqve videntur: Quòd Recti, Curuique ad inuicem habitudinem tanti fecerunt, et Curuum Deo, Rectum creaturis ausi sint comparare.”

Brahe Tycho , De mundi aetherii recentioribus phaenomenis (Uraniborg, 1588), 194; quoted from Boas Marie and Hall Rupert A. , “Tycho Brahe's System of the World”, Occasional notes of the Royal Astronomical Society, iii, no. 21 (1959), 253–263, p. 263.

Ibid.

Kepler , De cometis libelli tres (Augustae Vindelicorum, 1619), 97: “Olim existimaui esse reale quippiam; itaque de causis Physicis philosophabar. Sed est mera visus deceptio, vt et stationes et regressiones Planetarum.” The notion had been with him at least since 1604. In the discussion of his suggestion that the speed of the comet of 1577 in its conjectured straight line of motion was probably non-uniform, Kepler related the apparent curvature to the Earth's motion: “For assuredly by introducing the Earth's motion that apparent circular motion is easily provided” (“Nam insinuans se motus Telluris, circularitatem illis facile conciliat”, “Appendix de motu Cometarum” in Astronomia pars optica (Francofurti, 1604)).

Ibid., 98: “Denique quot sunt in Coelo Cometae, tot sunt argumenta (praeterea quae à Planetarum motibus deducuntur), Terram moueri motu annuo circa Solem. Vale PTOLEMAEE, ad ARISTARCHUM reuertor duce COPERNICO.”

Kepler to Maestlin , 3 October 1595; Gesammelte Werke, xiii (Munich, 1949), 34–36.

Brahe , op. cit., 191.

Kepler to von Hohenburg Herwart , 7 October 1602; Gesammelte Werke, xiv (Munich, 1949), 284: “Ita hic nihil a Tychone differo, nisi quod cometis circulo adimo, conciliavit.”

Ibid., 283: “Sententia tamen haec est: Si quis Copernici sequatur hypotheses, illum hoc defendere posse. Cometas nihil esse aliud qvam trajectiones aetherias: Moveri scilicet in linea recta pene aequabiliter.”

Gesammelte Werke, ii (Munich, 1939), 287: “Mihi in pluribus, quorum descriptas obseruationes sum nactus, successit hac viâ leuius: Si, quod natura rerum suadet, rectas ipsis lineas tribuerem, quas aequalibus temporibus vt plurimum aequaliter traiicerent, solum initio et fine paulò tardiores, et quieti viciniores, vt et caeterae traiectiones solent.”

Kepler , Hyperaspistis (Francofurti, 1625), Appendix. A translation appears in Drake and O'Malley , op. cit.

Gesammelte Werke, iv (Munich, 1941), 59: “Doch halt ich ihre der Cometen Bewegung unangesehem sie im himmel drinnen sen ein gerade lini wie eines Ratetels und nicht circularisch wie der immerwehrenden Planeten.”

Kepler , De cometis, 3: “… cùm non sit verisimile, eorum quae nunquam eodem redeunt, motus esse circulares: Contrarium igitur est verisimilius, motus eorundem esse rectilineos.”

Ibid., 93–4: “Et cùm differentia perennium temporariorumque corporum sequatur in eorundem etiam motus; circulares vtique reuolutiones erunt perennium corporum, seu Sol moueatur, seu eius loco Tellus; rectilinei verò vanescentium: Habent enim vtrique conditionis suae causam in forma quisque sua; aeternitatis in circulo, mortalitatis in linea recta, quae infinita vtique nequit esse. Iungimus igitur cum veteribus suffragia nostra, Cometis rectilineos motus aptos esse.”

Kepler , Hyperaspistis, 193: “Prima ea fuit Conceptio traiectoriae rectilineae, nondum tentatis Numeris.”

See Pav Peter A. , “Gassendi's Statement of the Principle of Inertia”, Isis, lvii (1966), 24–34.

Ibid., 28.

Ibid., 28.

Ibid., 27.

Gassendi Pierre , Syntagma philosophiae , Liber V. , “De Cometis & Nouis Sideribus”, in Opera omnia (Lugdvni, 1658), i. The date of composition is not precisely known, but the text refers to the comet of 1652 and was quoted by Seth Ward in 1653; see Ward , De cometis (Oxoniae, 1653), 26.

Seneca , Natural Questions , translated by Clarke John and Geike Arthur and published as Physical science in the time of Nero (London, 1910), 300–1.

Gassendi , op. cit. (ref. 25), 710: “Non obstare etiam specialem formam, specialem motum, & similia; posse enim rerum naturam tali varietate gaudere; vt quemadmodum in iis rebus, quae generatur, & corrumpuntur, diuersissimae formae sunt, & motus etiâ plané diuersi; sic in perpetuis operibus, quaedam formâ rotundâ sint, & in orbem moueantur, veluti Planetae; quaedam oblongâ, & moueantur rectà, veluti Cometae; quippe, cum, vt poteat perpetuus motus inesse Planetis ob dispositionem figurae, cui nec principium, nec finis est; sic possit inesse Cometis, ob Vniuersi immensitatem, quae nusquam incipiat, nusquam definat.”

Ibid., 706: “…maxime inde est coniectura, esse motum Cometae propium, non circularem, sed rectilineum (quod Keplerus primus fuit suspicatus) ac esse quidem in se aequalem; siue vniformem; sed apparere tamen nobis inaequabilem, seu increscentem, decrescentémve, eadem ratione, quâ incessus viatoris aequali passu per viam rectam non procul à nobis dissitam gradientis, nullus, tardúsve conspicitur, dum ille procul adhuc est, aut procul iam abiit; velox autem, dum proprior est; & velocissimus, dum proximè transit.”

Ibid., 711: “… non inesse Cometis, nisi vnum simplicem motum, ipsumque rectilineum; nam quotidianum, quo videntur dietim ferri ab Ortu in Occasum, affingi ipsis ab oculo, ob diurnum motus Telluris; cùm etiam portio motus annui, qui Telluri competit, ita comparetur ad semitam rectam, quam Cometa instituit, vt provt ocyor, tardiorve est, aliquam curuitatem, siue deflexionem à rectitudine affingat.”

Ward , De cometis, 28: “Nempe si corpora Cometarum in omni aeternitate, lineis perpetuò rectis feruntur, immensa erit mundi moles; si verò circulis vel ellipsibus, uti Planetae reliqui, circa centra sua ferantur multum revera a Gassendi immensitate abscindemus.”

Ibid. , 31: “… ipse Keplerus in Appendice ad Hyperaspisten, sive Trutinatore Galilaei ostendit eodem modo se rem habere sive stet terra sivè moveatur.”

Kepler , Hyperaspistis , 195: “Tibi vero Sarsi si qua videtur inesse concinnitas in traiectoria recta' causa nulla est, quin ea fruaris etiam in Systemate Tychonis luxatili. Quod enim à me fulta est, te censore, traiectoria recta, motu Terrae; fulciet eam aeque firmiter Tycho, motu Systematico Concomitantiae, qui rapiat ipsam etiam traiectoriam rectilineam….”

According to Hall A. R. and Whiteside D. T. the strange Latin form “luxatili” that I have rendered as “pulled out of its joints” in reference to changes in the rectilinear path may be used instead to characterize Tycho's system as “loosely put together”. The form could be diminutive. If the term refers to Tycho's system even in a mildly disparaging way, the passage would be of interest to those concerned to understand the reception of Third World Systems or Kepler's relation to Tycho. Even if the term does not refer to a transformation in the rectilinear path, the difference between geocentric and heliocentric maps of the path remains implicit in the passage. In any case, Ward might have been confused by Kepler's wording, although he could have recognized Galileo's expressions in II Saggiatore as evasions. He must not have thought very deeply about the matter. O'Malley's translation, “you may … enjoy that dislocation under Tycho's system …,” gives some support to my rendering, but overall his translation of the passage (see ref. 5 above) is not a happy one.

Ward , op. cit., 31: “… certè sic ratiocinatur Keplerus, Motus circularis est aeternorum Deinde (ex praeoccupatione vulgatae disciplinae) Assumit corpora Cometarum non esse aeterna; ergo nec circulari motu circumferri; Dicimus nos rectum non esse, circularem esse; concludat igitur esse eos corpora aeterna.”

The dispute started over the validity of Hevelius's observation on 18 February 1665 (new style) that the comet was then over against primum Arietis. All other astronomers, starting with Adrien Auzout, were sure that it was then some 2° to the west of that star and that when three weeks later the comet did pass near a bright star in Aries the star was secundus Arietis. The disputed observation was printed in Prodromus cometicus (Gedani, 1665). Its defence was conducted by Hevelius through a long series of letters, particularly to Oldenburg for the Royal Society, and Mantissa prodromi cometici published with a second work, Descriptio cometae 1665 (Gedani, 1666). During the defence, Hevelius adopted views he normally believed to be repugnant—quiescent Earth and motion for the comet along a closed lenticular path—in order to demonstrate the neat lawlike changes in apparent position on the celestial sphere when his disputed observation was accepted.

Hevelius Johannes , Cometographia (Gedani, 1668), 562: “… Planetae, qui corpora sunt aethera perfecta, aeterna, motum nunquam non continuum, & perpetuum exercentia. E contra, Cometae corpora tantùm sunt aetherea imperfecta, & quidem temporanea, quae certo tempore generantur & dissolvuntur, ac nunquam motu suo integrum absolvunt circulum. Ideoq́ nullum possident motum continuum, nee perpetuum; sed magis conveniens aptumq;… quippe perennia gyrantur in orbem, at interitura rectis trajiciunt lineis.”

Ibid., 418: “… pro diversis exspirationibus, diversissimi etiam nuclei generatur.”

Ibid., 478: “Sol enim fortissimis suis radiis, Cometam à parte observâ & ab utroq́; latere illuminans feriensq́; materiam istam tenuiorem, & subtiliores istas aethereas exhalationes, iisdem lateribus adhaerentes magis rarefacit, extenuat ac dissipat, quàm eas à latere Cometae à Sole averso; adeò ut calore suo, & vi radiorum eas expirationes Solem respicientes propellat in plagem Soli oppositam.

Ibid., 430: “Nam, nisi Planetae se motu gyrationis tuerentur, ingens illa sphaera Solis, quae verus ignis & realis est, efficaciâ suâ, ea corpora dissolveret; hoc autem motu conserventur in tenore suo, ut sint prorsùs indissolubilia.”

Ibid.: “Caeterùm quaecunq́; corpora circumrotari debent, oportet ut sint perfecta, perpetua, integra omninò globosa, ac in suo naturali loco constituta; atqui Planetae cùm sint talia; utiq́; circumvolvi possunt.”

Ibid.: “E contra, Cometae, cùm sint corpora naturae imperfecta, temporanea, minimé sphaerica, sed tantum discea, tum partes, sive effluvia tantùm aethereorum ordinariorum corporum; itemq loco propio naturali suo particulae expulsae, ac extrusae; ergo nullâ ratione circa axem gyrantur, nec ad circumvolutionem apta sunt.”

Ibid., 431: “De reliquo, si Cometis motus ille gyratorius attribuatur, necessariò etiam Caudo (quae ex refractione & reflexione Solarium oritur …) de die in diem, imò in horas diversissimam indueret formam….”

Ibid., 658: “… Cometae neutiquam in exquisitâ lineâ rectâ, ut quidem Keplerus, alliq́; arbitrati sunt, sed in lineâ ex parte inflexâ, & incurvata, cujus concavita perpetuò Soli prona est….”

Ibid., 646.

Other astronomers of the period assigned circular or elliptical orbits to comets supported by a quiescent Earth (notably, Cassini G. D. , Pierre Petit, and—with considerable reservations—Adrien Auzout) or by a moving Earth (notably John Flamsteed in 1677, though not in 1681). The underlying philosophical bases of these moves however have not been determined. Astronomers such as Christopher Wren, Christiaan Huygens, and—without trying the numbers—John Wallis opted for rectilinear or quasi-rectilinear paths within the Copernican system, but their basic theoretical reasons are likewise unknown. It seems plausible that at least some of these astronomers were influenced by ideas like those under discussion in this paper, but the evidence remains to be found. George Doerfel, an otherwise obscure German clergyman, adapted Hevelius's views wholeheartedly to the comet of 1680 and presented a parabola drawn in such a fashion with the Sun at the focus to map far more curvature than Hevelius himself probably would have allowed. See Armitage Angus , “Master Georg Dörffel and the Rise of Cometary Astronomy”, Annals of science, vii (1951), 303–15. Doerfel and Flamsteed were the only observers to pronounce immediately that the two sets of appearances in 1680 and 1681 were due to the same comet because the other astronomers including Newton and Huygens believed that to do so violated the principle that the apparent track lies approximately along a single great circle path, which manifestly was not the case in 1680–81. Robert Hooke demonstrated in Cometa, printed in Lectures and collections (London, 1678), that any number of kinematical schemes might work to save the phenomena to the usual standards of accuracy permitted in cometary theory. He urged the need for better observations and a fresh start from a new paradigm. Hooke was convinced that a successful theory could be constructed only on the basis of vastly-improved observations interpreted within the framework of simple dynamical principles grounded in experience and not on the basis of metaphysical harmony or mere curve fitting. The influence on the forty-year-old Newton of these various theoretical treatments needs to be reassessed. There is little doubt however that Newton began to think of comets within the context of a theory of universal gravitation only after about 1683 or 1684.