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Professor of Astronomy

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A Comet of the Enlightenment

Part of the book series: Vita Mathematica ((VM,volume 17))

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Abstract

Although Lexell during his apprenticeship with Christian Mayer had learned the art of observing by means of astronomical instruments, it was clear that his talent and inclination lay principally in the field of theoretical astronomy. As a mathematical subject, it suited him perfectly, and by adopting Euler’s approach and rigour to the problems at hand, he learned to master the science to a great perfection.

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Notes

  1. 1.

    The size of the Moon is not negligible in comparison with its distance to the Earth, and as Kepler’s laws are formulated for point-like bodies, the distance of the centre of mass of the Earth-Moon system to the Moon’s centre had to be determined.

  2. 2.

    An alternative to the purely astronomical methods to determine longitude was to measure, by means of an accurate chronometer, the difference between the moment of noon and the simultaneous reading of a timepiece. The method is beautifully expounded in Euler’s Lettres à une princesse d’Allemagne sur divers sujets de physique et de philosophie, Vol. III, 1772, Lettres CLXIII–CLXIV (OO Ser. III, Vol. 11, pp. 1–312. E417). However, the great distances on the Earth, the slow means of transportation and the unreliable timepieces made it technically very difficult to determine longitude with sufficient accuracy.

  3. 3.

    An ingenious method of deducing the diameter of the Earth was invented by Eratosthenes of Alexandria (ca. 276–195 BC).

  4. 4.

    The astronomical unit is essential for determining the distance to the stars using the so-called annual parallax effect.

  5. 5.

    Observations of the transit of Mercury in 1631 gave the first quantitative evidence of the size of the planets and the dimensions of the planetary disc.

  6. 6.

    The virtual path of the Sun around the Earth, or the plane in which the Earth orbits the Sun, is called the ecliptic.

  7. 7.

    Precise astronomical knowledge meant better maps, which in the long run offered a strategic benefit in the command of the overseas territories. For the significance of the eighteenth century Venus transits in general, see e.g. [4, 136, 156, 167, 176]. An analysis of the methods involved has been given by Verdun [167].

  8. 8.

    The fact that T ♀ is very close to \(\frac{5} {8}\)

    is a remarkable numerical coincidence, which has puzzled many an astronomer.

  9. 9.

    Halley’s influential paper “Methodus singularis qua Solis Parallaxis sive distantia a Terra, ope Veneris intra Solem conspiciendae, tuto determinari poterit” appeared in the Philosophical Transactions of the Royal Society, Vol. XXIX, pp. 454–464. Considering that the following Venus transit would occur in 1761, Halley was indeed looking very much ahead of his time.

  10. 10.

    Expositio methodorum, cum pro deteminanda parallaxi Solis ex observato transitu Veneris per Solem, tum pro invendiendis longitudinibus locorum super Terra, ex observationibus eclipsium Solis, una cum calculis et conclusionibus inde deductis, NCASIP XIV Part II, pp. 321–554, 1769 (OO Ser. II, Vol. 30, pp. 153–231. E397) [28, pp. 342–574]. For an analysis of the work, see e.g. [167, 168].

  11. 11.

    Even Catherine II, assisted by F. U. T. Aepinus, observed the rare phenomenon at the Oranienbaum palace some 40 km from St. Petersburg [120, p. 205]. These observations apparently did not suffice for scientific purposes, however.

  12. 12.

    This thesis (presented pro exercitio) contained the results of Anders Planman’s observations of the transit of Venus in Kajaani (Cajaneborg), Finland. Both in 1761 and 1769, the Royal Swedish Academy of Sciences had sent Planman on an astronomical mission to north-eastern Finland to observe the transit of Venus. In 1761, due to the late arrival of spring, Planman had to stop at the town of Kajaani, which nevertheless was at a sufficiently high latitude for observing the phenomenon. Also in 1769, Planman observed in Kajaani using a 21 foot telescope. In 1761, Planman managed to observe all four contacts, but in 1769, because of bad weather and smoke, only two. He also witnessed an optical phenomenon called the “black drop” (gutta nigra). On the way back to Åbo, Planman also determined (for the first time) the latitude and longitude of six locations in Finland [67, 91].

  13. 13.

    Guryev, present-day Atyrau in the Republic of Kazakhstan.

  14. 14.

    Tsaritsyn, or present-day Volgograd, has also been known as Stalingrad.

  15. 15.

    Petr Inokhodtsev (Петр Ворисович иноходдев) (1742–1806), astronomer and Lowitz’s Adjunct [119]. He assisted Lowitz in the observations of the 1769 transit of Venus in Guryev and determined the latitude and longitude of numerous places in Russia. In 1779, he was appointed academician. Besides being an active astronomer and meteorologist, he was a historian of astronomy.

  16. 16.

    The value 8. 67″, obtained at the moment of the transit (when the distance

    was 1.0154 times the mean distance) yields the mean parallax of 8. 80″. The distance between the Earth and the Sun is stated as 23,436 times the mean radius of the Earth, while with today’s values, it is on average 23,480 times the Earth’s mean radius, corresponding to a parallax of approximately 8.794″.

  17. 17.

    In fact, a minor scandal arose a century later when the Viennese astronomer Karl Ludwig von Littrow (1811–1877) attempted to prove that Father Hell had falsified his results. However, later on Simon Newcomb (1835–1909) analysed Hell’s notes anew and found no evidence of forgery [4].

  18. 18.

    Det enda som jag welat bewisa, är at Pat: Hell haft orätt då han criticerat de räkningar som förekomma uti XIV Tomen af Comment: samt at Hans egna räkningar äro så swårt felaktiga, at af dem ingen ting kan slutas. Det fägnar mig, at jag kunnat bringa Pat: Hell til så mycket billighet, om Planman miströstar jag mera, likwäl måste han medge mig då jag war i Åbo, at ingen anledning är, at misstänka Pat: Hell observation för at wara updiktad.

  19. 19.

    Emedlertid må Herr Professorn tillåta mig at upriktigt tilstå, det jag hade förmodat lite mera öfwerläggning af Herr Professorn hwad detta ämne angår, som wäl ei är af de aldra benigaste och i sanning mera fordrar en sund logica och riktig critique, än diupsinnig Mathematique. Aldra minst hade jag wäntat, at Herr Professorn emot mina skäl, allena tyckes wilja sätta en wiss auctoritet, som med al aktning för Herr Professorns person och egenskaper, jag icke kan finna mig uti at erkänna. Herr Professorn kan wara öfwertygad at Euler, den stora Euler, ingenting förmår öfwer mig blott genom auctoritet, mycket mindre någon annan.

  20. 20.

    Maximilian Hell: Supplementum ad Ephemerides Astronomicas Anni 1774 ad Meridianum Vindobonensem. Viennae, 1773.

  21. 21.

    Referring to [Lexell 27]. We have included this letter in the list of Lexell’s publications even if Lexell himself was opposed to publishing it. It is of course supplemented with Hell’s own footnotes and refutations of Lexell’s arguments.

  22. 22.

    Enfin j’ai reçu le supplément de l’Abbé Hell sur la parallaxe; je l’ai trouvé tel que je me l’avois imaginé et même pire encore. Il faut bien, que Vous Monsieur, l’aviez parcouru bien à la hâte, lorsque Vous m’écrivîtes il y a un an, que j’aurai raison d’être bien content de l’Abbé Hell. J’en conviens volontiers, si je pourrois m’imaginer que ce soit par complaisance pour moi, qu’il persiste encore sur les objections, qu’il a faites contre les calculs sur la parallaxe dans le XIVe Tome des Commentaires; qu’il defend toutes les fautes qu’il avoit commis lui-même; qu’il fait imprimer une de mes lettres sans m’en demander la permission; qu’il y ajoute quantité des notes en partie triviales et pour la pluspart absurdes; qu’il s’approprie le droit de corriger ou plustôt pervertir mes calculs sans les entendre; qu’il propose plusieurs insinuations et imputations odieuses contre moi. Je dis, que si je serois assez bête pour me persuader, que tout ceci soit à mon avantage, j’aurois beaucoup à me louer de l’Abbé Hell. Soyez Vous-même Monsieur, mon juge s’il Vous plaît. Mais permettez aussi que je remarque le contraste singulier, qu’il y a entre Votre conduite envers l’Abbé Hell et moi. Vous approuvez la conduite de l’Abbé Hell, sans l’avoir examiné et quand je Vous demande Votre sentiment sur des choses controversées entre lui et moi, Vous vous excusez par Votre peu de temps. Je ne Vous ai demandé, que Vous disiez quelque chose au désavantage du caractère personnel de l’Abbé Hell, j’ai seulement voulu sçavoir si selon Votre sentiment il avoit tort sur une telle question, ou non?

  23. 23.

    In fact, an expression for the apparent breadth of the Moon given in [Lexell 42] became known as “Lexell’s formula” (Lexellsche Formel, la formule de Lexell) [160].

  24. 24.

    The method was used at least to the end of the nineteenth century, when exact chronometers made it obsolete.

  25. 25.

    The angular distance between the Moon and a celestial object (a fixed star).

  26. 26.

    Mayer’s book Theoria Lunae was published posthumously in London in 1767.

  27. 27.

    Page 567: “Tabulas vero Illustris Euleri quod attinet, eae fere tales sunt, quales per computum Theoriae superstructum deductae, quare si simili modo ac Mayerianae per observationes corri- gantur et emendentur, non dubitamus quin aliquando praestiturae sint exactitudinem quae hoc in negotio desideratur, maximam.”

  28. 28.

    This method was invented and developed by the Danish astronomer Ole Rømer (1644–1710), who by observing seasonal variations of the frequency of these occultations was able to show that light arriving from Jupiter to the Earth takes time to propagate. By estimating the diameter of the Earth’s orbit Rømer managed to determine the speed of light in 1676, for the first time in history.

  29. 29.

    The irregularities are mainly due to the flattening of Jupiter’s body, a fact that was not known at the time.

  30. 30.

    Wargentin’s studies of the moons of Jupiter began in his thesis entitled Specimen astronomicum, de satellitibus Jovis … (12 December 1741), presided in Uppsala by Anders Celsius.

  31. 31.

    Latin for hair; thus, a comet is like a hairy ball.

  32. 32.

    Nevertheless, from the affinity of the tails of comets and the phenomenon known as the northern lights, Euler had speculated that the phenomena could be related, cf. “Recherches physiques sur la cause de la queüe des comètes, de la lumière boréale, et de la lumière zodiacale”, Mémoires de l’Académie des Sciences de Berlin, 1746, pp. 117–140 (OO Ser. II, Vol. 31, pp. 221–238. E103).

  33. 33.

    Mount Maenalus is a name, no longer used, of a stellar constellation situated between Virgo and Boötes.

  34. 34.

    Friedrich Wilhelm Bessel (1784–1846), astronomer and mathematician, was appointed director of the Königsberg Observatory in 1810. His essay entitled “Untersuchung der wahren elliptischen Bewegung des Kometen von 1769” (published in the Astronomisches Jahrbuch (Berlin) for the year 1810, pp. 88–124) was awarded the astronomical prize of the Berlin Academy.

  35. 35.

    Man sieht aus dieser Schrift, dass Hr. Euler, der wegen Mangel des Gesichtes nicht selbst schreiben konnte, dieselbe dem Herrn Lexell in die Feder angegeben, und ihn vorgesagt, was er in Zahlen und meistens mit Hülfe der logarithmischen Tabellen zu rechnen habe. Ausser dieser Rechnung und der Orthographie ist alles übrige Eulerisch, nemlich der Styl, die Anordnung des Wertes, die Wendungen in den Rechnungen, und die nachgeholten Verbesserungen dessen was anfangs nicht genug überdacht war. Denn Hr. Euler läßt fehlgeschlagene Versuche im Rechnen eben so wie die gelungenen in Druck erscheinen, und mag vielleicht seine besondere Gründe dazu haben.

  36. 36.

    A. G. Kästner (1719–1800), born in Leipzig, was Professor of Mathematics at the University of Göttingen. Kästner was feared for his sarcastic attitude, and although not much renowned for original research, he educated many first-rate mathematicians and physicists. He also published histories of mathematics [32] and translated the proceedings of the Royal Swedish Academy of Sciences into German. When Lexell met with Kästner personally in 1780 (see the letters to Wargentin in Sect. 9.4), he no longer seemed to hold a personal grudge against Kästner.

  37. 37.

    Lexell says that he is quite certain that none of the Berlin academicians have written this review since it reveals that the author is very little versed in the science of calculations relating to comets. He confesses that his suspicions fall solely on Mr Kaestner because he knows no one else with such a strong disposition to criticise and quibble about what the most famous mathematicians have written, without himself being capable of assessing the merits and benefits of their work.

  38. 38.

    Lexell’s comet belongs to the Jupiter family comets, such as comet Churyumov-Gerasimenko, which is the target of the European Space Agency Rosetta mission. (Personal communication: Professor Anny-Chantal Levasseur-Regourd).

  39. 39.

    Lexell writes: “À cause de l’action de Jupiter, il pourra même devenir douteux, si, à l’avenir, on a la satisfaction d’observer la comète dans la même orbite qu’elle parcouroit en 1770; car si les élémens que nous venons d’établir étoient tout à fait exacts, la prochaine conjonction de Jupiter avec la comète se feroit l’an 1779 le 23 d’Août à 12 heures à peu près, la longitude de ces astres étant alors 6s.3∘34′. Or le calcul prouve, que pour cette longitude, la distance de la comète à Jupiter est à peu près la 491eme partie de sa distance au Soleil, d’où il s’en suit que l’action de Jupiter surpassera celle du Soleil 224 fois, ce qui ne manqueroit pas de produire un changement total dans le mouvement de la comète. Quoiqu’on ne puisse pas compter sur la plus scrupuleuse exactitude de cette conclusion, vû que des petites variations dans les élémens peuvent donner des résultats très différens; néanmoins toutes les circonstances bien considérées, on peut soutenir, qu’au moins dans l’une ou l’autre des conjonctions de Jupiter avec la comète du 1767 ou 1779, l’orbite de la comète a dû souffrir des changemens sensibles, par l’action de Jupiter.”

  40. 40.

    [O]n y voit les comparaisons des calculs avec des observations & les différentes suppositions ou les essais de calculs par lesquels M. Lexell s’est assuré que toute autre orbite ne représenteroit pas aussi bien les observations.

  41. 41.

    As in the processing of the observations of the Venus transit, the method of least squares was not available.

  42. 42.

    A discussion of the mass of the comet Halley (which had re-appeared in 1759) is found in Johann Albrecht Euler’s prize-winning essay entitled Meditationes de perturbatione motus cometarum ab attractione planetarum orta, St. Petersburg, 1762.

  43. 43.

    Nevil Maskelyne (1732–1811), Astronomer Royal at Greenwich.

  44. 44.

    The British Astronomer Royal John Flamsteed (1646–1719) had catalogued and designated over 3,000 fixed stars (Historia coelestis Britannica, 1725). Apparently Uranus figured among them, erroneously designated as “34 Tauri”.

  45. 45.

    Named after Johann Daniel Titius (1729–1796) and Johann Elert Bode. Titius formulated the rule in 1766, Bode in 1772. The law has not been proven theoretically.

  46. 46.

    Erik Prosperin (1739–1803), Observator Regius, Melanderhjelm’s successor in the Chair of Astronomy at Uppsala and a specialist in orbit calculations [127].

  47. 47.

    Johann Gottfried Koehler (1745–1801), German astronomer, inspector of the “Mathematisch-Physicalischer Salon” (the Royal Instrument Cabinet) in Dresden.

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    Johan C.-E. Stén

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Stén, J.CE. (2014). Professor of Astronomy. In: A Comet of the Enlightenment. Vita Mathematica, vol 17. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00618-5_5

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