The Early Search for Stellar Parallax: Galileo,Castelli,and Ramponi

Hooke Robert , An attempt to prove the motion of the Earth from observations (London, 1674); reissued in Hooke , Lectiones Cutlerianae, or a collection of lectures, physical, mechanical, geographical, & astronomical (London, 1679). For Hooke's supposed observation of stellar parallax, see Hoskin Michael A. , Stellar astronomy: Historical studies (Chalfont St Giles, 1982), 27–32; Hetherington Norriss S. , Science and objectivity: Episodes in the history of astronomy (Ames, 1988), 17–21; and Hirshfeld Alan W. , Parallax: The race to measure the Cosmos (New York, 2001), 131–3, 144–9.

Moray Robert (Whitehall) to Christiaan Huygens (Paris), 29 Nov. 1663, in Oeuvres complètes de Christiaan Huygens (22 vols, Paris, 1888–1950), iv, 443–5 (no. 1173): “Mais il y a long temps que Monsieur Wren en parlant de la façon de tuyau dont il faut se servir aux lunettes qui requierent une longueur de 60. 80. pieds ou d'avantage il s'est proposé la mesme chose que vous me descrivez [ ibid. , 431–3 (no. 1167)]. Voicy qu'entre Monsieur Neile, pendant que J'escris ce que dessus, et me dit qu'il y a 10. Ans que Monsieur Wren et luy ont parlé de cette affaire. Mais ils n'ont pas songé à employer cette invention pour l'usage ordinaire. seulement il se proposoyent de placer un verre obiectif sur quelque grande hauteur et le fixer là pour observer et comparer les altitudes meridionales de quelque estoile afin de tascher de decouvrir sil y a quelque paralaxe &c.” Aerial telescopes were also constructed by Johannes Hevelius and the most powerful ones were built by Huygens himself and by Giuseppe Campani (1635–1715). See Willach Rolf , “Schyrl de Rheita und die Verbesserung des Linsenfernrohres Mitte des 17 Jahrhunderts”, Sterne und Weltraum , xxxiv (1995), 102–10 and 186–92, pp. 104, 105, 107–8.

Kircher Athanasius , Itinerarium exstaticum (Rome, 1656), reissued in a revised, augmented and annotated version by his friend Kaspar Schott under the title: Iter ex[s]taticum coeleste (Würzburg, 1660, ²1671). Barbara Bauer [ Mahlmann ], “Copernicanische Astronomie und cusanische Kosmologie in Athanasius Kirchers <<Iter exstaticum>>”, Pirckheimer Jahrbuch , v (1989/90), 69–107; Carlos Ziller Camenietzki, “L'Extase interplanétaire d'Athanasius Kircher: Philosophie, cosmologie et discipline dans la Compagnie de Jésus au XVIIe siècle”, Nuncius , x (1995), 3–32; Siebert Harald , “Vom römischen Itinerarium zum Würzburger Iter: Kircher, Schott und die Chronologie der Ereignisse”, in Spurensuche: Wege zu Athanasius Kircher , ed. by Horst Beinlich Hans-Joachim Vollrath Wittstadt Klaus (Dettelbach, 2002), 163–88; and Johnson Trevor , “Jesuit space-travel in the age of Galileo: Athanasius Kircher's Ecstatic voyage of 1656”, unpublished paper presented to the Reformation Studies Colloquium, Warwick University, April 2000.

Kircher , Itinerarium (ref. 3), 266–8, 275, 347–9; Kircher , Iter (ref. 3), 348–50, 355, 409–11; Siebert Harald , “Die große kosmologische Kontroverse: Rekonstruktionsversuche anhand des Itinerarium exstaticum von Athanasius Kircher SJ” (Ph.D. dissertation, Technische Universität Berlin/Université de Paris I, 2004), 208–15, 278–307.

Copernicus , De revolutionibus orbium coelestium libri sex (Nuremberg, 1543), f. 10r: “… quae [sc. the distance of the stars] faciat etiam annui motus orbem sive eius imaginem ab oculis evanescere”.

Galilei Galileo , Dialogo sopra i due massimi sistemi del mondo Tolemaico e Copernicano (Florence, 1632) = Le opere di Galileo Galilei , ed. by Antonio Favaro (20 vols, Florence, 1890–1909; hereafter: Galileo , Opere), vii, 21–520.

The absence of observable parallax was no longer a major argument of anti-Copernicans in the seventeenth century: Colombe Delle Ludovico , “Contro il moto della Terra” (Ms., 1610/1611), Galileo, Opere , iii/1, 251–90, pp. 281–3; and Ingoli Francesco , “De situ et quiete terrae contra Copernici systema disputatio” (Ms., 1615), ibid. , v, 403–12, p. 409. Giambattista Riccioli (1598–1671) quotes it among his 77 arguments against the motion of the Earth: Riccioli, Almagestum novum (2 vols, Bologna, 1651), ii, 450b–4a (Lib. 9, sect. 4, cap. 28). The Copernican explanation for its absence is granted by de Rheita Maria Schyrleus Anton ( Oculus Enoch et Eliae sive radius sidereomysticus (2 vols, Antwerp, 1645), i, 194b) and implicitly also by Kircher ( ltinerarium (ref. 3), 267–8, 350 and Iter (ref. 3), 349–50, 411).

Copernicus , De revolutionibus (ref. 5), 21.

Galilei , Dialogo , in Opere , vii, 413: “Salv[iati]. Vorrei che voi diceste, che quando una tal diversità [sc. parallactic shift] si scorgesse, niuna cosa resterebbe più che potesse render dubbia la mobilità della Terra, atteso che a cotal apparenza nissun altro ripiego assegnar si potrebbe. Ma quando bene anco ciò sensibilmente non apparisse, non però la mobilità si rimuove, nè la immobilità necessariamente si conclude, potendo esser (come afferma il Copernico) che l'immensa lontananza della sfera stellata renda inosservabili cotali minime apparenze….” Translation from Drake Stillman , Galileo: Dialogue concerning the two chief world systems (Berkeley, ³1962), 386–7.

Galileo , Dialogo , in Opere , vii, 409–12, 414–16.

Galileo , Dialogo , in Opere , vii, 399–416. In contrast Kepler's report on Tycho's failure to detect stellar parallax is given in only a single page: Kepler Johannes , Epitome astronomiae Copernicanae (Linz, 1618), 493.

Galileo , Dialogo, in Opere , vii, 399, 400, 404, and 413–14.

Galileo , Dialogo, in Opere , vii, 399.

Galileo , Dialogo , in Opere , vii, 404.

Galileo , Dialogo , in Opere , vii, 416: “Salv[iati]. A me par tutto l'opposito, perchè non ha del verisimile che, se alcuno l'avesse sperimentata, non avesse fatto menzione dell'esito, se succedeva in favore di questa o di quella opinione; oltre che nè per questo nè per altro fine si trova che alcuno si sia valso di tal modo di osservare, il quale anco, senza telescopio esatto, malamente si potrebbe effettuare”.

Galileo , Dialogo , in Opere , vii, 414, I. 36.

Kepler suggests a distance of 60 million Earth radii ( Epitome (ref. 11), 492), and this is the greatest distance a Copernican assumed explicitly in the first half of the seventeenth century; cf. the table in Riccioli, Almagestum novum (ref. 7), i, 419a. On the basis of Gottfried Wendelin's measure for the apparent diameter of the Sun, Riccioli ( ibid. , i, 419b) calculates a distance of 604,589,312 Earth radii.

Brahe Tycho , Epistolae astronomicae (Uraniburg, 1597), 167, cites 7,850,000 [Earth radii]. Tycho's calculation (2284 E.r. / tan (1/60) = 7,851,813.4 E.r.) is based on the apparent diameters of stars of almost third magnitude (1 1/12′: See Tycho, Astronomiae instauratae progymnasmata (Prague, 1602), 482; for Saturn's distance he assumes 10,550 E.r. ( ibid. 476)).

The same calculation is in his Progymnasmata (ref. 18), 481, where Tycho concludes: “quod absurdum est credere”.

Longomontanus Christian S. , Astronomia Danica (Amsterdam, 1622), ii, 19, 21; and Libertus Fromondus (Froidmont), Ant-Aristarchos sive orbis-terrae immobilis (Antwerp, 1631), 64–71. Overall the anti-Copernican arguments of Tycho's Epistolae astronomicae (ref. 18) were widely used by geocentrists. See Bucciantini Massimo , Galileo e Keplero: Filosofia, cosmologia e teologia nell'Età della Controriforma (Turin, 2003), 57–62.

Scheiner Christoph , Disquisitiones mathematicae, de controversiis et novitatibus astronomicis (Ingolstadt, 1614), 27; Michael Mästlin's comments on Rheticus's Narratio prima (²1541) as reprinted in the second edition of Kepler's Mysterium cosmographicum (Frankfurt, 1621), 113, 114–15; and Galileo , Dialogo , in Opere , vii, 389.

Brahe Tycho , Progymnasmata (ref. 18), 482. Combining the measurement of several instruments, Tycho determined with an accuracy of 25” the positions of several bigger stars: Wesley Walter G. , “The accuracy of Tycho Brahe's instruments”, Journal for the history of astronomy , ix (1978), 42–53, p. 51.

Mästlin's comments in Kepler's Mysterium cosmographicum (ref. 21), 114: “Nec enim ulla necessitas exigit, illam Infinitatis similitudinem eousque ampliari, donec Orbis Terrae Magnus ad Stellatum Orbem prorsus, ut Tycho putat, euanescat (licet idem Orbis Magnus etiam secundum Tychonis numeros nondum prorsus euanesceret, siquidem in Stellis fixis in parallaxin ultra duas quintas, hoc est, ferme ad semissem unius scrupuli primi procrearet) quia etiam longe restrictior eius altitude immensa, hoc est imperscrutabilis, et nullis instrumentis, nulloque artificio inuestigabilis est…”.

Ibid. 114: “Ergo Copernicum ad oculorum iudicium, non ad universalem omnis parallaxeos exclusionem respexisse, extra dubium est…”.

Galileo , Dialogo, in Opere , vii, 399; Kepler , Epitome (ref. 11), 493.

Galileo (Padua) to Kepler (Graz), 4 Aug. 1597, in Galileo , Opere , x, 67–68 (no. 57). For a ‘Microstoria’ of this letter, see Bucciantini, op. cit. (ref. 20), 49–68.

Kepler (Graz) to Galileo (Padua), 13 Oct. 1997, Galileo , Opere , x, 69–71 (no. 59): “Nunc abs te placet aliquid observationum postulare: Scilicet mihi, qui instrumentis careo, confugiendum est ad alios. Habes quadrantem in quo possis notare singula scrupula prima et quadrantes primorum? Observa igitur, circa 19 Decembris futurum, altitudinem eductionis caudae in Ursa [sc. ε UMi] maximam et minimam eadem nocte. Sic circa 26 Decembris observa similiter utramque stellae polaris [sc. α UMi] altitudinem. Primam stellam observa etiam circa 19 Martii anni 98, altitudine nocturna, hora 12; alteram, circa 28 Septembris, etiam hora 12. Nam si, quod opto, differentia quaedam inter binas observationes intercedet unius atque alterius scrupuli, magis si decem aut quindecim, rei per totam astronomiam latissime diffusae argumentum erit; sin autem nihil plane differentiae deprehendemus, palmam tamen demonstrati nobilissimi problematis, hactenus a nemine affectatam, communiter reportabimus. Sapienti sat dictum”.

Galileo writes his next letter to Kepler thirteen years later, on 19 Aug. 1610 (Galileo, Opere , x, 421–3, no. 379), having himself received two letters: Kepler (Prague) to Galileo (Padua), 19 April 1610 ( Galileo , Opere , x, 319–40 (no. 297)), and 9 Aug. 1610 ( ibid. , 413–17 (no. 347)). Arthur Koestler explains this silence by Galileo's taking offence at Kepler's exhortations, whereas Massimo Bucciantini alleges Galileo's prudence because of Kepler's being the disciple of Michael Mästlin whose books were put on the Index and who was in public dispute with Christoph Clavius over the Gregorian Calendar Reform: See respectively Koestler A. , The sleepwalkers (London, ⁶1968), 359–60, and Bucciantini , op. cit. (ref. 20), 74–81.

About Ramponi little is known; he had been baptized in Bologna on 19 ( Galileo , Opere , xx, 515b). On Roffeni see Denise Aricò, “Giovanni Antonio Roffeni, un astrologo bolognese amico di Galileo”, Il carrobbio , xiv (1998), 67–96.

Ramponi Bologna Galileo (Florence), 1 July 1611 ( Galileo , Opere , xi, 133–6 (no. 548)). Ramponi reveals his initial assumption concerning Galileo's detection of stellar parallax in his next letter: Ramponi to Galileo , 23 ( ibid. , 159–62 (no. 561)).

Ramponi Bologna Galileo (Florence), 23 July 1611 ( Galileo , Opere , xi, 159–62 (no. 561)); cf. the passage quoted above (ref. 9) from Galileo , Dialogo ( Opere , vii, 413).

Ramponi Galileo , 23 July 1611 (ref. 31): ”Per far questo, giudicarei che fussero molto a proposito quei luoghi ne i quali si veggiono le stelle frequentissime, come V. S. ha di già dissegnato nel Nuntio, perciò che per la loro quasi contiguità, per la quale sono comprese con lo stromento tenuto immobile, potrebbesi vedere con più facilità e sicurezza se mutino le configurationi e distanze tra loro; il che se fia, ecco dimostrata a un tratto la mobilità della terra, la distanza delle stelle fisse, da molti per la grande vastità abhorrita, e il sito delle stelle fisse, l'una più lontana dell'altra dalla congerie di questi nostri corpi, che solo credo poter essere cagione di questo truovamento, come appare qui accennato: Dove, al sito della terra in D vedesi la stella A congiunta con la C, et la B antecedere la C; là dove poi nel sito E vedensi le due A et C disgiunte, et la B seguire alla C. Quando in quelle stelle così frequenti apparisse una tale disordinanza nelle figure e distanze loro, parmi che la hipothesi Copernicana sarebbe dimostrata.”.

Neither Ramponi in his letter (“quasi contiguità”) nor Galileo in the Dialogo (“vicinissima”) describes the nearby stars as double stars: Galileo , Opere , xi, 161, *II. 75–79, and vii, 409, *II. 31–35 respectively. For this reason William Herschel, despite knowing very well Galileo's methods of detecting stellar parallax, considered himself to be the first to apply Galileo's second method to double stars: Herschel W. , “On the parallax of the fixed stars”, Philosophical transactions , lxxii (1782), 82–111, p. 88. However, as we will see below, the phenomenon of double stars turns up in Galileo's correspondance.

William Herschel surely contributed to this view by assuming that Galileo had only “pointed out” the method of direct measurement “first attempted by Hook” and had “suggested” a second method of relative measurement: ibid. 84 and 88. In contrast, Umberto Fedele (see ref. 63), 67, and, though without citing evidence, Emilio Bianchi (“Il problema delle parallassi stellari”, Rendiconti del seminario matematico e fisico di Milano , iii (1929), 224–50, p. 225) take it for granted that Galileo used his telescopes for the search of stellar parallax.

Hoskin Michael A. , “Stellar distances: Galileo's method and its subsequent history”, Indian journal of history of science , x (1966), 22–29, p. 28: “… it was fitting that two of the three successful measurements, and in particular the one that carried immediate conviction in the astronomical world, were made by the technique of double stars that Galileo had proposed more than two centuries before.” Galileo describes this second method in Dialogo ( Opere , vii, 409, and 411–12).

Cf. Ramponi Galileo , 23 July 1611 ( Galileo , Opere , xi, 161 (sketch)), and Galileo , Dialogo ( Opere , vii, 412 (drawing)).

Drake Stillman , “Galileo's first telescopic observations”, Journal for the history of astronomy , vii (1976), 153–68, p. 159: “I think it likely enough that by March 1610 he [sc. Galileo] had managed to make a 30-power telescope…”.

Scheiner Christoph , Tres epistolae de maculis solaribus: Scriptae ad Marcum Velserum (Augsburg, 5 Jan. 1612) ( Galileo , Opere , v, 21–33).

Galileo (Villa delle Selve) to Marcus Welser (Augsburg), 4 May 1612, published in Galileo , Istoria e dimostrazioni intorno alle macchie solari e loro accidenti (Rome, 1613) ( Galileo , Opere , v, 94–113, p. 95). Galileo's claim to priority is confirmed by Angelo de Filiis, member of the Accademia dei Lincei, in his preface to this book: Galileo , Opere , v, 84. Galileo had mentioned his sunspot observations for the first time in print in Galileo, Discorso intorno alle cose, che stanno in su l'acqua, o che in quella si muovono (Florence, (May) 1612): Galileo , Opere , iv, 58–141, p. 64.

Harriot Thomas (1560–1621) never published his sunspot observations, which he had made in December 1610. Fabricius David (1564–1617) and his son Johannes (1587–1616), however, did publish theirs: Johannes Fabricius, De maculis in Sole observatis, et apparente earum cum Sole conversione narratio (Wittenberg, 1611). Kepler (Linz) reports this publication in his letter to Oddo van Maelcote (Brussels), 18 July 1613 ( Galileo , Opere , xi, 536–7 (no. 902)). For the chronology of these observations see especially Galileo, Dialogo , ed. by Besomi Ottavio Mario Helbing (Padua, 1998), ii, 720–35. See also Shea William R. , “Galileo, Scheiner, and the interpretation of sunspots”, Isis , lxi (1970), 498–519; Feldhay Rivka , Galileo and the Church: Political inquisition or critical dialogue? (Cambridge, 1995), 256–91; and Biagioli Mario , “Picturing objects in the making: Scheiner, Galileo and the discovery of sunspots”, in Wissensideale und Wissenskulturen in der Frühen Neuzeit , ed. by Wolfgang Detel Claus Zittel (Berlin, 2002), 39–96, pp. 53–96.

Faber Giovanni (Rome) to Galileo (Pisa), 15 Dec. 1611 ( Galileo , Opere , xi, 238–9 (no. 614)); Welser Marcus (Augsburg) to Faber (Rome), 16 Dec. 1611 (Galileo, Opere , xi, 246 (no. 622)); Welser (Augsburg) to Galileo (Florence), 6 Jan. 1612 ( Galileo , Opere , v, 93 and xi, 257 (no. 637)). The day of publication of Scheiner's Tres epistolae de maculis solaribus is given on the title page (“M.DC.XII. Non. Ian.”).

See Ramponi's third letter to Galileo where he refers to his unanswered second letter of 23 July 1611: Ramponi (Bologna) to Galileo (Florence), 21 May 1612 (Galileo, Opere , xi, 299–300 (no. 679)).

Ramponi to Galileo , 23 July 1611 (Galileo, Opere , xi, 160 (no. 561)), and 21 (ibid., 300 (no. 679)).

From Ramponi's four letters to Galileo published in Galileo, Opere and cited in this paper, there is evidence for only one reply from Galileo (to Ramponi's first letter). In his last letter Ramponi begs farewell to Galileo, declaring that he will never write to him again, because he has not received replies: Ramponi (Bologna) to Galileo (Florence), 11 July 1612 ( Galileo , Opere , xi, 359–60 (no. 727)).

Hooke , op. cit. (ref. 1).

Lodovico Cardi/Cigoli (Rome) to Galileo (Florence), 30 June 1612: “Il Pasigniano, huomo molto di sua oppinione, à sentito da non so chi questa sua; et l'altra sera me la diceva, che lo avete chiaro, tenendo ancora duro la sua, et che non guarda più sole, ma che attende ai movimenti delle stelle, et che vede visibilmente che la terra si move in 24 ore, et d'altro moto che fa la state e 'l verno, et il sole sta fermo: Dove li soggiunsi che V. S. dice che si rivolgie in sè stesso ancora lui; dove egli se ne rise, et io ancora delle sue sentenzie così dintornate e risolute, senza mai dire altro che le cose ch'egli sente da il Signior Lucha o 'l Padre Gambergier, e le vole lucidare, e le storpia, che è cosa ridicola, et che si fa fare uno ochiale a Venezia, che sarà lungho tre braccia, con il quale spera da avere a vedere e speculare cose minimissime et nella luna e nel cielo.” Galileo , Opere , xi, 347–9 (no. 718), p. 348. My thanks to Giulia Giulianelli for verifying this passage. Cigoli had already reported on Passignano's telescopic activities in 1611: Cardi/Cigoli to Galileo, 16. 1611 ( Galileo , Opere , xi, 208–9 (no. 582)), and 23. 1611 ( ibid. , 212–13 (no. 587)). Galileo answered both letters: 1 Oct. 1611 ( Galileo , Opere , xi, 213–14 (no. 588)).

See Ramponi , op. cit. (ref. 44) and Kepler , op. cit. (ref. 28).

Galileo , Dialogo ( Opere , vii, 414–15).

Galileo , Dialogo ( Opere , vii, 409–11).

Galileo , Dialogo ( Opere , vii, 415).

Drake , “Galileo's first telescopic observations” (ref. 37), 159. In one of his undated observation notes Galileo mentions a 32-power telescope: Galileo, “Analecta astronomica” [Ms.] ( Galileo , Opere , iii/2, 872–80, p. 878; later references to this work will cite the page from Opere).

Galileo (Bellosguardo) to Cesare Marsili (Bologna), 5 April 1631 ( Galileo , Opere , xiv, 239–41 (no. 2137)).

For the year 1616 see below. For the years 1617 to 1631 see Galileo , Dialogo (ref. 40), ii, 795–6. The owner of the villa was Lorenzo Segni.

Castelli Benedetto (Pisa) to Galileo (Florence), 16 Nov. 1616 ( Galileo , Opere , xii, 296 (no. 1236)): “Ho osservata di novo la constellazione della prima delle tre stelle nella coda dell'Orsa maggiore post eductionem caudae, e mi è parsa tale la constituzione con quella che se li vede vicinissima con la vista naturale e quell'altra visibile solo con l'occhiale: Quella notata A è la prima delle tre etc.; quella notata B è la vicina etc., e finalmente quella notata C è la visibile con l'occhiale. Ma se mal non mi ricordo, questa estate a Bellosguardo la C era talmente situata con l'altre due, che in lei si formava un angolo retto, tirando le linee dalla C alla B et A. Però V. S. ci faccia un puoco di reflessione, quando ne habbia comodità…”.

The third star in question is of the eighth magnitude (HD 116798, TYC 3850-00257-1) and no longer known as Stella Ludoviciana (Ludwigs-Stern, or Louis's Star), the name given it by Johann Georg Liebknecht (1679–1749), professor of mathematics and theology in Gießen, whose sovereign was Landgrave Ernst Ludwig (1678–1738) of Hesse-Darmstadt. Watching this star on 2. 1722, Liebknecht mistakenly believed he had detected not only a new star but even its proper motion. In the following year he published his discovery and defended it subsequently against objections from Ludwig Philipp Thümmig (1697–1728), a disciple of Christian Wolff: Johann Georg Liebknecht, Sidus boreale stella noviter detecta stipatum et … Ludovicianum nuncupatum (Gießen, 1723), and Uberior stellae Ludovicianae noviter detectae consideratio (Gießen, 1723).

For a 30-power telescope of Galilean type the field of view is even more reduced. Mizar and Alcor are about 12 arc-minutes distant from each other and respectively 9 and 6 arc-minutes from the Stella Ludoviciana.

Castelli (Pisa) to Galileo (Florence), 7 Jan. 1617 ( Galileo , Opere , xii, 301 (no. 1241)): “Non manco d'andar in busca di stelle fisse; ma non trovo cosa al proposito, fuor che le avvisate nelle passate”.

Galileo , “Analecta astronomica” (ref. 51), 880.

Ibid. 879: “Facciasi un angolo di cartone, che, messo nella cima del telescopio, passi per le 3 stelle notate etc., come nell'esempio qui sotto: [sketch]”.

Castelli (Pisa) to Galileo (Florence), 7 Jan. 1617 ( Galileo , Opere , xii, 301 (no. 1241)): “Per l'osservazione della Canicola ho ritrovato un luogo nel quale si potrà collocare il lumicino, e di poi allontanarsi 150 braccia in circa per osservare: E quanto prima il tempo me ne dia licenza, mi metterò all'impresa”.

These three Sirius observations are recorded together with Galileo's sketch of the aperture mask on the same sheet of paper: Galileo, “Analecta astronomica” (ref. 51), 879. For the Sun's position we read respectively. The exact day to be deduced from the zodiacal position depends on the year in question, i.e. whether it is a leap year or the first, second or third year after a leap year. Assuming the year 1616 for Galileo's first observation we obtain the following dates: 22 December 1616 (), 27 March 1617 () and 21 April 1617 (). We have used Clavius's tables for determining the dates of Galileo's zodiacal notation: Christoph Clavius, In sphaeram Ioannis de Sacro Bosco commentarius, Opera mathematica (5 vols, Mainz, 1611–12; reprinted, Hildesheim, 1999), iii, 159–62.

Castelli (Pisa) to Galileo (Florence), 7 Jan. 1617 ( Galileo , Opere , xii, 301 (no. 1241)): “Non manco d'andar in busca di stelle fisse; ma non trovo cosa al proposito, fuor che le avvisate nelle passate. Desiderarei che V. S. Ecc.^ma, concedendoglielo la sanità, una sera desse un'occhiatina a quella stella di mezo delle tre che sono nella coda dell'Orsa maggiore, perchè è una delle belle cose che sia in cielo, e non credo che per il nostro servizio si possa desiderar meglio in quelle parti”.

Fedele Umberto , “Le prime osservazioni di stelle doppie”, Coelum , xvii (1949), 65–69 (reprinted in: Coelum astronomia: Edizioni scientifiche Coelum , liv (2002), 57–59). Fedele's almost forgotten article was brought to my attention by Leos Ondra, “Il volto nuovo de Mizar”, Coelum astronomia: Edizioni scientifiche Coelum , liv (2002), 52–56, who has also provided an English version: http://leo.astronomy.cz/mizar/fedele.htm.

Riccioli , Almagestum novum (ref. 7), i, 422a (Lib. 6, cap. 9): “Primus modus observandi diametros stellarum nititur oculari aestimatione…, quae coniectura errori proculdubio exposita est…, adeo ut stella unica videatur illa, quae media est in cauda Ursae maioris, cum tamen sint duae, ut Telescopium prodidit….” Ronchi thinks that Martin Horky saw the doubling of Mizar already on 24/25 April 1610: Vasco Ronchi, Galileo e il cannocchiale (Udine, 1942), 266. However, Fedele, op. cit. (ref. 63), 67, shows that Horky referred to the optical double star formed by Alcor and Mizar and not to the binary Mizar A and B.

Schürle Maria Anton mentions a triple star (“stella tricorporea”) described and illustrated as a multiple star, which he had observed in the Orion constellation: Rheita, Oculus Enoch (ref. 7), i, 198a and illustration (sheet G, figure 7) at the end of vol. ii. Johann Baptist Cysat ( Mathemata astronomica (Ingolstadt, 1619), 75), had published an observation of five double or multiple stars in Praesepe, but he considered them star clusters: “… quini stellularum cumuli qui in unica Nebulosa Cancri per Tubum spectantur, ex nubilo lumine constantes intermicantibus aliquot stellulis.” For Cysat's observation, see Siebert, op. cit. (ref. 4), Anhang (appendix).

Through statistical analysis Michell John (1724–93) demonstrated “with the highest probability … that the stars are really collected together in clusters in some places, where they form a kind of systems”: Mitchell J. , “An inquiry into the probable parallax, and magnitude of the fixed stars, from the quantity of light which they afford us, and the particular circumstances of their situation”, Philosophical transactions , lvii (1767), 234–64, p. 249.

For their idea of stellar systems Rheita and Kircher were both criticized by the von Guericke Otto Copernican , Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio (Amsterdam, 1672), 230a,b and 235b–236a respectively. Hodierna G. B. ( De systemate orbis cometici deque admirandis coeli characteribus (2 vols, Palermo, 1654), ii, Sectio quarta, Corollaria 1, 3, 4) does not exclude the possibility of (physical) multiple stars (see Domenico Ognibene's Italian translation of this very rare book on http://www.orsapa.it/hodierna/index.htm). For these non-Copernican conceptions of stars and the forgotten stellar astronomy of the Tychonics see Siebert, “Die große kosmologische Kontroverse” (ref. 4), 208–77.

Owen Gingerich's aphorism.

Huygens and Newton were the most prominent astronomers who tried to gauge the distance of stars by measuring their brightness. This was to be another project of William Herschel's. Stellar uniformity, however, was contradicted by Kircher and questioned by Rheita and Hodierna.

Huygens Christiaan , KOΣMOΘEΩPOΣ (The Hague, 1698), Oeuvres complètes (ref. 2), xxi, 815.

Castelli (Pisa) to Galileo (Florence), 22 Feb. 1617 ( Galileo , Opere , xii, 309 (no. 1248)): “Similmente le due della coda dell'Orsa si sono tra di loro allontanate, se ben poco; ma io che so benissimo come stavano, almeno quanto alla vicinanza tra di loro, non ho dubbio dell'essersi allontanate”.

Galileo , “Analecta astronomica” (ref. 51), 877: “Media caudae Elicis incidit secundum latitudinem in gr. 9 m, et latitudo eius est gr. 56. Terra est modo in 25 , ex quo locus * ab ea distat gr. 44.” Helice or Elice is another name for the Great Bear. Galileo measures for Mizar's position 56° ecliptical latitude and an ecliptical longitude of 159° (5 × 30° + 9°, Virgo being the sixth zodiacal constellation starting from the First Point of Aries). He deduces an angular distance of 44° between Mizar and the Earth whose position on the zodiac is 25° Cancer, which corresponds to an ecliptical longitude of 115°. The Sun's position in the zodiac is 180°, opposite to that of the Earth. Hence the zodiacal position of the Sun is 25° Capricorn. From Clavius's tables we read for this the date 15 January (for a year such as 1617, i.e. annus primus post bissextum): Clavius, In sphaeram (ref. 61), iii, 161. By taking as entry date of Capricorn 22 December ( ibid. 157) and adding (25°/360° × 365 =) 25 days we get the same date, which is also assumed for the year 1617 by Fidele (ref. 63), 68.

Galileo , “Analecta astronomica” (ref. 51), 877: “Inter mediam caudae Elicis et sibi proximam pono nunc gr. 0.0′, 15”. Semidiameter stellae maioris gr. 0.0.3”, minoris vero 2”, et intercapedo 10””.

The Tycho Double Star Catalogue [TDSC], ed. by Fabricius C. , 2002 (Mizar's TDSC Number is 35543), to be consulted on http://vizier.u-strasbg.fr/cgi-bin/VizieR (under Mizar's Henry Draper no. HD 116656).

Galileo , “Analecta astronomica” (ref. 51), 877: “Semidiameter orbis magni continet semidiametros ⊙ 226. Semidiameter ⊙ continet semidiametros stellae maioris 300. Distantia ergo stellae continet distantias ⊙ 300 (si stella ponatur tam magna ut ⊙), hoc est semidiametros ⊙ 67800.”.

Following the rule of stellar distances (d, in astronomical units) and stellar parallax (p, being half of the angle of a star's total shift in the sky) we obtain for Mizar A at a distance of 300 AU (p = arc tan 1 AU/300 AU =) 0.19° or 11.5′ as parallactic shift due to the Earth's revolution over three months.

Gauging the distance of Mizar B the same way Galileo did for Mizar A, we obtain 450 AU and thus a parallax of 7.6′.

The relative distance between Mizar A and B would vary by (11.5–7.6 =) 3.9′ over three months.

This is the only dated observation in Galileo's “Analecta astronomica” (ref. 51): “Apposita fixarum constitutio reperta est a me prope cuspidem ensis Orionis…. Haec observata sunt a me die 4 Februarii 1617 a Bellosguardo” (p. 880).

Galileo , “Analecta astronomica” (ref. 51), 880: “Incidit cuspis ensis Orionis in gr. 18 II cum latitudine australi gr. 30.” Hence Galileo had observed the θ¹ Orionis stars in the so-called Huygens Region before Giovanni Battista Hodierna ( De systemate orbis cometici deque admirandis coeli characteribus (2 vols, Palermo, 1654), ii, 19) and long before Huygens himself ( Systema Saturnium (The Hague, 1659), 8–9; Oeuvres complètes (ref. 2), xv, 237–8). Unlike Hodierna, however, who would be the first to discuss the Orion Nebula in print, Galileo did not even mention it.

Castelli (Pisa) to Galileo (Florence), 22 Feb. 1617 (Galileo, Opere , xii, 309 (no. 1248)): “L'osservazione accennatami da V. S. in Orione non m'è riuscita, perchè non ho mai ritrovate le stelle che lei mi nota”.

Galileo , “Analecta astronomica” (ref. 51), 880: “Distantia inter a, b iudicatur 3 2 semidiametros, ad quam distantia b g videtur tripla.” Thus the lower parallel side (a, b) of the trapezoid is three times Jupiter's apparent radius (3·33/2); this length is approximately 50” while its uper side is about 2′30” away. In contrast, the θ¹ Orionis stars of the Trapezium are not more than 20” from each other.

The lower parallel side of this larger trapezoid is formed by the variable star TYC 4774-00934-1 (mag. 6.2) and 43 θ² Ori (mag. 5, TYC 4774-00933-1); these are separated by 52” and so represent Galileo's a and b stars respectively, for which he measured a relative distance of 50 “(see ref. 82). In a range of 2′30” from b to the northeast as indicated by Galileo we actually find for his g-star 41 θ¹ Ori (mag. 6.5, TYC 4774-00953-1) at a distance of 2′27” from 43 θ² Ori (Galileo's b). Hence Galileo's g-star is one of the bright stars of the Orion Trapezium. Together with 41 θ¹ Ori (mag. 6.3, TYC 4774-00930-1) at a distance of 19” (missing in Galileo's sketch) it lies parallel to the lower (a, b) side of Galileo's trapezoid, whereas in his sketch the upper parallel side is made by the stars near g, i.e. c and i (forming a narrow isosceles triangle).

Galileo's g-star (see ref. 83), one of the Trapezium θ¹ Orion cluster, is itself a close binary (TYC 4774-00953-1, resolved in WDS 05353–0523 [AE] and in HIP 26220 [BH]) whose components (mag. 6.7 and 11.1) are separated by 4.1” today. They form a triple star together with the equally-near variable star (mag. 7.2, TYC 4778-01358-1), which is too bright to match Galileo's depiction, but is suspected to have an intrinsic variability. It is catalogued as an eighth-magnitude star (mag 8.2) in the Bonner Durchmusterung (1859–1903) and may have been still fainter in 1617. For the performance of Galileo's (mostly lost) telescopes, see the Galilean Telescope Homepage: http://www.pacifier.com/∼tpope/index.htm.

On the line between Galileo's b-star (43 θ² Ori, TYC 4774-00933-1) and his g-star (41 θ¹ Ori, TYC 4774-00953-1) separated by 2′30” (see ref. 83) lies another bright star of the Orion Trapezium, 41 θ¹ Ori (mag. 5, TYC 4774-00931-1), 2′16” away from b and missing in Galileo's sketch.

Galileo , “Analecta astronomica” (ref. 51), 880: “… duae vero c, i admodum exiguae, nempe vix 4^a aut 5^a pars ipsius g…. Duae c, i aequaliter distant a g, quam fere tangunt…. Insuper intercapedo inter g et quamlibet ipsarum c, i vix caperet alteram g.”.

Castelli (Pisa) to Galileo (Florence), 22 Feb. 1617 ( Galileo , Opere , xii, 309 (no. 1248)): “È ben vero che havendo ai 30 di Gennaio osservato tra ‘I Cane maggiore e la spalla sinistra d'Orione circa 'l mezo un triangolo e nell'angolo orientale una stella, restai in dubbio, dopo diligente e replicata osservazione, se era una o due; et hora, ritornato alla medesima osservazione, le ritrovo chiaramente due, sichè il gioco si fa.”.

Castelli (Pisa) to Galileo (Florence), 22 Feb. 1617 ( Galileo , Opere , xii, 309 (no. 1248)): “Similmente le due della coda dell'Orsa si sono tra di loro allontanate, se ben poco; ma io che so benissimo come stavano, almeno quanto alla vicinanza tra di loro, non ho dubbio dell'essersi allontanate.”.

Castelli (Pisa) to Galileo (Florence), 22 Feb. 1617 (Galileo, Opere , xii, 309 (no. 1248)): “Io ho ancora certe altre osservazioni, delle quali meglio trattaremo a bocca, compiacendosi lei di trasferirsi sin qua; e così ancora potra dar ordine all'altro capo dell'osservazioni, il che riuscirebbe esquisitamente di qua e di là d'Arno, stando noi a osservare nel Long'Arno esposto al mezo giorno, et il segno sopra le case che sono di là d'Arno. Haverei ancora qua nel giardino de’ Padri di S. Girolamo qualche sito per il Can maggiore, ma dubito che la distanza non basti; tuttavia, se lei si risolve di venire, trattaremo e concluderemo qualche cosa”.

Galileo , “Lettera a Francesco Ingoli in risposta alla Disputatio de situ et quiete Terrae” [Ms., 1624], Galileo , Opere , vi, 509–61, p. 553: “… ed in tanto vi dico, che non avendo voi per voi stesso fatte tali osservazioni, non dovete prestar così ferma fede a Ticone ed a' suoi strumenti, inabili per avventura a poter distinguere tali minuzie, che forse con altri strumenti, e molto maggiori e molto più perfetti ed assai diversi, potrebbero un giorno esser comprese.” Galileo refers to Ingoli Francesco , “De situ et quiete Terrae” [Ms., 1615], Galileo , Opere , v, 403–12, p. 409. On Galileo's response see Massimo Bucciantini, Contro Galileo: Alle origine dell'affaire (Florence, 1995), 149–74.

Fiocca Alessandra , “I gesuiti e il governo delle acque del basso Po nel secolo XVII”, in Maria Teresa Borgato (ed.), Giambattista Riccioli e il merito scientifico dei gesuiti nell'età barocca (Florence, 2002), 319–70, pp. 340–54.

Castelli (Rome) to Galileo (Florence), 7 Aug. 1627, Galileo , Opere , xiii, 372–3 (no. 1834): “Ho osservata la stella settentrionale delle tre della fronte del Scorpione, quale ha una stellina vicinissima, più settentrionale di essa, nella continovazione dell'arco delle tre della fronte, in questa maniera: [Castelli's sketch, see Fig. 6] [/] V. S. mi faccia grazia di scrivermi che gioco doverà fare, movendosi la terra, caso che lei sia assai più lontana dalla terra della altra compagna, visibile con la vista naturale.”.

The northern star in the head of Scorpius is 8 β Scorpii (also called Graffias or Acrab): Fedele , “Le prime osservazioni di stelle doppie” (ref. 63), 68; Ondra , “A new view of Mizar” (ref. 63). However, Castelli did certainly not mean the physical double star β Scorpii itself, whose components are visible without a telescope (mag. 4.5 and 2.5 respectively), whereas Castelli distinguishes only the brighter star with naked eye. Moreover the components are too distant from each other (separated by 24.7” in 1627) to match Castelli's description according to which the fainter star (“stellina”) is most close (“vicinissima”) to the brighter. Castelli's tiny star lying nearby north to Graffias (8 β¹ Sco) must be TYC 6208-00095-1, a star of almost eleventh magnitude (10.94). although it would be surprising if so faint a star were within reach of his telescope (see also ref. 84 above). In 1627 its distance to Graffias was about 9” and it continued the arc formed by the three stars in the head of Scorpius (6 π Sco; Dschubba, 7 δ Sco; Graffias, 8 β Sco) in accordance with Castelli's sketch). For recalculating the stars' position the software Redshift™ from United Soft Media was used.