Galileo and Satellite Prediction

Favaro A. (ed.), Opere di Galileo Galilei (2nd edn, Florence, 1929–39), iii, 412.

Meeus Jean , “Tables of the satellites of Jupiter”, Journal of the British Astronomical Association, lxxii (1962), 80–88.

Opere, iii, 183–4, from Kepler Johann , Narratio de observatis … (Frankfurt, 1611), written at Prague, 11 September 1610.

These include inexactness of recording observed elongations, slowness of motion at maximum elongations, inadvertent cancellation of a satellite in conjunction with another, mistaken identification of nearly adjacent satellites, eclipsed satellites, and the like.

Opere, iii, 427–39; p. 948, last entry.

Opere, x, 483.

Opere, iii, 439.

Galileo gave times in hours after sunset, Florence meridian.

Opere, iii, 440. This set of observations was communicated by letter to Christopher Clavius the next day, but without Galileo's deductions from it. As Favaro remarked, the note may not have been written at once, though I think it most probable that it immediately followed his transcription of the data for his letter to Clavius.

Opere, iii, 440.

Opere, iii, 822–23.

Opere, iii, 439.

In fact the period of I is nearly 42 ½ hours, and on 6 January 1611 at the sixth hour after sunset it was already some 20° beyond apogee and nearly far enough from Jupiter for Galileo to have seen it on a clear night. It had thus made more than 13 revolutions since 14 December, but not 13 ½ as Galileo supposed. It is noteworthy that in this first forecast of his he left it open whether any conjunction was apogee or perigee, information he obtained on the final day predicted; see below.

Opere, iii, 440.

Opere, iii, 441.

Opere, iii, 441.

Opere, xi, 76, where the value ascribed to Magini contains a misprint.

Opere, iii, 441.

Without entering into details, it was Galileo's initial placement of apogee for III at the fourth hour and his almost immediate shift of this to the fifth and finally the sixth hour that convinced me that his note of 24 January was written at that time or not much later. Otherwise it would have been natural for him to suppose that one satellite was in conjunction with Jupiter at his first observation on 15 March, as indeed was the case.

One of these, made at Siena on 24 March, was invaluable to him when he began his analysis, for only one satellite was seen and he was able to mark this c, probably a few days later; see below.

Opere, xi, 80–81.

Opere, iii, 948. The dates 5 January and 5 March transcribed by the editors at the top of this entry are certainly incorrect. That the second should be 15 March is evident from the table, and Galileo had recorded no observation for 5 January other than at the fourth hour, from which perigee of II an hour later would be quite impossible.

Opere, iii, 946. Without this facsimile it would, I believe, have remained impossible to arrive at a plausible chronology of the events from Favaro's partial printed transcription.

See ref. 19, above. Galileo appears to have started by taking the fourth hour after sunset as the tentative apsidal time of all four satellites on 15 March—that is, one hour after he had first found all to be invisible to him—and then to have adjusted the time for each satellite according to other records or estimates in his journal of observations. Thus he can only have explained his seeing but three satellites at the beginning along the line previously outlined.

Opere, iii, 442. The basis for the times estimated here is not clear except for II, which Galileo could have supposed to be one-half radius from the western edge of Jupiter at 2:00, where he could not see it. But from his previous assignments of speeds the times of I and III appear to be reversed.

Opere, xi, 167 (letter to Nicholas Wickens).

Mayr Simon , Mundus Jovialis … (Nuremberg, 1614); in the translation by Prickard A. O. in Observatory, xxxix (1916), p. 408. On p. 405 Mayr dated his establishment of the periods of IV and III to about June 1610, however, in seeming conflict with both Kepler's statement and Mayr's own claim to have had complete tables at that time.

Cf. Drake S. , “Galileo's first telescopic observations”, Journal for the history of astronomy, vii (1976), 153–68, pp. 161–3.

Mayr , op. cit., tr. Prickard Prickard , 405.

Opere, iii, 491–517.

Opere, iii, 858. A mistaken epoch puts the satellite nearer to Jupiter than observed in two diametrically opposite quadrants and farther away in the other two, from which both the nature and the direction of the error may be known; moreover, the errors do not increase with time as do those arising from mistaken periods.

At the least, it seems to me, this throws in doubt the view that by 1611 Galileo was already a Copernican zealot anxious to find every possible argument for the Earth's motion.

Opere, xi, 430 (10 November 1612).

Mayr , op. cit., tr. Prickard , 409.

Opere, xi, 205, 214–15, 219–20, 225–6. Galileo's replies to Agucchi are lost.

Opere, iii, 446, 539, 859. Having first estimated this as 50”, he found it to diminish from 41 ½” in January to 39 ½” in June as the Earth-Jupiter distance increased.

Opere, iii, 446, last entry; see also the prefatory remarks in Galileo's Bodies in water. G. A. Borelli described the device in his Theoricae Mediceorum planetarum … (Florence, 1666), pp. 142–5 and diagram 57. It utilized superposition of images based on the method Galileo had recommended in the Starry messenger for determining the power of a telescope, the latter being also closely associated with his manner of calculating Jupiter's diameter; cf. ref. 36, above.

Opere, iii, 527–42.

Mayr , op. cit., tr. Prickard , 446.

Drake S. , Discoveries and opinions of Galileo (New York, 1957), p. 51, n. 18 and p. 233, n. 4. Cf. Pannekoek A. , A history of astronomy (New York, 1961), 231.

Opere, iii, 898.

See Meeus , op. cit. (ref. 2), 84. In contrast, Mayr had gone to special pains to prove that IV must be eclipsed during every revolution about Jupiter; cf. Mayr , op. cit., tr. Prickard , 446.

This was Galileo's one unequivocal assertion of the Earth's motion.

Opere, v, 247–9. Galileo did well to mention that errors might be found in his forecasts. The first of the eclipses described, on 24 April, did not in fact begin until about the time Galileo said it would end. The other three, however, took place almost precisely as he said, the greatest error being about twenty minutes in the time on 24 April. As is well known, ignorance of the speed of light prevented precise prediction of eclipses at first. For eclipse predictions, Galileo's epochs of February 1612 were imprecise a year later, though of course for prediction of satellite positions the speed of light was irrelevant because the tables showed relative positions only.