Rethinking and Rebuilding Galileo's Jovilabe Guido Dresti and Rosario Mosello Jovilabe is tbe term used for different types of nomograms and instruments devoted to describing tbe orbits of four Jupiter satellites, fìrst observed by Galileo Galilei in December 1610, using a self-made telescope. Galileo quickly understood tbe importance of tbese observations and tbeir implication in the criti- cism of the Ptolemaic model of tbe sky and the potential practical use for the determina- tion of longitude on tbe sea. He started to study tbe satellites movements with the aim to defìne the ephemerids, using paper nomo- grams, fìve of wbicb have been preserved. ln tbe following decades severa! otber models of jovilabes were proposed and used by differ- ent astronomers, most of them as nomograms on paper or cardboard. A brass versi on of the jovilabe, of unknown author, was found in tbe legacy of Cardinal Leopold de' Medici in 1675, about 30 years after Galileo's death, and it is now part of the Galileo Museum collec- tions in Florence. The paper describes the reconstruction of tbis instrument done by Guido Dresti, an amateur scholar of antique astronomica! instruments (sundials, astrolabes, equatoria, torquetum, Dondi's astrarium). Besides practical details on the instrument construction, the paper will summarize the astronomica! approach and tbe attempts ofGalileo to get advantages from bis discoveries, botb for reaching a position at the court oftbe Medici, and for his criticism to the Earth centric model of the uni verse. Introduction ln January 1610, observing the night sky with a self-made telescope 1 , Galileo noticed three small bright stars, curiously arranged on lines parallel to tbe ecliptic. Continuing the obser- vations in the following nights, he observed tbe presence of a fourth brigbt body and, un- expected, he noticed that distances of the four 'stars' from Jupiter changed, even pass.ing from east to west of the planet. Eventually be realized that the new bodies were satellites ro- tating around Jupiter, a fact not in agreement with the Ptolemaic conception ofthe heaven, already criticized from observers sucb as Tycbo Brahe and Joannes von Kepler. 2 The four satellites were indicated, from the in- ner to the outer, by Roman numbers from I to IV, later named as lo, Europe, Ganymede and Callisto. As the pian of rotation of Earth around the Sun is very close to those of tbe four moons around Jupiter, the observation from Earth shows their movements as trans- versal motion, approaching or moving away from Jupiter. To describe and quantify these motions, since January 1612 Galileo started to use a micrometer-like instrument, formed of a scale he attached to tbe outside of the 14 satellite Jupiter maximum elongation Fig. 1 Maximum elongation of one of the Jupiter satellites. counter-clockwise graduation devised a nomogram, which he called 'jo - vilabe', formed by a graph representing in scale the orbits of the four satellites around Jupiter, observed from a point perpendicular to the piane of rotation (Fig. 2). The mea- surements of distance of the satellite from Jupiter was signed by parallel vertical lines, separated by a distance proportional to a Ju- piter radius. The reading is simple. Suppose that, by observing satellite II (Europe) at tbe telescope, we count an elongation equa! to 8 rays of Jupiter west from the planet. On the jovilabe we count 8 lines and we look at the two intersections of the line with the orbit of Europe (see Fig. 2). Two values of tbe position ofthe planet are identified on the extemal scale, at 301 or 239 degrees. This cboice can be made observing in the follow- ing evenings the position oftbe planet: ifthe elongation is decreasing the satellite is in the lower part of the orbit (239°), if it is in- creasing it is in the upper part (301 °). We bave received fìve jovilabes built by Galileo, ali drawn on paper, the most wom of which is therefore the most used, tums out to be the last. 4 Fig. 2 J ovilabe scheme, with orbitai radii of Jupìter 's satellites and vertìcal lìnes spaced by one radius of Jupit er. An example of the measure of Europe ( li ) positìon is shown (see the text). These measurements were done assuming Earth as a reference system, and this be- came criticai wben Galileo tried to quantify the revolution speeds of the satellites. 5 To overcome tbis point, he need- ed to refer tbe movements to the Sun, which was done mea- suring the jovicentric angle a, obtained from the ratio be- tween the satellite elongation (RS) and its orbit radius (OS) (Fig. 3). Also in this case Gali- leo devised a graphical method to calculate the correction to be made, a correction that he telescope tube. In this way he observed with one eye the instrument, wbile observing with the other the moons through the telescope; the brain perceives tbe two images as super- imposed, allowing a precise measure of the distance s. Since tben he started to take note of the movement of the satellites, using as measurement unit the dimension of Jupiter's radius. 3 He realized the rotation speeds were decreasing from inner to outer satellites, and measured the values ofthe maximum elonga- tion of each planet, obtaining values not far from those accepted today (see Tab. 1 and Fig. !). To make these calculations easier, Galileo called 'prostaferesis' (Fig. 4). He drew the Earth and Jupi- ter orbits around the Sun in the real ratio of 1 :5 ,2 and he found that the value of the prostaferesis varies in the range between about ± 11 °, to add (A) or remove (S) to the jovicentric angle, in relation to the position ofthe Earth in its orbit (Fig. 4). 6 Further important observations concerned eclipses and occultation of the satellites with respect to Jupiter. 7 These events allow a more precise definition of time compared to the planet's motion alone, and the distance of Ju- piter from the Earth is such to make negligible the parallax error. The measure of locai time on tbe ship, from sun or star position, permits Bu ll etin of the Sc ientifì c ln st rument Society No. 140 (20 1 9)