A quantitative analysis of the observations in the Sidereus Nuncius

1 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius A quantitative analysis of the observations in the Sidereus Nuncius A. Longhin Neutrino Telescopes 29 September 2025 Aula Magna G. Galilei del Bo’ di Padova https://arxiv.org/abs/2503.12543 https://www.youtube.com/watch?v=AlmjKkVt0qE 2 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Context 2 ●the name of this conference ●+ this evocative location ●+ a recent personal interest in the work of Galileo ●+ my background (neutrinos) ●+ the kind invitation of the organizers This presentation! I was here 3 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius This presentation 3 This presentation! I was here Disclaimer: I am not an historian of Physics. My focus: try to understand the accuracy & limitations of the observations of Galilei in the Sidereus Nuncius (especially Jupiter). As you will see, this exercise has “automatically” turned into a tribute to the experimental skills of Galileo. 4 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Galileo and Padova 4 ●Galileo lived in Padova from to 1592-1610 (28-46 years old) ●from Pisa where he had already started his academic activity ●he had been hired as professor of “mathematics” ●developed here most of the greatest scientific work of his career ●Important partnerships ●Developed instruments with his collaborators ●Observation of the 1604 SuperNova ●the groundbreaking astronomical discoveries with his “cannocchiale” ●March 1610: the Sidereus Nuncius is published in Venice (Starry Messenger) ●An instant best seller throughout Europe ●The satellites of Jupiter dedicated to Cosimo de Medici (“Medicean satellites”) ●Galileo leaves for Florence in 1610 as a world-level star after having had the recognition of Kepler at those times the imperial astronomer, in Prague “The best 18 years of my life …” 5 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Galileo and the telescope 5 ●Starting from ~1608, being initially a “military secret”, low magnification telescopes based on concave lenses (“Galileian”) had begun spreading widely through Europe. ●Seen as “scientific toy/curiosity” w. moderate magnifications (<10x) ●In 1609 Galileo manages to have one of these instruments in Venice ●He starts grinding lenses with longer focal lengths to increase the magnification. Lenses were a well known technology. Used for glasses and had short focal lengths. ●August 1609 he manages to make a telescope with ~8x . ●Demonstration to the “Doge” of Venice. Increase in salary. ●In late 1609 he manages to reach 20-30x instruments that open the scene to a “shrine” of groundbreaking discoveries! ●In the Sidereus he, fairly, does not claim the discovery of the telescope. Still, according to some historians (i.e. Camerota, Giudice, Bucciantini) it seems that he “engineered” it with collaborators (most notably Paolo Sarpi). Not “acknowledged” due to “strategic” reasons … he did not take it well! From a toy to a forefront scientific instrument August 1609 6 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Where did Galileo observe from? 6 ●From his house in Padova (presently a private residence at via G. Galilei 17) ●It is at ~ 650 m from here on foot, not far from Prato della Valle and the “Basilica del Santo” ●We know from letters that a few observations where done from Venice ●where he was to prepare the printing of the Sidereus Nuncius (!) Loggia e Odeo Cornaro 7 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 7 Specola tower The “crime scene” The skyline to the south with the Basilica del Santo Ponte Molino tower http://www.galileogalilei.padova.it/FotoGallery.aspx 8 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 8 ●Position in the sky of Jupiter for the Sidereus Nuncius observations from Galileo’s house (alt., azimuth) ●Color indicates the observation time Loggia e Odeo Cornaro Basilica del Santo The “crime scene”: consistency checks Early night Late night 9 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 9 Jupiter is high in the sky in the constellation of the Bull, towards East in good company: the Pleiades, the Moon, Orion, Cancer (beehive cluster), famous actors in the Sidereus Nuncius Galileo uses this star to show the motion of Jupiter in the sky in the last measurements The sky scene on Jan 7th 1610 https://stellarium-web.org J + I E G C 16 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 13-15 January 1610 1 6 On the 13th for the first time all the 4 satellites are seen! Galileo starts taking this very seriously: after the 15th notes passes from Italian to Latin (in view of a publication), multiple observations during each night, reports angular separations in the text (not just drawings) 13 Jan 15 Jan Europa Ganymede Io Callisto Io Europa Ganymede Callisto The “sampling rate” needs to be high as satellites are fast: Io orbit takes ~1.8 days, Callisto 16.7 days 17 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The breakthrough 1 7 “It was therefore established by me, and concluded beyond all doubt, that there are in the heavens three wandering stars revolving around Jupiter, similar to Venus and Mercury around the Sun; which was finally observed more clearly than in broad daylight through many subsequent observations: and not only three, but four were found to be the wandering stars performing their revolutions around Jupiter ... And I also measured the intervals between them with the method explained earlier.” 18 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Vertical displacements 1 8 Notice the correspondence of the “vertical displacements” The orbits are almost perfectly circular and lying almost exactly at the the Jupiter equatorial plane The rotation axis of Jupiter forms an angle of 3.1◦ with respect to the Ecliptic The inclination of the Jupiter’s orbit forms with the Ecliptic an angle of 1.3◦ From ephemerides: 19 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius A multi-s Copernican evidence! 1 9 Even though Galileo seems genuinely surprised and “conservative” in the first observations, at this point he appears fully convinced of having discovered a “miniature solar system” in which Jupiter was the center of orbits A “smoking gun” for Copernicanism! The Earth is surely not the privileged center of revolutions! Seems so natural to us … how much more data is then needed ? 20 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The Jupiter dataset 2 0 ●64 observations! ●From Jan 7 to Mar 1 ●From about 1h after sunset until about 2 a.m. ●The last observation of March 1st is only 10 days earlier than the release in press of the Sidereus Nuncius! 21 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Big discovery needs big evidence 2 1 ●Still, collecting “a lot of data” was probably not a bad choice: ●the “prior” for this evidence was rather controversial (in hindsight...) ●It served as a “protection” against potential competitors ●Simon Mayr, Harriot ... ●Morever, as I will try to show: ●1) convincing the “experts” at the eyepiece was not obvious: the first demonstration of Galileo to his colleague Magini in Bologna was a “failure”. People started to say that the instrument was producing artifacts (Spica, a-Virginis, appeared as double). ●2) these observations did not come absolutely “for free”! ●measurements were DIFFICULT and making good telescopes not easy. 22 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Experimental data + powerful instruments 2 2 ●Whatever the reason… this stress on “experimental data” is particularly charming for a “modern scientist” (especially considering how easily claims are put forward nowadays) as well as the iconic demonstration of the power of new scientific instruments! ●PS: also the time between the collection of data from a new “frontier” instrument and the (single-author) “publication” induces some envy ... Let’s have a deeper, systematic look to what this man was capable of in those 54 frantic days → The size of the marker is a proxy for magnitude 23 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Collaborative weather 2 3 ●It is interesting to notice that the weather was very “collaborative” in 1610 in Padova: just 10 cloudy days over 54 against an average of >50% nowadays https://weatherspark.com/m/69432/1/Average-Weather-in-January-in-Padova-Italy 24 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The dataset 2 4 Can exploit two datasets ●1) the digitized sketches in the Sidereus Nuncius. We express distances in fractions of the Jupiter disk as in the sketches themselves ●2) the angular measurements reported in words in the text (usually reported as separations between adjacent satellites) 2) are the real measurements 1) are passed through the printing process. We have 64 sketches. Angular measurements appear after some days but sometimes we have the angles but not the sketches. 25 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius How data are presented: example 2 5 … On the 18th day, at the first hour, there were three stars, two to the west and one to the east: the eastern one was 3 minutes from Jupiter; the nearer western one 2 minutes; the other, farther west, was 8 minutes from the middle one. All were exactly on the same straight line, and nearly of equal size. But at the second hour, the Stars nearest to Jupiter were equally spaced, since the western one was 3 minutes away as well. Then, at the sixth hour, a fourth little star appeared between the eastern one and Jupiter, in the following configuration. The farthest east one was 3 minutes from the next, that one 1 minute and 50 seconds from Jupiter, Jupiter 3 minutes from the next western one, and that one 7 minutes from the farthest western one: they were nearly equal; only the eastern one closest to Jupiter was a little smaller than the others; and they were on the same straight line parallel to the Ecliptic... 8’ 3’ 2’ 3’ 3’ 3’ 3’ 7’ 1’50” No sketch 32 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Satellite-tagging with simulator 3 2 We have then used the simulator (stellariumweb) to tag the observations to satellites and produce four separate datasets (~“cheating”) →new Lomb-Scargle analysis 33 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Lomb scargle of tagged samples 3 3 Io Europa Ganymede Callisto 34 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Sinusoidal fits 3 4 Amplitude, phase, frequency: free parameters 35 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Sinusoidal fits (dataset 1 - digitized) 3 5 The error bars are determined as the error “a posteriori” (to make c2 /N-3 = 1) they are an estimate of the uncertainties Unit = Jupiter diameter in the sketch 36 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 3 6 The error bars are determined as the error “a posteriori” (to make c2 /N-3 = 1) they are an estimate of the uncertainties Unit = primes Sinusoidal fits (dataset 2 – meas. angles) 37 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Residuals 3 7 Interesting: the estimation of the uncertainty in the Sidereus is “just one minute, or two” in agreement with the analysis! 38 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Precision on the parameters 3 8 ●The uncertainties on the periods are O(0.1-0.2%), on the amplitudes O(1-4%) ●The datasets are compatible in the f-w plane (small tension for Europa) 39 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Accuracy 3 9 Bullets: Galileo fits (•,*) Histogram: modern data Periods: largest deviation 0.7%, typical 0.2-0.3% Amplitudes (“shape”) In this case we have rescaled the fitted elongations to the true semiaxis of Ganymede and compared the others: largest deviation 9% (Callisto, dataset 1), typical ~5% pivot 40 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Kepler III law + 1:2:4 resonance 4 0 ●The data clearly show that T2 µ A3 ●(but remember Galileo could not disentangle the individual T in 1610 – we used the simulator!) ●Kepler law was formulated in 1619 (Harmonices Mundi) when the periods had been determined ●The ratio 1:2:4 of the periods of the inner satellites (resonance) is compatible with modern data As before, we have rescaled the fitted elongations to the true semi-axis of Ganymede and compared the others pivot 41 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Accuracy of the angular amplitudes (dataset-2) 4 1 But what happens if we do not normalize to Ganymede but attempt an absolute comparison: measured angular elongations vs those expected from the ephemerides (not the fit with free amplitudes) → Accuracy gets worse: the data are overestimated systematically w.r.t. to predictions by a factor (1.47, 1.53, 1.45, 1.37) for Io, Europa, Ganymede and Callisto. Dash = ephemerides, solid = fit 48 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Other observations in the Sidereus Nuncius 4 8 ●Appetite comes with eating: ●after having exploited in depth the Jupiter dataset and profiting of Stellarium-web we have done some additional “fact-checking” on the observations of ●the Pleiades, the Orion belt, the Orion Head, the beehive cluster and the Moon ●Moon: comparison with the 6 inkwashes thata are the basis for the illustrations in the Sidereus (more rough/imprecise) 49 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The Pleiades 4 9 50 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The Pleiades 5 0 This is the most accurate representation: the pattern is extremely well reproduced despite some “deformations”: the F.O.V. is ~15’, the cluster ~90’ Galileo could see stars up to magnitude almost 9 (i.e. 8.94 for HD2336). Quite remarkable considering the small aperture of the telescope. Helped by the total absence of light pollution in Padua, unlike nowadays... Proper motions: could the positions of some of the stars might really have changed in 415 years ? 60 mas/year →0.5’ corresponding to about half the size of the Jupiter disk. →sub-leading on a field of view of ~ 90’ 51 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The Orion belt 5 1 The area is huge wrt to the FOV of the telescope (might have used a lower magnification one?) Not so accurate … BUT → 52 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The Orion belt: notes vs printed 5 2 Passing from sketches to the printed version there were some errors Sketches are more accurate! 53 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The Orion head 5 3 Red stars pattern is quite convincing. The rest requires assuming large distorsions ... Meissa 54 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius The beehive cluster 5 4 M44 open cluster in Cancer (Praesepe). Larger stars are the ones visible by naked eye (Galileo’ convention): the “little donkeys” (g and d Cancri) The rest is much less faithful than the Pleiades (tried also assuming flipping of the printing). Tentative matching. The real cluster is much more compact. Also here the cluster is much larger than FOV 55 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 5 5 Inkwashes of the Moon We know with a precision O(min)! when this observation was made thanks to the occultation of q-Librae 56 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius 5 6 ●Galileo had been working systematically on the Moon phases in Nov-Dec 1609 before J. satellites in Jan 1610 became “top priority” ●The dates of the sketches have been debated. We considered the dates that are generally accepted. ●The white line is the terminator from the inkwash. Moon 57 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Replica of one of the telescopes of Galileo 5 7 64 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Tagged dataset: Europa 6 4 65 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Tagged dataset: Ganymede 6 5 66 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Tagged dataset: Callisto 6 6 67 A. Longhin Neutrino Telescopes, Padova, 29 September 2025 A quantitative analysis of the observations of the Sidereus Nuncius Replica 6 7