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Earth's Obliquity and Stellar Aberration Detected at The Proceeding Paper Earth’s Obliquity and Stellar Aberration Detected at the Clementine Gnomon (Rome, 1703) † Costantino Sigismondi 1,2,3 1 ICRA/Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy; [email protected] 2 Istituto Scienza e Fede, Ateneo Pontificio Regina Apostolorum, via degli Aldobrandeschi 190, 00163 Rome, Italy 3 ITIS Galileo Ferraris, via Fonteiana 111, 00152 Rome, Italy † Presented at the 1st Electronic Conference on Universe, 22–28 February 2021; Available online: https://ecu2021.sciforum.net/. Abstract: The Clementine Gnomon was built in 1700–1702 by the astronomer Francesco Bianchini, upon the will of Pope Clement XI. This meridian line is located in the Basilica of santa Maria degli Angeli e dei Martiri in Rome, and it is visited by thousands of students and tourists per year. This 45-m meridian line was designed to measure the secular variation of the obliquity of the ecliptic " and to verify the tropical years’ length used in the Gregorian Calendar. With a pencil and a meter, a synchronized watch and a videocamera, we can obtain an accuracy of up to one arcsecond in the position of the solar center. The observations from 21 November 2020 to 19 January 2021 are analyzed to recover the solstice’s instant in Capricorn, the ingresses into Sagittarius and Aquarius, and the corresponding observational uncertainties. Astrometric corrections to the total length of the meridian line and to the pinhole’s height are found. The 501100 Eastward deviation of the meridian line between the two solstices, found by comparing our observations and the ephemerides, and the aberration of Sirius’ light explain the timing of the solstices and equinoxes calculated by Bianchini for 1703. The aberration in declination of Sirius explains the variations of its meridian position observed in 1702-3. Citation: Sigismondi, C. Earth’s Obliquity and Stellar Aberration Keywords: ephemerides; optical aberration; stellar aberration; nutation; refraction; solstices; equinoxes; Detected at the Clementine Gnomon equation of time; Earth’s rotation; obliquity; eccentricity; air turbulence; penumbra (Rome, 1703). Phys. Sci. Forum 2021, 2, 49. https://doi.org/10.3390/ ECU2021-09323 1. Introduction: The Great Clementine Gnomon as in the Texts of Francesco Academic Editor: Magdalena Bianchini (1703) Kersting The meridian line was completed in about two years—1701 to 1702—including all the images of the zodiacal signs and the stars over the floor. The stars are located along Published: 22 February 2021 the projection of the celestial equator, and of the projected paths (hyperbolae) of Sirius, Arcturus and the Sun on the 20 August 1702 (visit of the Pope Clement XI). Another group Publisher’s Note: MDPI stays neutral of seven stars on a circular sector at 35 m 80 from the pinhole’s base approach Sirius’ with regard to jurisdictional claims in hyperbola. published maps and institutional affil- iations. In 1703, Francesco Bianchini (1662–1729) published [1] the results of the measurements made at the meridian line in the book De Nummo et Gnomone Clementino, and the four instants of solstices and equinoxes (anni cardines) were written on a marble slab included in the wall of the presbyterium, at about five meters from the Capricorn sign. Bianchini called the great meridian line Clementine Gnomon, because, with this Copyright: © 2021 by the author. instrument, dedicated to Clement XI, it was possible “to know” the position of the Sun. Licensee MDPI, Basel, Switzerland. The word Gnomon includes the Greek root for knowledge, knowing. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Phys. Sci. Forum 2021, 2, 49. https://doi.org/10.3390/ECU2021-09323 https://www.mdpi.com/journal/psf Phys. Sci. Forum 2021, 2, 49 2 Phys. Sci. Forum 2021, 2, 49 2 of 11 2. Measurements and Comparison with Ephemerides 2. Measurements and Comparison with Ephemerides 2.1. Ephemerides for 1703 2.1. Ephemerides for 1703 IMCCE provides a service for computing the beginning of the seasons back to the IMCCE provides a service for computing the beginning of the seasons back to the year year 4000 BC. I refer to these computations, which are not available on the NASA web 4000 BC. I refer to these computations, which are not available on the NASA web interface interface Horizons (only back to 1800 AD). Horizons (only back to 1800 AD). The comparison between IMCCE UTC dates and Bianchini measurements, published The comparison between IMCCE UTC dates and Bianchini measurements, published in local time, also required to “translate” the local time of 1703 into UTC with a slightly in local time, also required to “translate” the local time of 1703 into UTC with a slightly different equation of time with respect to the present time, as well as a different position different equation of time with respect to the present time, as well as a different position of of the apsides of the Earth’s orbit. the apsides of the Earth’s orbit. 2.2. Aberration2.2. Aberration in Stellar in Stellar Coordinates Coordinates BianchiniBianchini measured measured the difference the difference of time of time between between the transits the transits of the of theSun Sunand andthe the transittransit of Sirius. of Sirius. He Healso also measured measured this this differ differenceence in indaylight daylight during during the the solstice solstice of of June, June, as as reportedreported in in his his book, book, so therethere isis nono doubt doubt he he also also carried carried it outit out during during Sirius’ Sirius’ night night transit transitin December,in December, and and in twilight in twilight at both at both equinoxes. equinoxes.The The Stars’ Stars’ Catalogue Catalogue, published, published in 1700 in by 1700Philippe by Philippe de la de Hire la Hire (Paris (Paris Royal Royal Observatory), Observatory), was usedwas used by Bianchini, by Bianchini, and on and the on meridian the meridianline, the line, coordinates the coordinates “precessed” “precesse ford” 1701 for have 1701 beenhave writtenbeen written [2,3]. [2,3]. WhileWhile the stellar the stellar coordinates coordinates in the in catalogu the cataloguee are measured are measured at night at night with with a “passages a “passages instrument”,instrument”, i.e., a i.e., meridian a meridian instrument, instrument, the observation the observation in daylight in daylight deals deals with with the aber- the aber- ratedrated coordinates coordinates of the of the same same star, star, and and the the noon noon transit transit of of a a star carries aa differencedifference of of 41.2” 41.2”with with respect respect to to the the midnight midnight transit’s transit’s coordinates. coordinates. The Thedifferences differences between between IMCCE IMCCE ephemerides ephemerides and andBianchini’s Bianchini’s calculated calculated times times re- re- flectsflects the influence the influence of the of aberration the aberration of Sirius of Sirius’’ stellar stellar coordinates, coordinates, namely namely its aberration its aberration in in eclipticecliptic longitude, longitude, not included not included in Bianchini’ in Bianchini’ss computations, computations, because because it was it wasdiscovered discovered in in GreenwichGreenwich 24 years 24 years later later by James by James Bradley. Bradley. 2.3. Polaris’2.3. Polaris’ Stellar Stellar Aberration Aberration BianchiniBianchini in 1701 in 1701 could could not nottake take into intoaccount account the thestellar stellar aberration aberration because because it was it was discovereddiscovered in 1727 in 1727 by James by James Bradley, Bradley, but buthe observed he observed and andmeasured measured its effects, its effects, as in as the in the latitude that he measured during the nights from 1 to 8 January 1701 by averaging the latitude that he measured during the nights from 1 to◦ 8 January0 00 1701 by averaging the 00 extremesextremes of the of thealtitude altitude of Polaris. of Polaris. He Heobtained obtained 41°54 41′2754″, 27while, while the correct the correct value value is 16 is″ 16 less.less. This This difference difference is due is dueto the to stellar the stellar aberra aberrationtion of the of Polaris the Polaris coordinates coordinates in these in these dates, dates, and it is written on the marbles of the boreal gnomon (see Figure1) as 41 ◦5403000 [3]. The and it is written on the marbles of the boreal gnomon (see Figure 1) as 41°54′30″ [3]. The stellar aberration is a special relativistic effect measurable with the Clementine Gnomon. stellar aberration is a special relativistic effect measurable with the Clementine Gnomon. FigureFigure 1. The 1. TheCelestial Celestial North North Pole Poleis elevated is elevated over over the horizon the horizon of 41°54’30’’, of 41◦540 30on00 ,the on yellow the yellow marble marble tarsia. The vertical brass line is the boreal gnomon [1,2]. tarsia. The vertical brass line is the boreal gnomon [1,2]. Phys.Phys. Sci. Sci. ForumForum2021 2021,, 22,, 4949 3 of3 11 2.4. Aberration Effect Effect on on Sirius Sirius Bianchini observed the the change change of of the the meridi meridianan coordinates coordinates of of Siri Siriusus along along the the seasons seasons with aa telescope,telescope, whosewhose axis axis was was on on the the meridian meridian line. line. Over Over the the pinhole pinhole of Santa of Santa Maria Maria degli Angeli,degli Angeli, a window a window of 40 of cm 40× cm60 × cm 60 wascm was opened opened to allow to allow these these observations. observations. Nowadays Nowa- (2021),days (2021), this can this no can longer no longer be carried be carried out without out without taking taking the risk the of risk breaking of breaking the coat the of coat arms of Clementarms of Clement XI, in which XI, in the which pinhole the pinhole is located.
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