Differential refraction, 2017 winter solstice timing and true ecliptic obliquity measured at the meridian line of Santa Maria degli Angeli in Rome

Abstract

The declination of the Sun along the year varies according to a sinusoid. Around the solstices this curve is approximated by a parabola. In kinematics a parabola is obtained with a constant acceleration. This acceleration has been estimated in the days 21-29 December 2017, from the measurements taken at the meridian line in the Basilica of Santa Maria degli Angeli in Rome made by Francesco Bianchini in 1702 with purpose of measuring the variation of the obliquity of the ecliptic. The parabola equation is fitted to the data to obtain the solstice's instant with an accuracy of one hour. The departure of the measures is within 4 arcsec (the daytime seeing during these solar transits) from the ephemerides of IMCCE. The pipeline of the algorithm used to obtain the angular data of the center of the Sun, starting from the ground measurements affected by the atmospheric refraction, and corrected by the Cassini equation, is described. Bianchini in 1703 reduced the error on the solstices timings by using the difference in right ascension between the Sun and a star observed at the same meridian line even in daytime (as he did with Sirius in June-July 1703). The present one is an absolute measurement, without stellar references. The meridian diameter is averagely measured 24 arcsec less than the true value, with 20 arcsec of standard deviation, because of different luminosity contrasts in the sky and in the Basilica. Conversely the center of the image is much better defined (the contrast acts symmetrically without moving the center of the image), allowing an accuracy to the nearest arcsecond in the determination of the true obliquity.