  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.

Popular Physics;History and Philosophy of Physics