



The Basilica di Santa Maria degli Angeli e dei Martiri is a section of the remaining structure of the Baths of Diocletian (Thermae Diocletiani, built about AD 300) on the Quirinal Hill of Rome, nowadays the Piazza della Repubblica.







At the beginning of the eighteenth century, Pope Clement XI (1649-1721) commissioned Francesco Bianchini (1662-1729) to build a meridian line within the basilica to check the accuracy of the Gregorian reformation of the calendar (1582).



The sun shines through a small hole in the southern wall to cast its light on the meridian line each day (aperture gnomon).











The aperture gnomon.



The mean transit time (solar noon) is 11:10 UT, which varies according to the equation of time from around 10:54 UT to 11:24 UT.



The distance d of the disk of light along the meridian line and the size (horizontal and vertical) are increasing from summer solstice to winter solstice, whereas the time t to cross the meridian line remains nearly constant. The value of pc (partes centesimae) is the distance of the disk of light in units of 1/100 of the aperture height above the pavement.







The diameter S of the disk of light is mainly determined by the apparent diameter α of the Sun:

S = D · tan α



The duration t (in seconds) of the meridian transit depends on the Sun's diameter α (arc seconds) and the declination δ:











The diameter a of the aperture and an amount due to diffraction (2 · D ·1.22 · λ/a ≈4 mm) has to be added to S.



summer solstice

α= 0.525°



20 x 21 cm

d=6.79 m



t=2.3 min pc=33.3 equinox α= 0.535°

α= 0.531°



26 x 35 cm

d=18.2 m

t=2.2 min pc≈89.5 winter solstice α= 0.542°

47 x 113 cm

d=44.25 m

t=2.4 min pc=217.8

The diameter of the aperture is 6.6 mm

The image is of greatest sharpness if the distance D from the aperture (diameter a) to the surface is given) by (wavelength λ ):





D = 19.8 m (for a=6.6 mm, λ =550 nm)





My photos of the meridian transit on 2009, October 15:



computed time of transit: 10:55:45 UT, partes centesimae scale 121.6

















In Europe the Julian calendar was in use since the 4th century. The spring equinox was set to the date 21 March in the year 325 by the council of Nicea. By the year 1582, the spring equinox was occurring on March 11.

Pope Gregory XIII ordered that 10 days would be removed from the calendar so that the spring equinox would return to March 21. It was decided that the days October 5-14 of the year 1582 would be skipped during the transformation from the Julian to Gregorian calendar.







The tomb of Pope Gregory XIII in St. Peter's Basilica







Detail of the tomb of Pope Gregory XIII in St. Peter's Basilica:

discussion of a calender reform.







In the past centuries the obliquity of the ecliptic decreased by 0.013° per century. The result is a shift of the sun spot on the meridian line:





Summer

Solstice

Winter

Solstice 1400 6.76 m

44.46 m

1600 6.77 m

44.43 m

1800 6.78 m 44.38 m 2000 6.79 m 44.31 m 2200 6.80 m 44.25 m



