The Sun's Meridian Transit

The Meridian of the Cathedral of Milan

 The coordinates of the Basilica are: 41° 54' 11'' N, and 12° 29' 51'' E Height of the gnomon hole. Enter value and press return key. The year is 2009. Use the keys "y", "m", or "d" to increase the year, month, or day, or shift key and "y", "m", or "d" to decrease the year, month, or day. Use the command key and "u" or "d" to move up or down. Use "Reset" from the Details menu to reset the position and zoom. Select "Write Data" or "Write Table" from the Details menu to open data windows.

Milan Cathedral (Duomo di Milano) as seen from the square.

The solar meridian line near the main entrance of the cathedral.

The sun shines through a small hole in the southern wall to cast its light on the meridian line each day (aperture gnomon). The length of the meridian line is limited by the northern wall (at d=55.01 m).

The aperture gnomon.

The mean transit time (solar noon) is 11:23 UT, which varies according to the equation of time from around
11:00 UT to 11:37 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 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° 24 x 26 cm d=9.63 m t=2.3 min equinox α=0.535° α=0.531° 32 x 46 cm d=24.06 m t=2.2 min winter solstice Wall α=0.542° 53 x 50 cm d=55.01 m t=2.0 min

The diameter of the aperture is 7 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 = 22.3 m (for a=7 mm, λ=550 nm)

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.

is

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 d Winter Solstice Wall h 1400 9.598 m 2.629 m 1600 9.607 m 2.608 m 1800 9.618 m 2.582 m 2000 9.634 m 2.548 m 2200 9.647 m 2.514 m

 Web Links Le Meridiane nelle Chiese (DOC) Books Carlo Ferrari da Passano, Carlo Monti, Luigi Mussio: La meridiana solare del Duomo di Milano, Veneranda Fabbrica del Duomo di Milano, 2001 J. L. Heilbron: The Sun in the Cathedral, Cathedrals as Solar Observatories, Harvard University Press, 1999. Frans and Margret Bruin: The Limits of Accuracy of Aperture-Gnomons, in: Y. Maeyama and W. G. Saltzer (Editors): Primata, Naturwissenschaftliche Studien, Steiner, Wiesbaden 1977, pp.21-42.

Updated: 2011, Jun 23