The Sun's Meridian Transit

The Meridian of the Cathedral of Milan



latitude longitude
The coordinates of the Basilica are:
41° 54' 11'' N, and 12° 29' 51'' E
gnomon hole

Height of the gnomon hole.
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year century
The year is 2009.

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Milan Cathedral

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

meridian line milan cathedral

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).

meridian milan



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.

disk of light

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:

duration Sun meridian transit

sun meridian transit duration time


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°
summer solstice
24 x 26 cm
d=9.63 m

t=2.3 min
equinox α=0.535°
α=0.531°
equinox
32 x 46 cm
d=24.06 m
t=2.2 min
winter solstice
Wall
α=0.542° equinox 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):

formula
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


obliquity of the ecliptic

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

Santa Maria degli Angeli e dei Martiri (Wikipedia)

S. Maria degli Angeli e dei Martiri: La Meridiana

Meridiana del Duomo di Milano

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