The Sun's Meridian Transit

Saint-Sulpice in Paris



coordinates
The coordinates of the church Satint-Sulpice are:

48.851° N
2.335° E

gnomon height

Height of the pin hole gnomon:
(about) 25 m.
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year century
The year is 2011.
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details

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2011, June 15:

transit: 13:51 CEST, altitude 64.46°

photo:  13:35 CEST, altitude 64.26°, azimuth 171.5°

1743, June 15:

transit: 13:50:26 CEST, altitude 64.49°

1743, June 22:
transit: 13:51:56 CEST, altitude 64.63°
x=11.144 m (H=23.5 m)
23.47421°

1743, Dec 22:
transit: 13:49:41 CEST, altitude 17.72°
x=73.547 m (H=23.5 m)
23.47421°
h = 5.08

2011, June 21:
transit: 13:52:22 CEST, altitude 64.59°
x=11.164 m (h=23.5 m)
23.43738°

The present church Saint-Sulpice, erected over a church of the 13th century, was founded in 1646 and mostly completed in 1732. It is second largest church in Paris after Notre-Dame de Paris.

The French astronomer Pierre Charles Claude Le Monnier (1715 – 1799), member of the Academy of Sciences, constructed the meridian Saint-Sulpice in 1743 "Ad Certam Paschalis Aequinoctii Explorationem", to explore the date of spring equinox on which depends the Easter date, and to determine the nutation and the obliquity of the Earth's axis.



obelisk


table


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

hole

The aperture gnomon.

laengen

The mean transit time (solar noon) is 11:51 UT, which varies according to the equation of time from around
11:34 UT to 12:05 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:

duration Sun meridian transit

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
26 x 29 cm
d=11.87 m

t=2.3 min
equinox α=0.535°
α=0.531°
equinox
36 x 55 cm
d=28.63 m
t=2.2 min
winter solstice
Obelisk
α=0.542° equinox 56 x 53 cm
d=57.64 m
t=2.4 min

The diameter of the aperture is supposed to be 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):

formula
D = 19.8 m (for a=6.6 mm, λ=550 nm)

In the past centuries the obliquity of the ecliptic decreased by 0.013° = 46.8'' per century. The result is a shift of the sun spot on the meridian line:


Summer
Solstice
Winter
Solstice
Obelisk h
1400 11.834 m
6.616 m
1600 11.844 m
6.595 m
1800 11.857 m 6.569 m
2000 11.874 m 6.534 m
2200 11.889 m 6.501 m



Web Links

Église Saint-Sulpice, Paris (Wikipedia)

Gnomon of Saint-Sulpice (Wikipedia)

Pierre Charles Le Monnier (Wikipedia)



Books
Michel Rougé: Le gnomon de l'église Saint-Sulpice, Paroisse Saint-Sulpice, Paris 2006.

Saint-Sulpice, Paroisse Saint-Sulpice, Paris 2003.

J. L. Heilbron: The Sun in the Cathedral, Cathedrals as Solar Observatories,
Harvard University Press, 1999.





Updated: 2011, Jun 21