The analemma is, in astronomy, the orthographic projection of the Sun’s apparent motion onto the plane of the local meridian; it is used to determine the altitude of celestial bodies, in particular that of the Sun, because it is useful for building sundials (also called quadrants or analemmatic clocks).
Often, when looking at sundials, a figure-eight curve can be seen crossing the hour lines. This curve is called the analemma.
The analemma, however, with a photographic trick, can also be seen projected in the sky: in the history of astronomical photography, Dennis De Cicco was among the first, in the ’90s, to devise the idea of photographing the Sun for a year (when it passes the meridian) always at the same time and at constant daily intervals. The result is the “figure-eight” curve projected in the sky toward the South. This insight later spread so widely that analemma photos are still very common today.
The curve photographically visible in the sky, however, loses the name “analemma” and takes the name “lemniscate”, and it represents the equation of time. This equation is the difference between the time shown by the clock and true solar time, which varies every day as a consequence of the eccentricity of Earth’s orbit and the tilt of its axis. Equation of time: Et=Ts-Tc, where Ts is the Solar time that elapses between two consecutive passages of the Sun over the same meridian and Tc is the civil time measured on the clock and depends on the time zone.
Following this idea, I created a photographic composition by combining with the lemniscate curve two other curves made with the same technique but at different times: the one on the left at 07:20 UTC and the one on the right at 15:00 UTC. Also, on the day of the winter solstice I captured the Sun’s path throughout the whole day. You can notice the curves near twilight are strongly tilted, unlike the one at the meridian, which is vertical.
I shot the three curves from Viterbo Airport, but from my position I was unable to capture the panorama because military installations were visible, so I decided to move 30 km, considering that this difference does not visibly change the lemniscate.
Technical data for the analemma curves:
Start of shooting March 2022, end of shooting March 2023, shooting frequency: on average one shot every 15 days, with minimum intervals of 7 days and maximum of 20 days. Depending on cloud conditions.
Shot times: 07:20 -11:10-15:00 UTC
Camera: Nikon Z9 set to 32 ISO
Lens Nikon S14-24/2.8 stopped down to f/22 and used at 14mm focal length
Shutter speeds: from 1/32,000 to 1/8000 depending on sky conditions.
80 shots of the solar disks were taken, but only 68 used.
Shooting site Viterbo Airport (42.22.228N-12.05878E)
Technical data for the panorama:
Shot on 1 November 2022, 11:10 UTC
Camera Nikon Z9 set to 32 ISO, with shutter speed 1/160 and white balance set manually
Lens Nikon S14-24/2.8 stopped down to f/6.2 and used at 14mm focal length
Sum of two 360-degree panoramas of 12 shots each: one for the ground and one for the sky.
The panorama has an extent of 360 degrees of azimuth and 130 degrees of height.
Shooting site: Arcatelle aqueduct (Tarquinia, Vt - 42.258649N-11.815915E)
Photo processing with Photoshop and analemma study with Starry Night 8 and Photopills. Having captured both the panorama and the curves with the same focal length (14mm) made it easier to preserve the curves’ elevations and azimuth angles.
Polar-coordinate versions
