"If someone observed the Moon in the sky vault at the same time on two consecutive days, on the second day they would find it shifted farther east compared to the day before; to find it again in the previous position they would have to wait on average about another 51 minutes (the time interval varies greatly from day to day due to countless lunar anomalies and falls within a range of about +/-15 minutes). This happens because the Moon, during its revolution, returns to the sky vault at a point very close to that of the previous day on average every 24h 51 minutes: this is due to the combination of the orbital motions of the Moon and the Earth.
Let’s see why: the sidereal lunar month is defined as the interval between two successive alignments of the Moon and a star on a meridian, and this span lasts 27 days, 7 hours and 43 minutes. This value indicates the real revolution time, which also corresponds to the true period of rotation around the Earth. The synodic month, or lunar, is the interval between two identical Moon–Sun alignments (oppositions or conjunctions) and lasts on average 29 days, 12 hours, 44 minutes. This period varies during the year and also indicates the duration of a lunar phase cycle. The time difference between the synodic month and the sidereal one originates from the fact that while the Moon orbits the Earth, the Earth–Moon pair also goes around the Sun. If the Earth did not orbit the Sun but stayed still with respect to it, then the synodic month and the sidereal month would coincide. But the Earth moves around the Sun by almost 1° per day (360°/365 days per year gives ~1° per day) and therefore in the 27 days and more of the sidereal month the Earth (and consequently the Moon as well) shifts by about 27°. To realign again to new moon, the Moon must rotate by 360° + 27° + another 2° because while it covers the additional 27°, the Earth, even if slightly, has moved further. In short, while in the sidereal month the Moon must orbit the Earth by 360°, in the synodic month it must orbit by about 389°: hence the different length of the month, which is 27 days in the first case and over 29 days in the second, so each day it must rotate for another 51 minutes in order to return to the same meridian as the day before. This explains why, observing the Moon day by day at the same time, it always appears shifted farther east.
Intrigued and fascinated by this peculiarity of celestial mechanics, I decided to photograph the curve the Moon traces across the sky vault, joining the points it returns to day after day every 24h 51 minutes and waiting each time for it to come back to the meridian. I then compared this curve resulting from the lunar revolution with the solar analemma generated during the solar revolution. On the web I found some curves of the lunar revolution already photographed and wrongly called “lunar analemma”: this is a linguistic stretch because only the “figure-eight” curve made by the Sun can be called an “analemma” by its etymological definition. The analemma (from the Greek ανάλημμα) indicates the pedestal of the solar sundial and therefore cannot refer to the Moon. In my view this lunar curve should be called the “synodic curve”.
I took the photos in the time span between two full moons: from the Full Moon of November 4th to that of December 3rd (the highest and brightest Moon of 2017, reaching perigee the following day), so I placed the disks on a south-facing panorama with the Meridian at the center. The result is a heart-shaped curve with the second full moon about two degrees higher than the first. This is because by shooting in the month of November I was approaching the Winter Solstice; if instead I had photographed in the months after December, the second full Moon would have been lower.
The shots assembled on the frame were taken every 74h 33 minutes, corresponding to three days plus the respective 51 minutes of the Moon’s daily delay. All shots of the lunar disks were taken with a Canon 5DMK3 DSLR with an EF 24-70/2.8 lens set to 30mm, while the panorama with a Sigma 14 mm f/1.8 Art. With Photoshop CC I both processed the disks shot in daylight by increasing contrast and darkening the sky, and assembled the curve.
The fort in the background is Fort Michelangelo, a fortress that protected the historic port of Civitavecchia (RM). The fortress was begun in 1508 and completed in 1537 under the pontificate of Paul III, under the direction of Antonio da Sangallo the Younger. A local tradition holds that the keep, that is the fortress’s main tower, was designed by Michelangelo Buonarroti, hence the name Fort Michelangelo
Solar analemma
Visual comparison between the synodic curve and the solar analemma
