Lunar Synodic Curve

July 25, 2018

Analemma-lunare-con-dischi-senza-aloni (1)

Photographer: Marco Meniero 
Summary Author: Marco Meniero 

If observing the Moon at the same time on two consecutive nights, on the second night you would notice that the Moon would have moved more to the east than the night before; to find it in the same position as the previous night you'd need to wait another 51 minutes. This occurs because the Moon, during its revolution around the Earth, winds up at a place in the sky that's very close to where it was the day before on average every 24 hours and 51 minutes -- due to the combination of the orbital movements of both the Moon and the Earth.

We define the lunar sidereal month as the interval between two successive alignments of the Moon and a star on a meridian -- occurring every 27 days, 7 hours and 43 minutes. This value indicates the Moon's actual revolution time, also corresponding to the true period of rotation around the Earth. The synodic or lunar month is the interval between two equal Moon-Sun alignments (oppositions or conjunctions) --occurring on average 29 days, 12 hours, 44 minutes. This period varies during the year and also dictates the duration of a cycle of lunar phases. The temporal difference between the synodic month and the sidereal month derives from the fact that while the Moon revolves around the Earth, the Earth-Moon couple also revolve around the Sun. So while for a sidereal month the Moon must rotate around the Earth by 360 degrees, for a synodic month it must rotate by about 389 degrees. As a result then each day another 51 minutes of rotation is required to return to the same meridian as on the day before.

As shown above, I photographed the curve that the Moon describes during a month, joining the points on which it returns day by day every 24 hours and 51 minutes -- waiting until it returns to a selected meridian. By the way, the analemma indicates the pedestal of the solar sundial and therefore cannot be referred to the Moon. In my opinion, this lunar curve should be called a synodic curve.

I took these photos from Civitavecchia, Italy, during the period between two full Moons; from the full Moon of November 4, 2017, to that of December 3, 2017 (the highest and brightest Moon of 2017). I positioned each lunar disk in a view facing south, placing the meridian in the middle. The result is a heart-shaped curve with the second full Moon higher than the first by about two degrees. If I had taken the photos in the months following the December solstice, then the second full Moon would have been lower in the sky. Note that the Castle in the background is the Forte Michelangelo.

Photo Details: The shots mounted on the frame were taken every 74 hours and 33 minutes, corresponding to three days plus the respective 51 minutes of the daily lunar delay. All the shots of the lunar disks were snapped with a DSLR Canon 5DMK3 camera; with the EF 24-70 / 2.8 optics close to the focal length of 30 mm; panorama taken with a Sigma 14mm f / 1.8Art. With Photoshop CC I processed the disks taken during the day, contrasting them and also darkening the sky, and then mounted the curve.