Perhaps you are familiar with the concept of a Solar Analemma. Set up a camera pointing toward the southern sky so it will record the position of the Sun. Take a picture of that same part of the sky at the same time every day for a year. Adjust for daylight saving time changes in the spring and fall. Some days will be cloudy. Enough clear days will allow images to capture the Sun’s location and resulting pattern in the sky over the course of the year.
The team of Alan Smith and Joe Startin of the Orwel Astronomical Society near Ipswich, Suffolk, UK, reported on their efforts to do just that in 2014-2015. Their story is here. They used a webcam pointing south controlled by a computer. It took a picture mid-day for a year. They created an animated GIF with the images. Below is a screen shot of their GIF after a year of solar images. It is called the analemma. The shape of the analemma is primarily due to two factors. The Earth’s axis is tilted with respect to the plane of its orbit, hence the up and down variation. And, Earth’s orbit is not circular causing the left and right variation. The Earth’s axial tilt also has an effect on the left-right variation. A more detailed explanation of the shape of the analemma can be found courtesy of Louis Strous of the National Solar Observatory, Sacramento Peak, NM.
Winter months cause the Sun to be low in the sky toward the bottom of the figure eight. Summer months cause the Sun to be high in the sky near the top of the figure eight. The tilt of the Earth on its axis, obliquity, causes that vertical change in the figure. If the Earth’s axis was not tilted with respect to the plane of our orbit, the Sun would always track across the sky in the same path with no north-south variation.
What about the left-right variation in the analemma figure? The Earth’s orbit around the Sun is not circular. During winter months in the northern hemisphere, our planet is slightly closer to the Sun and hence travels slightly faster than average. Clocks keep track of the average time it takes the Sun to pass through noon. During the months prior to the winter solstice Earth is gaining speed and the Sun is moving more south in the sky. The Sun passes through noon a few minutes before the clocks say it is noon. We say the Sun is fast. It is imaged in the lower right part of the analemma.
During summer months in the northern hemisphere, our planet is slightly farther from the Sun and hence travels slightly slower than average. During the months prior to the summer solstice, Earth is losing speed and the Sun is moving more north in the sky. The Sun passes through noon a few minutes after the clocks say it is noon. We say the Sun is slow. It is imaged in the upper left part of the analemma.
Does the Moon trace out a similar figure as it goes through its orbital cycle? The Moon’s orbit is inclined slightly more than 5˚ to the plane of Earth’s orbit. That causes changes in its position up and down in the sky as it orbits. The Moon’s orbit is not a perfect circle. The small amount of eccentricity changes its orbital speed and hence where it appears left and right in the sky. An excellent example was published by the Astronomy Picture of the Day site on 7 May 2020.
Unlike a solar analemma where images are taken at the same time on consecutive days, Moon images are taken 50 min and 29 sec later each time. The Moon slowly orbits to the east. One must wait that much time later each night for it to be in the same framed position for the camera. I considered trying to photograph the Moon on consecutive days. But, winter in the midwest is too harsh. Maybe another time.
I found AuroraMax in Yellowknife, Canada, uploads an all sky video each day from the night before. Here is a link to the most recent video. You can also search for videos from previous dates with the search tool above-left of their current video.
I started looking at nightly video on 5 February. I saved a frame of the video with the Moon visible. It was 6:36 pm in Yellowknife. The next 2 nights were completely cloudy. I was fortunate to get images from video for the next 12 nights. I put these images into a movie format. Dates and times are in the lower right. Night to night variation in weather and visibility are obvious. But, the travel of the Moon is clearly part of a figure that looks a bit like part of an analemma.
I wanted to confirm whether the images were actually going to trace out an analemma. Desktop software let me simulate the sky view from Yellowknife. The time advance was set for 24 hr + 50 min + 29 sec. I stepped through 2 months of time seen in this video. The Moon traced the figure and repeated in the next month.
Would the analemma figure be the same for observers in a different part of the world? Yellowknife is about 62˚ North and 114˚ West. Under ideal condition, they could see this. South horizon is down.
Imagine the view from a Pacific island 50˚ South and 114˚ West during the same time period. North horizon is down.
The view from equatorial Quito, Ecuador, puts the figure more directly overhead but still oriented N-S. A change in the observed date range will cause a change in the figure’s shape. It can become a figure 8.