Found this picture online, was wondering why the trajectory has taken such a beautiful shape ?
This is a digitally enhanced composite set of images of the Moon, with successive images taken 24 hours and 40 minutes apart. There's also a long gap in time between the left half and right half of the composite. The creator of the photograph took artistic license to enlarge the Moon; she thought that that made the composite image look better. Images of the new Moon / nearly new Moon are also enhanced.
Had consecutive images been taken 24 hours and 51 minutes apart the resulting composite would form a more or less closed curve. Successive images were instead taken 24 hours and 40 minutes apart so as to intentionally create a non-closed curve. The first image is at the top right while the last image is at bottom left.
I don't believe that this can be a simple repeated exposure of the moon.
On the right, we see a thin crescent, such a moon is only possible when the moon is a couple of days old, and so must be in the West. On the left, we see an old moon, Such a moon is only visible in the very early morning, and that must be in the East, so the image must span nearly 180 degrees.
But the moon is only 1/2 a degree across, and by my measurement, this makes the image span less than 20 degrees.
An longer analysis is on reddit https://www.reddit.com/r/Astronomy/comments/9k5gqu/lunar_fake/
You can get interesting curves like this by recording the position of the moon in the sky at intervals of about a day (or perhaps 24 hr 50 min , since you get the superposition of the moon at a about the same direction, but its height in the sky changes as the moon doesn't orbit around the equator, but in roughly the same plane as the sun. This can be called a lunar annalemma. These have appeared in the astronomy picture of the day https://apod.nasa.gov/apod/ap200507.html and https://apod.nasa.gov/apod/ap050713.html. These images also required some digital manipulation, to bring out narrow crescents taken during the day.