Solar Analemma - but with a star instead We (homeschool students and I) are trying to find the answer to this question.  Does a star also create Solar Analemma figure 8 when photographed daily for a year?
Has anyone published an experiment where the same star is photographed every night at the same time?
We tried answering this ourselves by googling it, but only come up with websites mentioning the sun.   Is this because it is only possible with the sun?
An analemma shows the position of the Sun in the sky from a fixed location on Earth at the same mean solar time. It gets its north-south shape because of the tilt of Earth's axis makes the declination of the sun change across the year, and the sideways shape due to the orbit nonuniformity.
The star analemma would get a point at the same time every sidereal day (slightly different from the solar day). To a first approximation that fixes the star's right ascension: it will not move along the celestial equator. The celestrial equator of course rotates one turn per year as seen from the ground, so in one sense the analemma is just a circle around the pole of the sky. But if you look at it in the coordinate system of the celestial sphere the star is fixed.
...Except that there will be some stellar parallax due to Earth's different locations along its orbit during the year. The star will seem to move along a tiny ellipse when compared to distant stars in the background. I think the parallax ellipse is the closest counterpart to the sun analemma.