What is the maximum displacement a star can appear to make due to annual parallax?

The maximum displacement a star can appear to make due to annual parallax is indeed a small fraction of an angle. Annual parallax refers to the apparent shift in position of a star against the background of more distant stars as observed from different positions of Earth's orbit around the Sun.

This effect is most pronounced for nearby stars, where the angle of parallax can be measured. The typical maximum angle for the parallax of stars visible to the naked eye is usually measured in arcseconds, where 1 arcsecond is equal to 1/3600 of a degree. The closest star, Proxima Centauri, has a parallax angle of about 0.77 arcseconds, which underscores that for most stars, the displacement is exceedingly small.

In contrast, the other choices present measurements or concepts that do not accurately reflect the nature of parallax. The maximum displacement being equal to the star's actual distance from Earth misrepresents how parallax works, while suggesting it could be as much as one degree or comparing it to the visibility difference between night and day underestimates the scale of this angular change. Overall, the parallax effect is subtle, requiring careful measurement to detect even for the nearest stars.