What describes annual proper motion of a star?

The annual proper motion of a star refers specifically to the angular shift of the star's position against distant background stars, measured over the course of a year. This motion is typically expressed in arcseconds per year and is a result of the star's actual movement through space relative to the Solar System. This angular measurement is crucial for astronomers, as it helps to determine the star's velocity and trajectory.

The other concepts mentioned do not accurately define proper motion. While the distance a star travels in one year is related to its velocity, it does not capture the measurement in angular terms. Brightness variation pertains to the changes in luminance over time, often associated with variable stars, which is unrelated to their motion across the celestial sphere. Lastly, the effect of Earth's gravity influences the apparent position of nearby stars slightly (a phenomenon known as gravitational lensing), but this is not what is meant by annual proper motion, which focuses on the intrinsic movement of the star itself.