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Why are several observation dates needed to separate stellar parallax from proper motion?

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Diagram illustrating how astronomers calculate the distance to a star using parallax: Earth is shown in two positions on opposite sides of its orbit around the Sun, with lines extending to a nearby star X and further to distant background stars. The apparent shift in star X's position, measured as angle A, is used to determine its distance, with the baseline labeled as 186,000,000 miles. — Parallax Calculating stellar distances.

Several observation dates are required to measure stellar parallax because a star’s apparent position on the celestial sphere is influenced by two distinct factors: its annual parallax and its proper motion.

Annual parallax is the small, periodic shift in a star's position caused by the Earth’s revolution around the Sun, which creates a back-and-forth elliptical motion over the course of a year. Simultaneously, stars exhibit proper motion, which is their independent movement across the sky at right angles to the observer's line of sight.

Because these two motions occur at the same time, a single observation is insufficient to distinguish between them. Astronomers must take multiple sets of observations over several epochs—typically a minimum of three—to effectively separate the linear, cumulative effect of proper motion from the periodic, cyclical signature of the star's parallax.1