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Why does a star’s annual parallax trace an apparent ellipse during the year?

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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.

A star’s annual parallax traces an apparent ellipse during the year because of the Earth’s revolution around the Sun.1

As Earth moves in its orbit, our viewpoint of distant stars changes continuously throughout the year. Because the Earth’s orbital path is circular (or elliptical) relative to the star's position in the sky, the star appears to shift its position against the background of more distant objects. This back-and-forth displacement, when projected onto the celestial sphere, creates the shape of an ellipse. The size of this ellipse depends on the distance of the star; the closer the star, the larger the parallactic displacement.1

It is important to note that this geometric effect is distinct from the constant of aberration, which also causes an annual shift in stellar positions due to the combination of Earth's orbital velocity and the finite speed of light.2