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Why do distant background stars appear nearly fixed in parallax measurements?

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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.

Distant background stars appear nearly fixed in parallax measurements because of their extreme distance from Earth.1

In the geometric method used to determine stellar distances, astronomers observe the apparent shift of a nearby star against a background of much more remote stars as Earth moves along its orbit around the Sun. Because these background stars are so incredibly far away, their own parallactic displacement is negligible, effectively serving as a stationary reference frame.12

The shift of a nearby star is inversely proportional to its distance; therefore, the further away an object is, the smaller the observed angle of movement. While nearby stars exhibit a measurable shift—such as Proxima Centauri with a parallax of approximately 0.77 arc seconds—the vast majority of stars in the Milky Way Galaxy are so distant that their positions remain essentially fixed to our perspective, providing the stable "background" necessary to calculate the distances of closer objects.132