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How is the parallax angle of a star measured against background stars?

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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.

Stellar parallax is measured using the principles of trigonometric parallax, which relies on the apparent shift of a nearby star against a background of more distant, essentially fixed stars.1

Because the stars are too far away for a perceptible shift to be observed from different locations on Earth, astronomers use the diameter of Earth's orbit around the Sun as a baseline. By taking observations of a star at two different times of the year—typically six months apart—astronomers view the star from opposite sides of the Sun.4231

The star appears to move in a small ellipse relative to the distant background stars. By measuring this angular displacement, astronomers can calculate the distance to the star using the known radius of Earth's orbit. Because stars also possess their own proper motion across the sky, a minimum of three sets of observations over several epochs is generally required to accurately isolate the parallax effect. This method is most effective for nearby stars, as the parallax angle decreases as distance increases.42351