What challenge arises if a star exhibits significant proper motion during the parallax baseline observation period?

The positional data cannot be fitted to a clean ellipse but must be modeled as a complex trajectory

Parallax measurement fundamentally relies on fitting the observed positional data points to a clean, predictable ellipse caused by Earth's orbital motion around the Sun. If the target star possesses a significant proper motion—meaning it moves substantially across the sky while the Earth travels along its baseline—the observed path deviates from a perfect ellipse. The combined motion of parallax and proper motion means the data must be modeled as a more complex trajectory involving two distinct components. This increases computational demands and introduces potential modeling errors, complicating the accurate separation of the geometric distance component from the physical sideways velocity component.