Geometry from a changing viewpoint
A nearby object changes direction against distant background objects when seen from separated locations. Earth’s orbit provides widely separated seasonal viewpoints, although stellar shifts remain tiny.
For a given baseline, nearby stars generally show larger shifts. The measurement uses angular geometry rather than first assuming a standard intrinsic stellar brightness.
An orbital radius and a six-month displacement
The conventional annual parallax angle refers to a baseline of one astronomical unit, the orbital radius. Six-month observations can be separated by approximately an orbital diameter, with the projected displacement depending on direction.
The full separation between two observed positions must therefore be distinguished from the conventional parallax angle. Distance follows from a known baseline and measured angle, keeping radius and diameter consistent.
Repeated observations separate effects
Observed stellar motion combines annual parallax with proper motion. Parallax repeats with the observing orbit; proper motion describes the changing sky direction associated with actual stellar motion. Multi-year monitoring separates these effects.
Small parallaxes place demanding requirements on instruments and analysis. Treating an arbitrary image displacement as pure parallax mixes causes, so astrometric surveys solve for position, parallax and motion together.