Final answer:
Stellar parallax is the apparent positional shift of a star due to Earth's orbit, with a baseline of 1 AU used for calculation. The parallax of 1 arcsecond corresponds to 1 parsec or 3.26 light-years. Accurate measurements are challenging for very distant stars due to smaller parallax angles.
Step-by-step explanation:
Definition of Stellar Parallax
Stellar parallax is the apparent shift in the position of a star when observed from two different points in Earth's orbit around the Sun. This shift occurs due to Earth's movement and is used to measure the distance to the star. The baseline used in determining the parallax of a star is the diameter of Earth's orbit around the Sun, which is approximately 1 Astronomical Unit (AU).
Length of the Baseline
The baseline has a length of 1 AU because astronomers use only one half of the Earth's orbital diameter to define the parallax angle. Therefore, the baseline for parallax measurements is 1 AU, equivalent to about 149.6 million kilometers (93 million miles).
Distance Measurement and Limitations
A parallax of 1 arcsecond corresponds to a distance of 1 parsec or 3.26 light-years, which is about 206,265 AU or 3.1 × 1013 kilometers. However, the effectiveness of stellar parallax measurements diminishes with increasing distance to a star. This is because as stars become more distant, the parallax angle becomes smaller and harder to measure accurately.