Final answer:
Space-based trigonometric parallax is limited in its effectiveness for measuring distances to stars beyond about 300 light-years due to the very small parallax angles involved, which are challenging to measure accurately.
Step-by-step explanation:
Parallax measurements use the apparent shift in the position of a nearby star relative to distant stars, observed from opposite ends of Earth's orbit, to determine the star's distance from us. The parallax angle, which is half the total observed angular shift over a six-month period, allows for the calculation of distance using triangulation methods. However, this technique of determining distances using space-based trigonometric parallax has limitations. One major limitation is that parallax angles for distant stars become exceedingly small and difficult to measure precisely; distances beyond approximately 300 light-years result in angular shifts too minute to detect accurately even with sophisticated space-based instruments like the Hipparcos and Gaia satellites.