Why are measurements of stellar parallax difficult to make? What are the advantages of making these measurements from orbit?

Astronomical measurements are the foundation of understanding our universe. These measurements, which can include calculations of distance, speed, light intensity, and angular positions, are developed through keen observation and sophisticated instrumentation.

One crucial astronomical measurement is the distance to stars. Calculating these vast distances accurately has been a perennial challenge in astronomy. In the case of stellar parallax, the process involves observing the tiny shifts in a star's apparent position as Earth orbits the Sun. Understanding this shift is mandatory for calculating the true distance to stars. This calculation, in turn, helps astronomers determine various other cosmic parameters — like the luminosity of stars, their motion relative to each other, and even aids in the search for extraterrestrial planets.

Angular displacement refers to the change in the angle as observed from two different points. In the context of stellar parallax, it represents the apparent shift in a star's position against the more distant background, when viewed from opposite sides of Earth's orbit. As Earth travels around the Sun, nearby stars appear to sway back and forth due to this angular displacement.

The angles involved in these observations are minute, often measured in arcseconds—which is 1/3,600th of a degree. Utilizing this information, coupled with the known orbit of Earth, astronomers can employ trigonometry to determine the distance of stars. Given such small angles, it is clear why precise instruments and clear observation conditions are imperative; otherwise, the minuscule angular shifts cannot be accurately recorded.

Measuring stellar parallax from the vantage point above Earth's atmosphere brings numerous advantages. Space-based observations through satellites and telescopes, like the Hubble Space Telescope or the Gaia observatory, provide a clearer, unobstructed view of the cosmos.

In orbit, these instruments are not hampered by atmospheric turbulence and refraction, which can warp and blur the light from stars, making it challenging to specify their accurate positions. Moreover, the perpetual possibility to observe without the interference of the day and night cycle allows for continuous monitoring of a star's position. This contributes to a more reliable data collection and, therefore, more exact measurements of stellar parallax and the subsequent computability of astronomical distances.