Stellar parallax is the apparent shift of the position of a nearby star against the background of distant stars. It is the result of Earth’s orbital motion around the Sun. It is tiny and difficult to observe. Successful measurement of stellar parallax was done only after the 19th century.
Some flat-Earthers claim that stellar parallax has never been successfully observed, and they use it as ‘evidence’ Earth is stationary. In reality, stellar parallax has been successfully measured in 1838 and is now used as the basis for measuring stellar distances.
In 1632, Galileo defended Copernicus’ heliocentric system that the Sun is at the center of the solar system and Earth is in motion around the Sun. But if the Earth is in motion around the Sun, then we should be able to observe stellar parallax. The problem is that Galileo and other astronomers at that time were not successful in finding the hypothesized stellar parallax.
During Galileo’s time, they were not able to observe stellar parallax, but only because the technology was not there yet. Successful observation of stellar parallax was only achieved in 1838, nearly 200 years after Galileo died.
Stellar parallax is challenging to observe because it is so small. As an example, the star with the largest stellar parallax is Proxima Centauri. Its parallax is 0.7687 arcsec. The angle is comparable to an object with a width of 2 cm at a distance of 5.3 km.
Today, observation of stellar parallax is done using satellites, like Hipparcos, Hubble, and Gaia. Stellar parallax is the basis for the measurement of stellar distances.