Stellar parallax is the apparent shift of the position of any nearby star against the background of distant stars. It is the result of Earth’s orbital motion around the Sun. It is so small and hard to observe. Successful measurement of stellar parallax was done only after the 19th century.
Some flat-Earthers presume as if stellar parallax has not been successfully observed, and use it is ‘evidence’ the Earth is stationary. They are wrong.
Galileo was a proponent of the heliocentric system: the Sun is at the center of the solar system, and Earth orbits around the Sun. If the Earth is indeed in orbital 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 made in 1838, nearly 200 years after Galileo died.
Stellar parallax is very hard to observe because it is so small. To illustrate, the star with the largest stellar parallax is Proxima Centauri. Its parallax is 0.7687 arcsec. The angle is comparable to a 2 cm wide object 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 measurement of stellar distances.
The figure in the illustration is the motions of selected stars as observed by Hipparcos satellite. The motion lines are combinations of circular motion of stellar parallax and the star’s proper motion.
Sizes are not to scale.