Stellar parallax is the apparent shift of the position of any nearby star against the background of distant stars. It is caused by Earth’s orbital motion around the Sun. It is so small and hard to observe. Successful measurement of stellar parallax was done only after 19th century.
Flat-Earthers like to think stellar parallax doesn’t exist, and that 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 unable to observe the hypothesized stellar parallax.
During Galileo’s time, they couldn’t observe stellar parallax, but only because the technology wasn’t there yet. Successful observation of stellar parallax could only be 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 largest stellar parallax is Proxima Centauri. Its parallax is 0.7687 arcsec. The angle is comparable to a 2 cm wide object at the 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.