The parallax effect can be seen if we open only the right or the left eye while we see an object. The object seems to slightly change its position.
If the Earth rotates (or it is better to say it revolves) around the Sun then such an effect should be visible also for the position of a star. If we look a star in January and the same star in July where the Earth has completed ½ revolutions around the Sun the distance to the position in January is maximal and therefore the parallax effect should be optimally visible. As a result of the Earth's revolution, from day to day a particular star will or rise, or set ( transit) at earlier and earlier times.
Hipparchus tried to measure the parallax but he could not observe any visible effect.
A star A in January is seen in position B and in July as a star situated in C. The average distance to the Sun, the astronomical unit A.U. is approximately 150 million kilometers. This distance is small compared to the distance of the next star closest to the Earth after the Sun. It is around 250000 astronomical units. Therefore the so-called parallax effect is extremely small. The parallax angle of the nearest star is less than 1/3600 of one degree, it is like trying to see a penny size object from a distance 4 km away.
Ancient astronomers tried to measure the stellar parallax via careful naked-eye observations but failed. Bessel was the first to measure the parallax of a star (Cygni 61) only in 1838, thus making it possible to calculate its distance.
Even if Aristarchus assumed a heliocentric model, i.e. the Sun at the center and the Earth orbiting around the Sun this idea was not accepted. The Earth was not thought to be a “celestial” body, such as the luminous stars. If the Earth rotates around its axis, then why we do not feel any rotation effects. Wouldn’t clouds, air, birds, etc. be left behind if the Earth is moving?! No stellar parallax could be measured showing as a sign of the Earth revolution around the Sun. One had to assume that the stars have to be extremely far away. More than 250000 times further away than the Sun.
Aristarchus' claims were not generally accepted, and in fact some thought he should be indicted on a charge of impiety for suggesting that the Earth, thought to be the fixed center of the universe, was in motion (Bertrand Russell, quoting Plutarch about Cleanthes). The other astronomers didn't believe Aristarchus' theory for different reasons. It was known that the distance to the Sun was in excess of one million miles (Aristarchus himself estimated one and a half million miles, which is far too low) and they thought that if the Earth is going around in a circle that big, the pattern of stars in the sky would vary noticeably throughout the year, because the closer ones would appear to move to some extent against the background of the ones further away. Aristarchus responded that they are all so far away that a million miles or two difference in the point of observation is negligible. This implied, though, the universe was really huge -- at least billions of miles across -- which few were ready to believe.
Aristotle did not accept the heliocentric model because among other reasons he assumed that the centripetal acceleration would cause objects on the Earth to fly off at night. The effect is real we do weight less at night than at day for this reason. But the effect is small compared to the Eearth's gravity which keeps us on the ground.
The geocentric model complicates of course the model necessary to describe the position of the stars. Ptolemy had to describe complicated orbits of the planets if we fix the coordinate system to the center of the Earth. Nevertheless the model was very successful and accurate that even Copernicus model although correct did not describe the star and planet positions more accurately than Ptolemy's model.
Medieval Greece / Byzantine Empire