If he means the Objection of the Arrow and so forth, yes and no.

The objections were that if the earth turned to the east there would be a steady wind from that direction; also an arrow loosed straight upward would fall west of the archer because the earth would have turned below it in the meantime. Etc.

These objections were considered by Jean Buridan and his pupil Nicole d'Oresme in the 14th century and answered with impressed impetus. Buridan said that because the impressed impetus was permanent, motion would continue after the initial force until a contrary impetus was encountered. Thus, the air, the arrow, etc. were also turning to the east. Oresme concluded that the matter was not solvable by empirical experience and cited Witelo's principle of relativity: the motions depended on where the observer was placed.

The impetus was eventually reimagined as "momentum" and Buridan's statement that impetus was proportional to weight and speed of the body became the equation momentum = mass*velocity. Momentum is of course simply the Latin for 'motion.' Both Buridan's concept of the impetus and his early version of "Newton's First Law" have stood the test of time.

But there were two other objections, one ancient, the other more modern.

If the earth revolved around the sun, there should be visible parallax among the fixed stars. There is none evident. That was enough for Aristotle and Archimedes to "falsify" (as we say) the revolution of the earth. Galileo was not very empirical about his astronomy. He was not the meticulous observer that Kepler or Brahe or Grassi were. He reported no parallax. Neither did anyone else. (The telescopes of that day never would have been able to.)

Copernicus suggested that the parallax was not visible because the stars were much farther away than supposed. But you cannot save one unproven hypothesis by adding a second unproven hypothesis. If the distance to the stars could be measured as much farther, that would not demonstrate heliocentrism, but it would remove the falsification. Revolution wold no longer imply visible parallax. But the stellar distance had been carefully estimated using the apparent relative sizes of the stars and their apparent relative brightnesses and the figure was a mind-boggling 70 million miles. (Today we know that even the Sun is farther than that. Copernicus' intuition was right. But we have hindsight; they did not.) I don't know if Buridan or Oresme considered this particular objection.

The modern objection stemmed from Galileo's inertia. A body at the top of a tower would have a greater eastward velocity than a body at the base of the tower. Therefore, a dropped sphere ought to hit the ground slightly east of the plumb line. If it did not, the rotation of the Earth would be falsified. Galileo suggested dropping cannonballs from a tower, but although many are convinced he did so (from Pisa, no less), he never reported doing so. Himself suspects that he did the experiment, found no eastward deflection and kept mum. Others after his time also suggested the experiment, but no one seems to have done it. A curious omission, like the dog in the night time.

When Bellarmine counseled Galileo in 1616 (iirc), he said there was no objection to Copernicanism as a mathematical method. In fact, the Jesuit astronomers of the Roman College had been teaching it. But Galileo had publicly suggested re-interpreting scripture to accommodate the hypothesis and, in the midst of the Protestant thingie, this sort of individual exegesis was frowned on. Bellarmine wrote that if empirical proof could be provided, there would be no problem; but he was loathe to reinterpret scripture in the teeth of Protestant criticism just in case Copernicanism might be correct.

Galileo never did come up with empirical proof. He proposed the motion of the tides as proof, but this was known to be bogus. Aquinas had mentioned the role of the moon in causing the tides; and Kepler had also shown that there was a connection. Galileo denounced these views as "occult." (Just as he denounced Kepler's ellipses.)

More damning, his "ultimate proof" contradicted his own inertial reasoning about the air and the arrow (apparently cribbed without attribution from Oresme). The oceans would also be moving toward the east and would also have inertia.

The required empirical proof came about in the late 1790s, when Guglielmini dropped balls from the tower of the University of Bologna, doing so indoors down the center of the spiral staircase, so wind would not intervene. A colleague in Germany replicated the experiment using a mineshaft. Both of them found the predicted eastward deflection. The earth was definitely spinning. In 1803, Calandrelli reported parallax in the star a-Lyrae and published. The earth was revolving around the sun. Note that these are direct manifestations of the two motions.

Settele put these discoveries in his new astronomy text, and took it to the Holy Office. The Office looked it over and said, "Yup, that's the empirical proof that Bellarmine wanted, and they lifted the ban on teaching the method as empirical fact. Settele's book came out in 1820.

Prior to this, heliocentrism had been accepted in spite of the two blatant "falsifications" because a) the math was easier (once Copernicanism was abandoned for Keplerism) and b) Newton came up with a really neat theory as why it might be true. But this is mystical Platonism; not empirical Aristotelianism. LOL

Anyhow, hope that helps.

Nobody? One guy there has claimed that Galilean Invariance answered any and all objections to heliocentrism on the basis of inertia. Everything I've read says that this was only actually solved by Newton, but I can't find a detailed analysis that explains why. I'd like to answer him in detail.

Can anyone help?