This is an interesting comment. I assume the reference is to the fact that at least some nearby stars move slightly with respect to distant stars as we move from winter to summer or fall to spring or, in fact, any 6 month period. This would be the result of viewing the nearby stars from a position in space that differs by 186,000,000 miles (twice our distance from the sun.) I do believe that this has been observed and would give quite an accurate measurement of the distance to these nearby stars.
Correct me if I'm wrong about this.
OTOH, I'm trying to think of an alternative explanation for the shift in postion that would pass the smell test. If there is an explanation I would like to hear it.
Correct me if I'm wrong about this.
You're not wrong. But the reason Copernicus's view won acceptance despite active persecution by the church is that the motions of the planets make sense in a heliocentric system. You don't need epicycles and cycles within epicycles (for which no mechanism exists anyway) to make sense of it all.
Think about Venus. Venus catches up to us every so often, at first following the Sun down in the evenings, then passing so close to the Sun we can't see it, then appearing in the morning out in front of it. It's on an inside track so it has a shorter "year" to complete its orbit. All of this makes sense as we understand things heliocentrically with Kepler's Law.
If the Earth were at the center of the solar system, never mind the universe, the path of Venus through our sky would make no sense. It's not what Kepler's Law would predict at all. Pre-Copernicus, funny epicycles were invoked. Yes, Venus circles the Earth but it's really circling a point which circles the Earth. Except sometimes the real planetary motions are so ragged that they had to say the planet was circling a point circling a point circling the Earth.
People were ready for a simpler explanation. Galileo, Kepler, and Newton came through. Since Galileo's time, we can see other bodies orbiting in other systems (starting with the moons of Jupiter) and they don't do epicycles. They do Keplerian/Newtonian orbits.
The simplest explanation is the neo-Tychonic model: Earth stable at center, universe rotates, holding earth stable at center (expalined in the book). Sun revolves with the universe (though has a small difference in velocity), planets orbit the sun with elliptical orbits (earth is not a planet in this case). The stars revolution is centered on the sun.
This is an exact geocemetric inversion of heliocentrism.
Other more complex explanations are based on aether, aether flow, and abberation.
Mark Wyatt