Parallax and Heliocentrism

I Hope, For Galileo's Sake, He Did Retract · Parallax and Heliocentrism

Here is part of an essay written or promoted by Damien Mackey:

The idea that the Ancients cited an apparent absence of parallax shift in the nearest stars due to Earth’s hypothesised orbit about the Sun, that they favoured geocentrism in part because of this, and that Copernicus hedged against this criticism, is a complete falsehood that is almost universally accepted at present.

it leads to anachronistic misreadings of both Ptolemy and Copernicus, when we fail to realise the notion of a parallax shift in nearby stars relative to those further away never could have crossed their minds

Here it is on Academia:

Claim that Copernicus knew of Aristarchus
https://www.academia.edu/165256445/Claim_that_Copernicus_knew_of_Aristarchus

It seems to be identic to or rather an excerpt from:

Setting the Record Straight: How Copernicus Concealed His Debt to Aristarchus—and Claimed an Intellectual Priority He Knew Wasn’t His
CosmiCave | Daryl Janzen | Jul 30.2025
https://cosmicave.org/2025/07/30/setting-the-record-straight-how-copernicus-concealed-his-debt-to-aristarchus-and-claimed-an-intellectual-priority-he-knew-wasnt-his/

Now, this is actually more like an equivocation than a complete falsehood.

The "parallax shift in the nearest stars" is an idea that didn't cross their minds, because they (Ptolemy and Copernicus alike, with Galileo) didn't believe there were near or far stars, but all stars were equally far.

However, "parallax shift in the stars" did cross their minds. If Virgo and Pisces* are equally far from the centre of the universe, and that centre is not Earth, but the Sun, then they would be shifting in distance from Earth. In early March, Virgo would be the biggest, and in early September, Pisces would be the biggest. Inversely, in early March, Pisces is either way hidden by the Sun and in early September Virgo is either way hidden by the Sun. However, either side of the timeslot when it's invisible, either sign would be the smallest.

This is probably what Tycho meant where the reference is given in Spanish wiki:

por ejemplo, una de las principales objeciones de Tycho al heliocentrismo copernicano era que para ser compatible con la ausencia de paralaje estelar observable, debería existir un gigantesco y sumamente improbable vacío entre la órbita de Saturno y la octava esfera (la de las estrellas fijas).

For example, one of the main objections Tycho had to Copernican Heliocentrism was that, to be compatible with the absence of observable stellar parallax, there should exist a gigantic and highly improbable void between the orbit of Saturnus and the Eighth Sphere (that of the fix stars).

The only observable parallax that's possible if all fix stars, all non-planet-stars are on the same sphere is the one given about smaller or bigger views of star signs. He cannot have been speaking about differential parallax in the Galilean and modern sense.

The footnote 4 is given as:

See p.51 in The reception of Copernicus' heliocentric theory: proceedings of a symposium organized by the Nicolas Copernicus Committee of the International Union of the History and Philosophy of Science, Torun, Poland, 1973, ed. Jerzy Dobrzycki, International Union of the History and Philosophy of Science. Nicolas Copernicus Committee; ISBN 90-277-0311-6, ISBN 978-90-277-0311-8

While this Symposium was held was under Communist Poland, I'll presume they were not putting words into the mouth (or pen) of Tycho Brahe. And actually, Daryl Janzen credits the objection to Tycho and credits him with being the first to make it. And obviously, as Tycho also held to fix stars being in a sphere, the parallax he was talking of was not one star moving "in front of" another more distant one, wasn't differential parallax.

Now, since then, a phenomenon has been observed which is identified with Galileo's differential parallax. Friedrich Wilhelm Bessel in 1838. Before that, another astronomer had looked for it, Bradley, but what he found in 1728—29 was incompatible with parallax.

Calculation showed that if there had been any appreciable motion due to parallax, then the star should have reached its most southerly apparent position in December, and its most northerly apparent position in June. What Bradley found instead was an apparent motion that reached its most southerly point in March, and its most northerly point in September; and that could not be accounted for by parallax: the cause of a motion with the pattern actually seen was at first obscure.

Well, with a mechanistic world view, you are stuck with aberration of starlight and then differential parallax is observed against the background of that.

With a Christian world view, the whole movement of any star, as observed through telescope, both the part analysed as aberration and the part analysed as parallax, can be what the angel does in a kind of dance, to honour God.

As soon as Tychonian parallax is unobserved, there is no actual proof possible that the Earth is moving.

Hans Georg Lundahl
Paris
First Passion Lord's Day
22.III.2026

* My own and granny's and my mother's signs are opposite, so I don't need to verify any other couples that are opposite. I wouldn't like to become an expert in astrology. And please note, astrology signs on the zodiac are still better known than their synonym the "ecliptic plane" ...

Wikis consulted:

https://es.wikipedia.org/wiki/Paralaje_estelar

https://en.wikipedia.org/wiki/James_Bradley