I understand that this is meant as a parable and an exercise in "first principles" thought. However, since geocentricism and heliocentricism were mentioned, for historical accuracy, this is what Archimedes thought [quoting from Wikipedia]:

The original text has been lost, but a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work in which he advanced the heliocentric model as an alternative hypothesis to geocentrism:

You are now aware ['you' being King Gelon] that the "universe" is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the "universe" just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.

Aristarchus suspected the stars were other suns that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time.

I understand that this is meant as a parable and an exercise in "first principles" thought. However, since geocentricism and heliocentricism were mentioned, for historical accuracy, this is what Archimedes thought [quoting from Wikipedia]:

The original text has been lost, but a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work in which he advanced the heliocentric model as an alternative hypothesis to geocentrism:

You are now aware ['you' being King Gelon] that the "universe" is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account (τά γραφόμενα) as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the "universe" just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.

Aristarchus suspected the stars were other suns that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time.

I understand that this is meant as a parable and an exercise in "first principles" thought. However, since geocentricism and heliocentricism were mentioned, for historical accuracy, this is what Archimedes thought [quoting from Wikipedia]:

The original text has been lost, but a reference in Archimedes' book The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli) describes a work in which he advanced the heliocentric model as an alternative hypothesis to geocentrism:

You are now aware ['you' being King Gelon] that the "universe" is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account (τά γραφόμενα) as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the "universe" just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.^[4]

Aristarchus suspected the stars were other suns^[5] that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time.