The Mistakes of Astronomers

Wait. This author says that Copernicus makes the earth together with the moon trace out the orbis magnnus in a year, moving from east to west. But this is false and impossible and could never have been uttered by Copernicus.

This shows at the very outset that he is very ill-informed about the position which he refutes.

He makes it go in the opposite direction, from west to east in the order of the signs of the zodiac.

So that it appears that the annual motion belongs to the sun, which ‘is placed immovably in the center of the zodiac.

You see his excessive boldness, setting himself up to refute another’s doctrine while remaining ignorant of its basic foundations.

I have seen something similar argued against Copernicus by Tycho.

Copernicus first explains the remarkable consequences to the various planets deriving from the annual movement of the earth; in particular the forward and retrograde movements of the three outer planets.

Then he adds that these apparent mutations which are perceived to be greater in Mars than in Jupiter, from Jupiter’s being more distant, and still less in Saturn, from its being farther away than Jupiter, remain imperceptible in the fixed stars because of their immense distance from us in comparison with the distance of Jupiter or of Saturn.

Here the adversaries of this opinion rise up, and take what Copernicus has called “imperceptible” as having been assumed by him to be really and absolutely nonexistent.

Remarking that even the smallest of the fixed stars is still perceptible, since it strikes our sense of sight, they set themselves to calculating (with the Introduction of still more false assumptions), and deduce that in Copernicus’s doctrine one must admit that a fixed star is much larger than the orbit of the earth.

To reveal the folly of their entire method, I shall show that by assuming that a star of the sixth magnitude may be no larger than the sun, one may deduce by means of correct demonstrations that the distance of the fixed stars from us is sufficiently great to make quite imperceptible in them the annual movement of the earth which in turn causes such large and observable variations in the planets.

Simultaneously I shall expose to you a gigantic fallacy in the assumptions made by the adversaries of Copernicus.

To begin with, I assume along with Copernicus and in agreement with his opponents that the radius of the earth’s orbit, which is the distance from the sun to the earth, contains 1,208 of the earth’s radii. Secondly, I assume with the same concurrence and in accordance with the truth that the apparent diameter of the sun at its average distance is about one-half a degree, or 300 minutes; this is 1,800 seconds, or 108,000 third-order divisions.

Since the apparent diameter of a fixed star of the first magnitude is no more than 5 seconds, or 300 thirds, and the diameter of one of the sixth magnitude measures 50 thirds (and here is the greatest error of Copernicus’s adversaries), then the diameter of the sun contains the diameter of a fixed star of the sixth magnitude 2,160 times.

Therefore, if one assumes that a fixed star of the sixth magnitude is really equal to the sun and not larger, this amounts to saying that if the sun moved away until its diameter looked to be 1/2160th of what it now appears to be, its distance would have to be 2,160 times what it is In fact now.

This is the same as to say that the distance of a fixed star of the sixth magnitude is 2,160 radii of the earth’s orbit. And since the distance from the earth to the sun is commonly granted to contain 1,208 radii of the earth, and the distance of the fixed star is, as we said, 2,160 radii of the orbit, then the radius of the earth in relation to that of its orbit is much greater than (almost double) the radius of that orbit in relation to the stellar sphere.

Therefore, the difference in aspect of the fixed star caused by the diameter of the earth’s orbit would be little more noticeable than that which is observed in the sun due to the radius of the earth.

(note: Galileo’s numbers are Inaccurate, but serve the purposes of his argument; he seriously underestimated stellar distance, but nevertheless placed the stars well beyond more typical estimations made by those he proceeds to mention.)

It is wrong, since according to this author a star of the sixth magnitude would have to be as large as the earth’s orbit in order to justify the dictum of Copernicus.

Yet assuming it to be equal only to the sun, which in turn is rather less than one ten-millionth of that orbit, makes the stellar sphere so large and distant that this alone is sufficient to remove this objection against Copernicus.

The calculation is very short and simple. The diameter of the sun is 11 radii of the earth, and the diameter of the earth’s orbit contains 2,416 of these radii, as both parties agree.

So the diameter of the orbit contains that of the sun approximately 220 times, and since spheres are to each other as the cubes of their diameters, we take the cube of 220 and we have the orbit 10,648,000 times as large as the sun. The author would say that a star of the sixth magnitude would have to be equal to this orbit.