Have you got a spare 5 meters in your basement, cikljamas?
Ok, so if the sun is 1mm in diameter:
From the sun: and to our solar system scale:
Mercury is orbiting 4.1cm away
Venus is orbiting 7.7cm away
Earth is orbiting 10.7cm away
Mars is orbiting 16.3cm away
Jupiter is orbiting 55.9cm away
Saturn is orbiting 102.5cm away
Uranus is orbiting 216.2cm away
Neptune is orbiting 323.2cm away
Pluto is orbiting 424.8cm away
To get an even better understanding, at each distance, make a circle using the sun as the centre point.
Are you following me so far, cikljamas? Now, make a circle from the earth to the sun, using the earth as the centrepoint.
Now, start moving your sun around that circle around earth.
Do you see any problems, grasshopper?
Since you understand the difference between geocentric and heliocentric retrograde motion, you should be able to explain to us how and why Tycho's argument is not valid :
Although planet-like, the comets do not display retrograde motion, *Tycho* argued that the stations and retrogradations that we see in the motion of the planets must really be theirs rather than due to the motion of the earth as Copernicus claims:
_"In addition the two comets which were carried near the opposition of the sun showed clearly enough that the earth does not in fact revolve annually, since the motion of the earth did not detract in any way from their regular and established motion, as happens to the planets which Copernicus believes move backward because of the motion of the earth" (VII, 130).
In short, if the earth revolved annually around the sun, why would the comets not also display retrograde motion?"_
Your attempt of refuting Tycho's argument boils down to arguing that comets do display retrograde motion.
However, the author from whose book this excerpt is taken, doesn't share your opinion, since he proceeds (right after the paragraph above) with the following words (counter-"argument") :
Tycho's argument is not entirely consistent: in his system no less than
Copernicus's the stations and retrogradations of bodies revolving around
the sun are due to the position of the observer on earth, which is either
stationary while the sun is not (geoheliocentrism), or in motion while the
sun is immobile (heliocentrism). Therefore comets that revolved like the
planets around the sun would be expected to display retrograde motion
in both systems.He is obviously talking about one special hypothetical case in which comets revolve like planets around the sun.
1. How does such special hypothetical scenario is capable of disproving Tycho's argument?
2. How come that the author doesn't use your "counter-argument"? Maybe because he is not so fantastically stupid as you are, since if it was the case (if you were right) then it would be certainly the most elegant way of refutation of Tycho's argument, wouldn't it?
The author continues like this :
Nevertheless,
Tycho clearly believed that his argument from the behavior of comets was forceful (definite in expression or action). In a letter to
Magini, professor of mathematics at Bologna, dated 1590,
Tycho described his arguments about comets. The Copernican system, he proclaimed, with its
"triple motion of the earth will be unquestionably refuted, not simply theologically and physically, but even mathematically, even though Copernicus hoped that he had proposed to mathematicians sufficiently mathematical statements to which they could not object" (VII, 295).
Tycho was especially proud to announce a refutation of Copernicus on his own ground, responding to the latter's remark in the preface to
De revolutionibus that "
mathematics is written for mathematicians."
ASTR 1P01, CLIP 56: Epicycles; Retrograde Motions in the Geocentric and Heliocentric Models :
Geocentric motion - Awesome CG animation :