I am continuing this fixation with the heliocentric theory because I feel there remains a lot for budding theoreticians to learn from it. Obviously we know the planets do go around the sun, but that is not the point. Rather, I am hoping to show how things can go wrong in forming theories, and what sort of things make it right. The most likely place to go wrong can be summarized simply: if you start with a wrong premise, you may draw a wrong conclusion. Your conclusion may agree with observation, because a wrong premise can do that, as Aristotle pointed out. A wrong premise that brings considerable agreement with observation is extremely difficult to get rid of, because it has pervasive effects.
 
One reason why, in classical times, it was felt that the Earth must be stationary was that if the Earth moved, because of the premise that air rises, hence the fact that we have air at all must be because the Universe is full of it, means that through logic the Earth must move through air. If so, there would be a contrary wind, the speed difference of which on either side would depend on the rate of rotation. Note this argument holds even if the air is orbiting as well. There was no such wind, therefore no such orbit. We can forgive Aristotle here, but we forgive those who followed Archimedes less well. Had Aristotle known of Archimedes Principle, this argument would probably never have been made.
 
An important observation was that the Sun's output was known to have been constant for several thousand years, and a quick calculation showed that had it been powered by combustion, it should have faded. It had not. There was only one possible explanation the ancients could see: the Sun had to be moving, and by moving, it generated a lot of friction, because such friction would be the only physical means of powering the star. The earth did not generate heat, therefore it was not moving. Note that it was Aristotle, or someone earlier, who established that friction generated heat, not Rumford. It was too much to expect them to guess nuclear fusion, but it shows that when developing a theory, every now and again something turns up that should not be explained. There is no fault in admitting you do not know everything. Newton is often quoted as saying there should be no hypotheses. I do not think Newton really believed that. I think what Newton meant was, there should be no hypotheses unsupported by observational evidence. Unfortunately, in this case there was observational evidence; the problem lay with the use of the word "only".
 
Another problem with the heliocentric theory was that it did not calculate anything of interest. We had to wait for Newton.
 
There was also a final problem. Aristotle had stated that heavier things fall faster than light things. The ancients appreciated that orbital motion required the planet to be under constant acceleration towards the star, i.e. falling. If heavier things fell faster than light ones, the planet should fall to pieces, with light matter streaming off behind the planet. That did not happen, therefore the Earth could not be falling. The only way it could not be falling is if it were fixed at the centre. Therefore the heliocentric theory was wrong. It is here that Aristotle failed in his own methodology. He was always stating that only observation counts, and he advocated experimenting. Unfortunately, he never bothered to test this because it was obvious.
 
There was a deeper problem. He divided motion into two classes: eternal and constrained. Constrained motion caused the body to stop moving, and Aristotle assumed that it was a property of the body because some objects, when thrown, went further than others. What he should have done is to use his own methodology: either the constraint came from within the body, or was external to it. A few experiments would show it was external, for example, a stone dropping in air goes faster than one dropped in water. That in itself is not enough, and some further tests are required. Can you see why?
 
To summarize, get off to the wrong start with a theory and you can get into trouble. The question is, can this happen now? In my opinion, it has. I find the Copenhagen interpretation of quantum mechanics to be difficult to believe. How can the fact you observe something be the cause of it? Very homocentric! What do you think?

Before Christmas, I raised the question, how could the ancients have proven the Earth goes around the sun? I guess it is about time to get started on answering it. The first task was to review the literature. It then becomes obvious that you have to overturn Aristotle. There are various places where one can start, but one is to decide why we have day and night. Let us use Aristotle’s own methodology, which is to break the issue down into discrete issues. Thus we say, either the Earth is fixed and everything rotates around it, or everything is more or less fixed, and the Earth rotates. Aristotle had reached that step, and had “proven” that the Earth did not rotate. Therefore the day/night must occur through the sun orbiting the Earth. The heliocentric theory, despite its advantages, is falsified.
 
At this point, we should examine the methodology of the experiment. It is important to recognize that Aristotle was very clear on one point, and he has been badly misrepresented on this ever since. Aristotle clearly asserted that logic must be applied to experimental observations, and that observation alone was critical. So, what was his experiment? Aristotle argued that if you threw a stone vertically into the air, it always came back to the same place. Had the earth been rotating, the path length of a rotation increased with height, in which case the stone should drag back westwards. It did not, so the earth did not rotate. Note that at this point, Aristotle was effectively arguing for the conservation of angular momentum, or even better, the principle of least action. I wonder how many of my readers would recognize that, and know why it is so significant? Before reading any further, what do you think about Aristotle’s experiment? What is wrong, and how would you correct it, bearing in mind you have only ancient technology?
 
In my ebook, Athene’s Prophecy, my protagonist dismisses the experiment by arguing that vertical is defined as the point where the stone falls back to the same place. By defining the point thus, if the stone does not come back to the same place, it was not thrown vertically. He then criticizes Aristotle by arguing that the correct way to do the experiment is to simply drop the stone from a high tower. The reason is that while Aristotle would be correct in that there should be a drag to the west going up, exactly the opposite should occur on the way back down. What should happen if dropped from a tower is that the stone would strike the ground slightly to the east of the vertical position, and in Rhodes, where this was being discussed, also slightly to the south. Can you see why?
 
What happened next is that my protagonist refused to carry out the experiment. This is a somewhat difficult experiment to carry out, but in my opinion, it might be of considerable interest to senior school students, and it introduces them to many of the issues of science that still apply. They need a high tower (or some equivalent), and the first problem is to define the exact vertical spot below it. This is difficult enough to do today with modern surveying equipment, but in those days, the error range is likely to exceed the effect. The school could set this up, with the help of external surveyors, or even physicists if they can find any. The students have to select the right material (a small lead cone, dropped point down without tumbling would probably be optimal) and correct for wind speed. This experiment, more than any other I can think of that is suitable for schools, introduces the concept of experimental error, and they can get illustrations of this because the experiment, in theory, besides proving the Earth rotates, with a little mathematics permits two measurements of the size of the Earth. The answers are likely to be hilarious, unfortunately, once the student confronts the issue of required accuracy. The problem is the difference between the height and the earth's radius, but it may give a new appreciation to the extreme requirements of the large hadron collider, where protons (look up their size) circle a 26 km loop and collide.