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.

In my last post of 2013, I gave a problem that provides part of the plot of my ebook novel Athene's Prophecy: how could a Roman prove the heliocentric theory? The short answer is, it was not possible for a Roman to do this directly from then current knowledge. This is a fine example of how you cannot get from A to B directly, but have to through some other places first. That would have been possible, but it did not happen. Why not? The question is of interest because it goes to the heart of what science is about, and that is a more difficult question to answer than you might think, because most scientists do not really have the time to consider it.
 
As an example, during my early working time in an institution, only too much was wasted writing proposals, trying to get funding, trying to keep funding, trying to get or get access to equipment, in other words, doing just about anything except science. Then when I was doing science, the most important thing was to get the material for another paper, because failure to produce enough papers meant failure with the funding, etc. What happened to me was exactly what Kuhn argued would happen: I always started a project that I thought had a very good chance of success.
 
So, back to the question of the title. The first problem would be, why bother? Aristotle was generally believed to be correct, and even if he were wrong in something, who cared? The important point was that the then current theory was splendidly capable of predicting everything of general interest, and, more to the point, it "proved" that the heliocentric theory was wrong. The Ptolemaic model was perfectly adequate for calculating and predicting the timing of things of astronomical, agricultural and religious interest. There was no apparent need to change it. This is where I disagree, because the problem lay in an incorrect understanding of dynamics. As a consequence, their wrong dynamics arguably inhibited progress. I believe that if you understand what is correct, you are more likely to make advances.
 
Aristarchus challenged the "fixed earth" model, but he was hardly rewarded well for what he did, and even now, how many people realize he made more progress than Copernicus? The real problem lay in the proof of the fixed earth model, which relied on experimental proof, in which the observations were interpreted in terms of Aristotle's dynamics, and these were just plain wrong, oddly enough because in getting to them, Aristotle abandoned his own methodology and relied on "the obvious".
 
What Galileo did was to show the "proof" was wrong, he undermined Aristotle's dynamics, and further, he showed the satellites of Jupiter did not fit at all well with the model of Claudius Ptolemy. However, telescopes were not available to my Roman, so he had some work to do. In my next post I shall look at the actual problem in more detail, but in the meantime, how many scientists even now ask themselves whether the conclusions they reach from their experiments could be wrong because the theory they assumed in reaching it could be wrong? Obviously much of our theory is very well tested, but is all of it? Our understanding of electromagnetism is almost certainly correct, so our instruments should give us the correct results, but if we go deeper into our chemical interpretations, how much is actually dependent on a hypothesis that is difficult to test?

This update covers two months and focuses on some compositional issues. Why is composition important? In my theory, initial accretion is driven by chemical interactions, hence material that accretes at different temperatures may have different compositions. The mechanism of initial accretion in standard theory is undefined, but is usually considered to be due to gravitational interactions, in which case there should be no compositional differences, apart from outer bodies being icy. Unfortunately, the following does not show much light on this issue.

One paper involved the formation of the Moon (Nature 504: 27 - 29) The problems here are reasonably simple. Collisional dynamics suggest that which is flung off Earth comprises mainly material from the impactor, and this should have different isotope compositions from Earth, since it appears that certain isotopes varied in relative concentration by some radial function of their location in the accretion disk. However, isotope evidence indicates both bodies came from the same source. Thus the oxygen, chromium, titanium, tungsten and silicon isotope compositions of the two bodies are indistinguishable, which suggests common origin. The answers to this usually invoke extra processes, such as extensive mixing or a later gravitational resonance with the sun, but the feasibility of any of these as explanations is unclear. There are differences in composition between the Earth and the Moon. The Moon has less than 10% iron, and is poorer in volatile elements. The collision theory explains the former in terms of the iron core of the impactor merging with the earth's core, while the lack of volatile elements is consistent with these being lost from a hot disk.  It appears that refractory elements have similar abundance in both bodies. Seemingly, either the Moon formed from material from Earth's mantle, or that the Moon and the silicate portion of Earth each formed from an identical mix. My explanation is that both formed at the same radial distance and hence formed the same way from the same material, the Moon having come from either one or two bodies that grew at the Lagrange positions L4 or L5, and were dislodged when they became too big to remain in those positions. That concept is not original, but my theory makes accretion of solid bodies much more probable at our solar distance. Further, a late-forming body at L4 or L5 would have less iron, because the body, and the outer part of Earth, would form from material that started further from the sun (because it is the last part of material moving inwards).

The second major set of publications was the collection of papers in vol 343 of Science relating to results from Curiosity in Gale Crater, Mars. These results have already been announced, and as far as theories of planetary formation are concerned, these were not very interesting. One point that was of interest was the evidence of water flow and of aqueous leaching. The rover found sedimentary rock, smectites (clays, both Fe and Al rich being present) and calcium sulphate that had been precipitated from water. The evidence is in excellent agreement with the theory put forward some years ago that when an impactor struck Mars and formed a crater, it would also heat the ground beneath it and liquefy any ice. Calculations indicated this could remain in the liquid state for perhaps thousands of years. The water at Gale Crater was estimated to have been liquid for a minimum time of hundreds to tens of thousands of years. Such a short time is consistent with this impact theory, but of course since the measurements were taken inside an impact crater, it may not be relevant to Mars in general.

Finally localized sources of water vapour were detected by far infrared spectroscopy on the Herschel Space Observatory on the dwarf planet (1) Ceres (Nature 505: 525 – 527). This water vapour appeared to have been emitted from localized mid-latitude sources. The cause of the water evaporation could not be determined, but it could be due to either comet-like sublimation or to cryo-volcanism. The amount of water on Ceres is of interest because it might indicate that Ceres did not originate in the asteroid belt. More will be known about Ceres when the Dawn space craft reaches it.