Everyone knows about people like Galileo, Newton, etc, but how are such theories discovered? Now obviously I have no idea exactly how they did it, but I think there are some principles involved, and I also think some readers might find these of interest. I hope so, because therein lies the third task for my protagonist in my novel *Athene’s Prophecy*.

The reason that is in the novel is because the overall plot requires a young Roman to get help from superior aliens to avoid a disaster in the 24^{th} century. The reason for the time difference is, of course, relativity. Getting to the aliens involves being abducted by other aliens, but once taken to another world, the protagonist has to be something more than a specimen that can talk. To get the aliens to respond, he has to be someone of interest to talk to. Suppose you had the chance to talk to someone from the 16^{th} century, or to Galileo, who would you choose? My proposition is, Galileo, so the task for my young protagonist is to prove the heliocentric theory, i.e. that the earth moves around the sun. That is similar to what was in the film *Agora*. The big problem was, everybody was so sure the earth was fixed and everything else went around it. Not only were they sure, but they could also use their theory to calculate everything that mattered, such as when the solstices and equinoxes would be, when Easter would be, and when various planets would be where in the sky. What else did they need?

The alternative theory was due to Aristarchus of Samos. What Aristarchus maintained was that the earth was a planet, and all planets went around the sun, the moon went around the earth, and the solar system was huge. This latter point was of interest, because Aristarchus measured the system. His first measurement was to obtain the size and distance of the Moon, and what he did was to get two people to measure the angle at the exact moment an eclipse of the moon started. These two people were separated by as much distance as he could manage, and with one distance and two angles he had a triangle that would permit the measurement of the distance to the moon. The size then followed from its solid angle. The method is completely logical, although the amount of experimental error was somewhat large, and his answer was out by a factor of approximately two. He then measured the distance to the sun by measuring the angle between the sun and moon lines when the moon was half shaded, and used his moon distance and Pythagoras’ theorem. His error here was about a factor of five, and would have been about a factor of ten had not the error in the moon distance favoured him. The error range here was too great (to see why, check how tangents get very large as they approach 90 degrees) but he was the first to realize that the solar system is really very large. He also showed that the sun is huge compared to the earth.

Aristarchus, following Aristotle, also postulated that the stars were other suns, but so far away, and they would have to be going at even greater speeds. This did not make sense, so he needed an alternative theory. In my opinion, this is invariably the first step in forming a new theory: there is some observation that simply does not make sense within the old theory. Newton’s theory was born through something that did not make sense. If you believed Copernicus, or Aristarchus, if you had heard of him, or of Galileo, then the earth and the other planets went around the sun, but there was a problem: Mars could only be explained through elliptical orbits, and nobody could explain how a body could orbit in an elliptical path with only a central force. Newton showed that elliptical orbits followed from his inverse square law of gravity. Relativity was also born the same way. What did not make sense was the observation that no matter what direction you looked, the speed of light was constant. What Einstein did was to accept that as a fact, and put that into the classical Galilean relativity, and came up with what we call relativity.

So we now get to the second step in building a new theory. That involves reading about what is known, or thought to be known, about the subject. If we think about the heliocentric theory in classical times, we now know that much of what was thought to be correct was not. So, here is a challenge. If you had to, could you prove that the earth goes around the sun, while being restricted to what was known or knowable in the first century? Answers in the next few posts, but feel free to offer your thoughts.