Lecture 11 - The Copernican Revolution (2/7/96)

Seeds: Chapter 4

1. Copernicus continued
   • The orbital distance of superior planets can be found by using the time between opposition and quadrature compared to the Sidereal periods of the planets
   • Copernicus computed the orbital radii of the 5 other known planets relative to the size of Earth's orbit
   • Copernicus knew the difference between the sidereal period and synodic period of the planets
   • P = Sidereal Period - the time it takes the planet to revolve about the Sun and return to the same configuration between the Sun, Planet, and the distant fixed stars. Think "stars".
   • S = Synodic Period - the time it takes the planet to return to the same configuration with respect to the Sun and Earth (eg. from conjunction to conjunction or opposition to opposition). Think "sun".
   • For inferior planets, synodic period is time from (say) inferior conjunction to the next inferior conjunction. Example: Venus. Venus orbits faster than the Earth, so to return to conjunction, Venus must make an extra orbit -> 1/P = 1 + 1/S
   • For superior planets, synodic period is time from (say) opposition to the next opposition. Example: Mars. The Earth orbits faster than Mars, so the Earth makes an extra sidereal period plus has to catch up -> 1/P = 1 - 1/S
2. The Copernican Revolution?
   • Although Copernicus embraced the idea that the Sun was at rest and the Earth and planets revolved about it, he also firmly believed in the idea of uniform circular motions.
   • He regarded Ptolemy's use of the equant, with the planets moving in uniform circular motion about that instead of the center of the eccentric (or the Earth even), as a "cheat" because it violated his prized principle of uniform circular motion about the center of the circle.
   • The equant was introduced by Ptolemy to make the planets speed up and slow down in their orbits, as they are observed to. Copernicus had to introduce small epicycles, or epicyclets to get the same effect.
   • We tend to applaud his insight in choosing the simplicity and elegance of the heliocentric system over the complicated Ptolemaic geocentric system, while ignoring his slavish infatuation with the vaunted principle of uniform circular motions. It is likely that his contemporaries felt just the opposite, as this was the temper of philosophy at that time!
   • At the time of Copernicus, the choice between the heliocentric and geocentric models for the Universe was a philosophic one, not a scientific one.
   • The merits of the two opposing systems was debated for over half a centurty without any tests to see which was correct!
   • In fact, the Ptolemaic model, with its large numbers of adjustable parameters, was able to predict planetary positions better than the simpler (but still incorrect) Copernican model.
   • The death of the Ptolemaic system and the rise of the "Copernican" system was long and tortured - the Ptolemaic system was still being taught in the first years at Harvard after it was founded in 1836!
   • The philosophical implication of the Copernican model were huge. The Earth was just another astronomical body, unifying the heavens and the earth. In addition, the Earth was seen to be small while the Universe was large. And of course, we were no longer at the center!
3. What makes science Science?
   • Even with Copernicus, the choice of cosmologies was a philosophic endeavour, relying upon pure human thought (and as the Catholic Church would hold, divine inspiration) to discern the nature of the world. This was held to be the path to truth.
   • People at that time would not have supposed that there was a way to disprove one hypothesis and prove another through experiments and observations. The evidence of the senses was suspect, in the medeival mind.
   • Some terms:
     • hypothesis = a conjecture (eg. Earth revolves around Sun)
     • model = "analogue" of a natural phenomenon or part of the world (eg. heliocentric model, Ptolemaic model)
     • system = group of models and/or hypotheses describing the world or universe as whole (eg. Ptolemaic system)
     • theory = quantitative model or hypothesis capable of being tested (eg. Newton's theory of gravity, Einstein's theory of gravity)
     • natural law = a theory or princple that is part of a theory that has passed many tests and is assumed to be correct (eg. Newton's Laws of Gravity)
     • paradigm = the framework made up of all the theories and laws accepted into the "meta-model" of the universe (eg. The Big Bang + the standard model of physics + ...)
   • These terms are also often used as synonyms, so you will have to pay attention to the context (eg. "the standard model" is actually a theory that is part of the paradigm). The important distinction between hypotheses and theories is testability.
   • Our paradigm is made up of very many individual theories which have been separately tested and assembled into the whole. There may be, and probably are, many incorrect theories or hypotheses in the paradigm at any given time. This does not invalidate the paradigm per se, but is just a fact of life due to our incomplete knowledge.
   • Our job as scientists is to probe and test the paradigm and find those bad theories, then replace them with good ones. This is what moves science forward, and makes our model of the universe work.
   • Just like your car mechanic doesn't just sit around and think about your car (at least I hope not!) but prods and pokes and looks for problems and symptoms, uses test equipment, and examines the inside of the engine - we must do the same! We must be mechanics more often than philosophers.
   • We need to use our senses to observe the operation of the Universe, and to construct our working model.
   • The advance of science is largely due to the advance of observations and experiments.
   • We are helped in all this by the fact that our brains are (among other things) problem solving machines! We process our sensory data and fit it into an internal model and look for consistency (does it make sense? what is that thing? can I eat it? should I run away?). This is reflected in the pleasure we take in solving puzzles like crosswords, logic problems, murder mysteries, etc.
   • So far this course has been descriptive. I have told you how the sky appears to us and given you plausible explanations for the phenomena such as tides, motions of the Sun, Moon, planets and stars. Now we will try and see why we believe that the Universe is how it is, what the evidence is.