Thursday, December 21, 2017

What really happened in the history of cosmology

To complete last week’s post, I will offer here a summary of the history of Cosmology, from the Greeks to the paradigm shift that took place in the sixteenth and seventeenth centuries.
The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and the equant (•).
  • Greek cosmology (with the exception of Aristarchus of Samos) put the Earth at the center of the universe. Plato and, above all, Aristotle established the idea that, since the sky is perfect, the orbits of the planets must be exactly circular, because, for them, the circumference is the most perfect curve of all.
  • The Greek model explained well the movements of the sun and moon, and therefore made it possible to predict eclipses, but had a problem with the retrograde movements of the planets then known (Mercury, Venus, Mars, Jupiter and Saturn). Three centuries before Christ, Apollonius of Pergamum proposed that the orbits of these planets are epicycles, circumferences centered on another circumference (the deferent), which in turn revolves around a point located near the Earth, but apart from its center (the eccentric).
  • Claudius Ptolemy formalized and perfected the cosmological system devised by the great Greek philosophers and astronomers, and compiled experimental data. To reconcile the theory with the data, Ptolemy added the equant to the epicycles and the deferent: a point around which the planets rotate with constant angular velocity. To explain his system, Ptolemy wrote a text of cosmology (called Almagest, its Arabic name) that was used as the basic text of astronomy for almost one millennium and a half.
  • Copernicus found that calculating the orbits o to adapt to the experimental data is easier if the sun is placed in the center and the Earth becomes a planet that rotates, like the others, around the sun. In short, as I said in the previous post, this is a simple change of the reference system. The underlying physics is the same. In addition, as Copernicus decided to preserve the circular orbits of Aristotle, his system, although it makes calculations simpler, still needed epicycles and deferent, although smaller than those of Ptolemy.
  • Trying to maintain the balance between the two systems, Ptolemaic and Copernican, Tycho Brahe proposed an intermediate system, where the five planets would rotate around the sun, while the sun and the moon (the sun dragging the planets) would turn around the earth.
  • Johannes Kepler, disciple of Tycho Brahe, made the first really revolutionary proposal, by stating that the orbits of the planets are not circular, but elliptical, with the sun in one of the foci. This change meant the total elimination of epicycles and deferent and the perfect adaptation of the experimental and calculated data. Kepler discovered two additional empirical laws that describe the changing speed of the planets as they travel around these elliptical orbits, and the total time it takes them to travel around them.
  • The contribution of Isaac Newton consisted in the application to the movements of the celestial bodies of the new laws of mechanics, discovered by the French and English medieval researchers and improved by other researchers, such as Galileo Galilei. In doing so, he theoretically deduced Kepler’s three experimental laws, which gave scientific backing to his system.
  • The two alternative cosmological systems, that of Tycho Brahe improved with Kepler elliptical orbits around two different centers (the sun and the Earth), and that of Copernicus, equally improved with these elliptical orbits and with a single center (the sun) are totally equivalent, as they only differ by being based on different reference systems, something that, as Galileo showed, is irrelevant. Throughout the seventeenth century the Copernicus system, being simpler, imposed (a single center is simpler than two), but the proof that this was the correct reference system (that is, the demonstration that the Earth really moves around the sun) had to wait until the 19th century. In 1838, the mathematician and astronomer Friedrich Bessel discovered that the star 61 Cygnus presents a visible parallax, i.e. its apparent movement in the sky describes a small ellipse throughout the year, a reflection of the ellipse the Earth travels around the Sun.

Stellar parallax motion from the Earth's movement
In conclusion: the true Copernican change in Western cosmology was not made by Copernicus, but by Kepler, who was the first to dare opposing the Aristotelian dictum that all celestial bodies must travel in perfect circumferences. But the so-called Newtonian cosmology was not the work of a single person, but the result of the collaboration of many. As Newton said, if I have seen further, it is by standing on the shoulders of giants. Who were the giants? Plato, Aristotle, Apollonius, Hipparchus, Ptolemy, Buridan, Oresme, Copernicus, Tycho Brahe, Kepler, Galileo, and many others we have no room to name here.

Manuel Alfonseca
Happy Christmas to everybody

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