Copernicus’s concentric spheres

My browsing at the library begins with the work of Nicolaus Copernicus. He is not the first person to put forward a heliocentric worldview (meaning that the Earth revolves around the Sun). The Greek Aristarchus of Samos already did so around 250 BC (!) based on his own observations. His theory, however, had to give way to those of intellectual heavyweights like Aristotle and later Ptolemy, whose theories were more in line with mainstream religious views. But the reintroduction of heliocentrism in the West on the basis of new observations did ensure the so-called ‘Copernican revolution’ in early science and far beyond.

The real innovation in De Revolutionibus Orbium Coelestium lies in its depiction of the universe as seven concentric spheres, with a stationary Sun at the centre and the stars on the outer sphere. The planets (or at least those known at the time) move around the Sun on the remaining six spheres: Mercury, Venus, Earth, Mars, Jupiter and Saturn. A minor eighth sphere contains the Moon orbiting the Earth. According to Copernicus, the movement of the stars is caused by the rotation of the Earth on its axis. While this worldview offers some simple explanations, Copernicus also considers planetary orbits to be perfect circles and thus, ironically, still needs epicycles (auxiliary circles) to explain the planetary motion that he observed …

Kepler’s laws

It is the German scientist Johannes Kepler who will rid the ‘philosophy of nature’ of its artificial epicycles. His insights are mainly based on Danish astronomer Tycho Brahe’s measurement data on the solar system. In order to do so, however, Kepler must assume—against his will—that planets move on elliptical rather than circular orbits. This inevitable assumption results in Kepler formulating three highly elegant mathematical laws of planetary motion, published in his “Astronomia Nova seu Physica Coelestis” (New Astronomy, or Celestial Physics, 1609) and “Harmonice Mundi” (World Harmony, 1619). Today, these formulas are still known as Kepler’s laws.

To compensate somewhat for their “unnatural” elliptical orbits, Kepler goes to great lengths to show that the planets are at distances from the Sun that follow a (to him) “natural” and strictly mathematical arrangement. For this, he uses the properties of both regular polyhedra and sound harmonies (hence the title “World Harmony”). Today, of course, we know that these attempts will only lead to unconvincing results.

Galilei’s observations of the sky

Remarkably, the Copernican revolution does not come to a head until almost a century after the publication of the De Revolutionibus. A certain Galileo Galilei is its direct instigator, even more so than Kepler. In 1632, his Dialogo sopra i due Massimi Sistemi del Mondo Tolemaico e Copernicano is published in Italy, in Italian, in order to appeal to political rulers and as wide a (local) audience as possible. With this rather low-key ‘dialogue on the world systems of Ptolemy and Copernicus’, Galilei wants to convince his uneducated readers of heliocentrism, as his own observations confirmed this theory.

Galilei’s observations of the night sky take place on the roof terrace of his villa ‘Il Gioiello’ (The Jewel) in the hills of Florence. Today, it is owned by the Italian state and is open to the public. The furniture is no longer there, but there is definitely something magical about entering these 400-year-old rooms, especially Galilei’s study and terrace.

If you understand Dutch and want to know more about the copies of the Dialogo kept at KBR, then you can read the article ‘Copernicus in de Koninklijke Bibliotheek van België‘ by Patrick Vanouplines (VUB).

Carefully phrased, still banned

The title engraving of the Dialogo depicts it perfectly: this book deals with a fictional dialogue between three people: Salviati – the saviour – as the defender of Copernicus and Galilei’s ideas, Sagredo – the ordained – as an intelligent and initially neutral layman, and Simplicio – the simple – who adheres to the traditional views of Ptolemy and Aristotle. By making his argument for heliocentrism this way, Galilei tries to avoid trouble with the Church, but to no avail. He is forced by the papal Inquisition to renounce his ideas and his book ends up on the Index Librorum Prohibitorum (list of banned books). Just after his trial, he is said to have spoken the famous words “E pur si muove” (“And yet she moves”), referring, of course, to the Earth …

A mere five years after the publication of Galilei’s Dialogo, Frenchman René Descartes stirs up a commotion among scientists. You might recognise his Latinised pseudonym Cartesius from the Cartesian coordinate system. Descartes’ Discours de la Méthode pour bien conduire sa raison, et chercher la vérité dans les sciences (1637), again written in the vernacular, is an accessible and profound work that essentially promotes scientific thinking. Not very surprisingly, it also ends up on the Church’s banned books list.

Common sense and the vortex theory

The first sentence of Descartes’ Discours immediately hits the spot: “Good sense is, of all things among men, the most equally distributed; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess.” Even more famous is the quotation “Je pense, donc je suis.” Through his typical ‘methodical doubt’, Descartes comes to the dualistic conclusion that he cannot be sure that he has a body, but he can be sure that he has a mind.

Descartes’ theory of gravity, however, is not in his Discours. He develops it in his Traité du Monde around 1630 and the following years, but halts its publication when he learns of Galilei being convicted. Descartes’ vortex theory is therefore only made public posthumously, in 1664. According to him, a whirling ‘aether’ (a ubiquitous medium) explains how planets maintain their orbits. The aether concept is eventually definitively disproved by Albert Einstein, but Descartes’ idea of ubiquitous ‘vortices’ does remind us of modern field theories.

Towards universal gravitation

Only two decades separate Descartes’ Traité and the publication of Newton’s world-famous Principia (1687). During this period Isaac Newton rises to prominence, starting with the famous anecdote with the falling apple: during the plague epidemic of 1666, Newton has to interrupt his studies at Cambridge and returns to the family farm. In the orchard, he sees an apple falling from a tree. Newton suspects that the force pulling the apple to the ground may well be the same force that keeps the Moon in its orbit around the Earth. This application of an identical law of force to both ‘celestial’ and ‘terrestrial’ phenomena represents a deep rift with the two-thousand-year-old ideas of ancient natural philosophers.

The concept of a ‘universal gravitational force’ is elaborated by Newton in his Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy, often shortened as Principia Mathematica or simply Principia), which is considered one of the most influential scientific publications of all time. The first part is an extensive preface in which Newton disputes Descartes’ theory of vortices, among other things. It is followed by two smaller parts containing a series of definitions and axioms, such as the laws of motion of classical mechanics. Only in the third and final part does Newton derive the gravitational force between two planets of our solar system from Kepler’s laws. He subsequently generalises the result for any two masses.

Newton’s genius is reflected in the famous figure he adds to this derivation (from the second edition onwards). Since, according to Newton, the Moon always falls towards the Earth, a cannonball (terrestrial) launched with sufficient velocity should also end up in orbit around the Earth (celestial). Newton tests this assumption by comparing the centripetal acceleration of the Moon with the gravitational acceleration of objects near the Earth’s surface.

Newton is said to have finished the original Principia, which is thousands of handwritten pages long, in two years of day-and-night work. And although he developed a new field within mathematics (differential and integral calculus) while formulating his physical theories, Newton almost exclusively uses geometric proofs that are intelligible to a schoolchild today.

The scientific revolution

Newton undoubtedly plays a leading role in the so-called scientific revolution. In all natural sciences, it is now self-evident to combine mathematical modelling and experimental testing. This combination is an innovation that could be attributed to him, although Francis Bacon, Galileo Galilei and Blaise Pascal did preparatory work that cannot be ignored. This scientific revolution eventually leads to a transition from classical natural philosophy to contemporary natural science, which is still practised according to the generally accepted scientific method.

It takes more than a century for someone to succeed in applying and extending Newton’s science of nature on a larger scale. That honour belongs to Frenchman Pierre-Simon Laplace. His five-volume Traité de Mécanique Céleste (published between 1798 and 1825) is a magnum opus that unites and elaborates on all celestial mechanics known at the time. Laplace’s grand ambitions are immediately expressed in the memorable first sentences of his work: “Newton publia, vers la fin du dernier siècle, la découverte de la pesanteur universelle. Depuis cette époque, les Géomètres sont parvenus à ramener à cette grande loi de la nature, tous les phénomènes connus du système du monde, et à donner ainsi aux théories et aux tables astronomiques, une précision inespérée. Je me propose de présenter sous un même point de vue, ces théories éparses dans un grand nombre d’ouvrages, et dont l’ensemble embrassant tous les résultats de la gravitation universelle, sur l’équilibre et sur les mouvements des corps solides et fluides qui composent le système solaire et les systèmes semblables répandus dans l’immensité des cieux, forme la Mécanique céleste.”

Even Napoleon is impressed by Laplace’s Traité, but he wonders how anyone can write such a profound work on the universe without ever mentioning God as its creator. Laplace then speaks the famously atheistic words: “Je n’avais pas besoin de cette hypothèse-là.” For the first time in history, science is seen as a study of nature that can (or should) be independent of the existence of God or gods.

This brings us to the end of this anthology of pre-Belgian literature on gravity. Given his importance in our current understanding of gravity, I also want to mention Albert Einstein. He provides yet another paradigm shift in physics by approaching gravity in a very different way from his predecessors. According to the general theory of relativity, gravity is a fictitious force caused by the curvature of four-dimensional spacetime, due to the mass present in it. The mathematics required to understand this theory is not exactly suitable for laymen, but Einstein makes a first and still much appreciated attempt at vulgarisation in his Relativity: The Special and the General Theory (1916).

The holy grail

Einstein’s explanatory gravity model leads to more accurate results than Newton’s law of gravitation, among others on the deflection of light (which is indeed subject to gravity). Yet research on gravity remains unfinished. The holy grail of contemporary (theoretical) physics still consists in closing the gap between Einstein’s general theory of relativity and the laws of quantum mechanics. This is another example of the fact that scientific ideas are constantly evolving, sometimes even in leaps and bounds, but research will never be finished. To be continued, but for those interested, the basics are already available at KBR.