|Number 21: 05/08/2003
A scientific publication by SGF and NEODyS
NEOs' science history
Preface: What has Copernicus to do with NEOs?
It may seem rather strange that a magazine such as Tumbling Stone, which is mainly devoted to NEO research and related topics, should publish a series on the history of science. In fact the readers should not be surprised, because the scientific study of NEOs (and also, of course, of the threat that they may pose to us) involves the use of two fundamental tools: astronomical observations, and orbit computations.
Astronomical observations in the modern sense (i.e. with the abstract purpose of studying the Universe, and not to search for the hypothetical influences that it could have on human vicissitudes) were started by Galileo Galilei at the beginning of the XVIIth century. On the other hand, the computation of orbits is based on the theory of universal gravitation as delineated by Isaac Newton, and published towards the end of the same century. However, neither Galileo nor Newton were in the position of building without foundations. Their lines of research and their successes were, to a large extent, a consequence of the new intellectual climate established in Europe in the XVIth and XVIIth centuries. In particular we note the major transformations in such study that originated from the publication of the book De Revolutionibus Orbium Coelestium by Mikolaj Kopernic (Nicolaus Copernicus) in 1543.
The changes induced by that book are correctly termed the Copernican Revolution: it was a revolution that not only involved all aspects of the study of nature, giving rise to "science" as we know it, but also unhinged the basis of an entire philosophical system and produced fundamental modifications in the relationships between man and nature, man and society, and man and divinity. This was the most drastic change in human thought to occur in the last two millennia, with many consequences eventuating.
I am not a philosopher, nor a science historian, but I am a scientist and - most important - a scholar of dynamics and celestial mechanics. Therefore, I can try to address this question from an "internal" point of view, and the path that I follow in this short series of articles is simply the way in which a student of the motions of celestial bodies reflects on the birth of his own science.
The Copernican Revolution started with a scientific problem. However, its consequences went well beyond the solution of this problem, disrupting the underlying basis of society in the Middle Ages. By the end of the Revolution nothing remained as it was before.
The "Ariadne's thread" leading from the earliest stages of human history through to the epoch of science has indeed been the understanding of planetary motion. The starting point was a "fact", as always in the investigation of the physical world. This fact was to hand, in a natural way to those who observed the sky, but it would not have had any great significance unless men learned to ponder the facts of nature, and thus search for an understanding of how the world works.
The fact in question is deceptive in its simplicity: while most celestial objects visible in the sky do not change their relative positions from night to night, some of them move with respect to the others. This simple observation has originated a line of thought that through the centuries has given rise to astrology, to myths and religious beliefs, to cultural debates and political contests, quite apart from providing the foundations for the development of modern science, as explained here.
The main difficulty facing the first critical observers of the heavens was the irregular motion of these objects. All stars move, with respect to a terrestrial observer, as if they were fixed to an enormous sphere centered on the Earth. Exceptions are, of course, the Sun, the Moon, and the planets. [Indeed in ancient Greek the word "planets", which originally included both the Sun and the Moon, means "wanderers".] However, the motion of the Sun is fairly regular and so, to a lesser extent, is that of the Moon. To the contrary, as the planets move across the sky they display continuous changes in their apparent speeds, and sometimes also in their directions of motion. From the time of the Babylonians, about 25 centuries ago, it was possible to predict with considerable precision, limited only by the instruments available, the position of a star for many years into the future; the corresponding computations of the positions of the Sun and the Moon were more complex, but still feasible, to the point that the Babylonians were able to predict eclipses to some extent. However, the exact prediction of the positions of the most brilliant planets was a challenge for all geometric and mathematical models, and remained an unsolved problem until the XVIIth century.
From a technical viewpoint an important reason for this difficulty was an erroneous choice of the reference frame. Since the Earth moves around the Sun like all other planets (something unknown to the ancient observers), it does not represent a good reference point to use as the origin of celestial coordinates. All geocentric reference systems (horizontal, equatorial, ecliptical) suffer from the same drawback, and the ancient mathematics was not able to handle conditions of such complexity. Certainly some Greek scientists (Aristarchus in particular) supported the hypothesis that it is the Earth that goes around the Sun, and not the contrary, but this idea was counter-intuitive and clashed with the experience of absolute immobility that the human body "feels" when it is at rest with respect to the ground; nor was it possible to elaborate a mathematical theory able to explain it. Moreover, we must take into account that several great philosophers, from Eudoxus to Aristotle, built on the geocentric hypothesis a great cosmological theory which was perfectly acceptable to most: the few observed discrepancies therefore had to be resolved in the framework of the existing theory and were not considered a sufficient reason to alter the global picture. To these "scientific" motivations we must add those of a philosophical, religious, and political nature. A mobile Earth was simply judged "unnatural", and contrary to the required perfection of the celestial sphere.
Quite apart from the above, the real cultural misunderstanding that prevented, until the XVIth century, the elaboration of a complete and coherent theory was to think that the celestial bodies followed, in their motion, rules different from those governing terrestrial objects. Nobody would dare to maintain that there is no difference between the heavens (the domain of the gods, and of perfection) and the Earth (the abode of men, and of corruption). We must remember that the idea of Nature as a whole, always and anywhere subject to the same universal physical laws, is a very modern concept, known in the astrophysical domain as the cosmological principle. It is an assumption, not a theoretical demonstration: a reasonable axiom derived from experience.
In our path through the upset caused by the Copernican Revolution we will move from the situation of planetary astronomy just before the publication of De Revolutionibus Orbium Coelestium (1543). We will then examine quickly the contribution by Copernicus and his followers, and in the end we will compare it with the image of the physical world contained in the Philosophiae Naturalis Principia Mathematica by Newton (1687). We will see that a profound change in the intellectual environment occurred during that interval, modern science then being built on the resulting new understanding. We will face, with Johannes Kepler, the problem of predicting the motion of planets and the definition of the two basic concepts of mass and force; we will confront the difficulty that led Galileo Galilei to "invent" the experimental method and to formulate, even if only partially, the first laws of motion; and finally, we will follow the sometimes tortuous path through which Isaac Newton establish the foundations of the differential calculus, the analytical method that allowed him to treat uniformly the problem of motion. At the end we will find the scientia nova (new science), now equipped with all the tools necessary to describe the world using only mental reasoning and Galileo's sensate esperienze (meaningful experiments).
When Copernicus wrote his important book, De Revolutionibus Orbium Coelestium (1543), the status of planetary astronomy in Europe did not differ too much from that in Ptolemy's time, more than a thousand years before. Copernicus himself was a Ptolemaic, both because of his education in astronomy and because of a sincerely-held conviction. The modern concepts of mass and force, on which the Newtonian dynamical theory is based, were totally foreign to him, and Copernicus's mathematical methods were not greatly different from those used by his predecessors. His biggest merit, that makes him the real instigator of the scientific Revolution, was the ability to leave aside non-scientific considerations and to base his reasoning on the deepest intellectual honesty. This position is very explicitly clarified in the preface letter that Copernicus published with the De Revolutionibus, addressing it to Pope Paul III:
"It is easy to forecast, most Holy Father, that somebody, as soon as they learn that in these books... I ascribe certain movements to the terrestrial globe, will soon ask with loud voices that, because of this opinion, I should be banned...Therefore, I do not want to conceal from Your Holiness that I have been induced to think with a different method of computation of the motion of spheres, only because I am convinced that the mathematicians have no clear ideas about these movements...
As a matter of fact[they] were unable to establish with certainty any system definitely corresponding to the phenomena..."
The fundamental point expressed by Copernicus, underlined in the above quotation, is that the Ptolemaic astronomy did not solve, nor could it ever solve, the problem of planetary motion. Therefore, the basic structure of Ptolemy's theory had to be wrong. This apparently drastic conclusion was based on the evidence that the many astronomical models following that of Ptolemy (first through the Arabic and then the Mediaeval European traditions), all based upon the geocentric hypothesis, had produced a "monster", described by Copernicus in this way:
"What happened to them [the ancient mathematicians] was what would happen to a painter collecting hands, feet, head and other parts of the body from different models, then painting them in an exquisite manner and yet not as a single body and, since all these parts do not harmonise with each other, the result is a monster, and not a man."
So Copernicus, unlike many contemporary astronomers, was conscious of the fact that the Ptolemaic theory of the heavens, as well as its subsequent modifications, was based on a belief that is fundamentally incorrect. But this realisation was, so to speak, based only on principle, because the astronomical data on which Copernicus based his reform were insufficiently precise. Some of them were simply wrong, while others did not correspond to anything real, or were misprinted while copying. No astronomical theory, past or future, would have been able to fit with the available data.
The success of the Copernican theory
It is said that Copernicus was given the first copy of his book on his deathbed, in 1543. The book, therefore, was published and first distributed after its author had disappeared from the scene. In consequence the diffusion of Copernicus's ideas was very tardy. What is most surprising, however, is not so much this initial slowness in the spread of the book, but rather the delay in the onset of reactions to its content. One of the many reasons that have been identified for this delay is that De Revolutionibus is a technical work, written for specialists. It was difficult read, even for the best educated people of the time, unless they had specific training in astronomy and mathematics. Furthermore, all the texts used in academic education in that era, including that of Copernicus himself, had been written many years earlier and were invariably based on Ptolemy's theory.
Copernicus's ideas therefore became known rather slowly, and even then only in a rather limited professional circle. The wider reaction exploded, in an impressive crescendo, only at the beginning of the XVIIth century, more than 60 years after the publication of the book. But, why did this reaction occur? Why was it so harsh? And, last of all, why did Copernicanism win in the end?
In fact, the reaction in the Protestant domain was fairly rapid, such that in 1539, even before the book's publication, Luther criticised rudely a "twopenny-halfpenny astrologer, who has tried to demonstrate that it is the Earth to turn, and not the sky and the firmament, the Sun and the Moon...". Luther's leading disciple, Melanchthon, echoed his words: "...somebody...has established that the Earth is moving; and maintains that both the eighth sphere and the Sun are at rest...Well: it is a lack of dignity to publicly maintain such concepts, and the example is dangerous."
The ideas of Copernicus had, from the beginning, a difficult time also in the scientific sphere. The colleagues of Copernicus, all educated with the Ptolemaic system, were rarely converted to this novel hypothesis, mainly because the new concepts were not supported by convincing proofs. The inertia of the scientific world towards innovations has always been strong: it is a very conservative field of endeavour. To change one's opinions implies an admission that you had maintained an incorrect stance and taught wrong - or at least obsolete - doctrines. This requires a personal effort of revision, very difficult to do especially if you are of an advanced age.
The astronomers, however, soon realised that the Copernican theory was extremely useful, at least because it allowed them to compute the positions of the planets in a much simpler and more accurate way. This is proven by the Prutenicae Tabulae published by Erasmus Reinhold in 1551, based on the Copernican method. These tables were extensively used in reforming the calendar in 1582, under Pope Gregory XIII: the Catholic world had not yet come to the stage of regarding Copernicus as being a danger.
The most violent reaction, therefore, was not caused by scientific motivations. As Thomas Kuhn has much more recently explained,
"...if the choice between the traditional and the Copernican universes were a matter of concern only for astronomers, most probably the Copernican solution would have acquired gradually and smoothly the victory. This choice, on the contrary, was not exclusively, and not even principally, a competence of astronomers, and when the debate extended outside the astronomical circles, it became highly stormy."
Knowledgeable persons of that era, without a strong scientific background, found the Copernican ideas absurd and at odds with common sense. Cautiously supported by the professionals, but always from some distance, while being opposed and mocked by scholars in other fields, the theory had its strongest opponents in religion and politics.
We have already noted that the first reactions came from the Protestants. They were opposed to the Copernican statements concerning the "truth" of the Holy Scriptures, particularly some verses in the Book of Ecclesiastes. Today, it is clear (or, perhaps I should say, should be clear) to everybody, believer or not, that the statements of the Bible must be read with caution when they do not refer directly to facts of faith. At that time this was not true, and represented the major obstacle to the self-defence of Galileo. The Copernicans were accused of being "infidels" and "atheists", sometimes with impressive parallels to some of the most integralist positions that still exist nowadays. It must be noted, however, that the Catholic Church did not immediately join the movement against Copernicus: this happened only after 1610, following the first of Galileo's trials. In 1616 Copernicus and his followers were accused of heresy, and the De Revolutionibus was included in the list of prohibited books. But the battle was by then already effectively lost: the Copernican ideas, thanks largely to the work of Tycho Brahe, Johannes Kepler and Galileo Galilei, had been substantially accepted by the most influential professionals, and the adventure of science had begun.