April 8, 2012 | 15
Note: this is the third of three parts of the essay. The first two parts were published yesterday and the day before (see links at the bottom of the page).
The very first discovery in fundamental physics, made by Galileo, – the law of free fall – was also the first discovery in physics of gravity. It was the starting point for Newton’s law of universal gravitation a few decades later. Was it possible for Galileo himself to discover the law of universal gravitation at his level of mathematization and by his style of doing science?
Yes it was, although Galileo’s predisposition was quite unfavorable, since he rejected statements on attraction as an explanation of the Solar system. But nevertheless Galileo could come to the law of universal attraction by a way starting with his discovery that free falling projectile is moving on parabolic trajectory. He understood that parabolic trajectory was but an approximate result for “flat Earth”, or for small initial velocity. He didn’t know the form of trajectory in general case but he could grasp that very high initial horizontal velocity would make the projectile to go far away from the Earth.
Galileo is often reproached for his keeping to “backward” ideally circular planetary orbit despite the observational reality summarized in Kepler’s law of elliptical orbits. Indeed Galileo ignored rather than reject Kepler’s laws of planetary motion. Circular planetary orbit was the simplest model to probe into physics of planetary motion, and Galileo could do this. Even without knowing the general form of trajectory of free falling object, he could ask what initial horizontal velocity V would make a projectile to move at the same constant distance from the surface of the spherical Earth.
And he could answer this question by means of math no more sophisticated than the theorem of Pythagoras:
V = (gR)½,
where g is the acceleration of free fall and R is the radius of the Earth. This is the so called first cosmic velocity (~ 8 km/s) reached for the first time in October 1957 by Sputnik 1.
The motion at a constant distance from of the Earth resembles the Moon’s motion too much for Galileo to miss this resemblance. But Galileo would find that the relation V = (gR)½ holds for the Moon only if acceleration of free fall on the Moon’s distance from the Earth gM is about 3600 times less than gE he had measured on the Earth, since the distance to Moon RM is about 60 times larger than RE, and Moon’s orbital velocity is about 1 km/s. It would hint at relation
which is, in fact, very close to the law of universal gravitation, because here evidently the Earth determines the acceleration of free fall on specific distance from the (center of the) Earth. So the Earth is the source of such a universal acceleration in the space around it.
Combining this relation with the previous, Galileo would get a relation for the astronomically observable parameters
V ~ R- ½ .
Having verified this relation for the planets in the Solar system and for the satellites of Jupiter (discovered by himself in 1610), Galileo could realize that he got the 3rd Kepler’s law for circular planetary motion and could discern both a real sense in the unpleasing Kepler’s wording on heavenly planetary attraction and the connection of the 3rd Kepler’s law with the earthly phenomenon of free fall.
Then, in usual Galileo’s way of thought experimentation, he could be playing with placing a thought Moon further and further from Earth and closer to Mars. When the Moon is on equal distances from the both planets, he could ask whose satellite this thought Moon would be. This way he would come to the idea of combine action of the two planets making the thought Moon to move with combine accelerations, as the result of two attractions. And this would be virtually the law of universal gravitation, even if yet for circular movement.
Thus Galileo would come to the law of universal gravitation. Why didn’t he do it?
A probable reason was that he was too serious about his biblical worldview – regardless of how far he was from official theology. Galileo was unable to accept a friendly suggestion from the Pope (who was his admirer) to write about his science freely but without claiming that his theory was real truth rather than a hypothesis, even if the best one compare to others. If Galileo had been an atheist he could condescend to scientific backwardness of the religious authority, and in his writing to address to his colleagues the scientists with obviating repercussions by proper – hypothetical – wording.
But being an honest biblical believer he had to defend his truth-seeking. So he invented a literary form to obviate administrative restrictions in his Dialogues and had to spend too much time and effort for his kind of popular-science writing. Nevertheless he failed to circumvent the scientific ignorance of society and the Church and, as a result of persecution, his intellectual and social freedom was harshly restricted for the rest of his life.
Of course in the history of science Galileo’s “unnecessary” popular-science writings had played a very important role in propagating the new way of doing science all over Europe. But being too busy for too long with such writings and with opposition to ideological officialdom Galileo left the honor for developing his research into the law of universal gravity to Newton who started his quest in a lucky windy day by a legendary apple tree. Again there is no bad without some good – the story of how Newton came to his law can support the opportunity Galileo had had.
It is known that Newton came to the idea of inverse-square gravity in his twenties (in the 1660s) employing circular motion, parabolic approximation and Galileo’s kinematics, and sometimes Newton is reproached for being “excessive in offering credit to Galileo” (rather than to Decartes). Besides historical reconstructions based on Newton’s later writings there is only one sort of eyewitness evidence about his real way to his idea. It is the apple story written by a friend of Newton William Stukeley. 25 years after Newton’s death. Stukeley related their conversation on 15 April 1726:
“After dinner, the weather being warm, we went into the garden, & drank thea under the shade of some appletrees, only he, & myself. Amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. “Why should that apple always descend perpendicularly to the ground,” thought he to him self: occasion’d by the fall of an apple, as he sat in a contemplative mood: “Why should it not go sideways, or upwards? But constantly to the earths centre? assuredly, the reason is, that the earth draws it. There must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earths center, not in any side of the earth. Therefore dos this apple fall perpendicularly, or toward the center. If matter thus draws matter; it must be in proportion of its quantity. Therefore the apple draws the earth, as well as the earth draws the apple.”
That there is a power like that we here call gravity which extends its self thro’ the universe & thus by degrees, he began to apply this property of gravitation to the motion of the earth, & of the heavenly bodys: to consider thir distances, their magnitudes, thir periodical revolutions: to find out, that this property, conjointly with a progressive motion impressed on them in the beginning, perfectly solv’d thir circular courses; kept the planets from falling upon one another, or dropping all together into one center. & thus he unfolded the Universe. This was the birth of those amazing discoverys, whereby he built philosophy on a solid foundation, to the astonishment of all Europe.” 
From my extensive experience in oral history about events that happened a few decades earlier (including written recollections), I’ve learn that this kind of source is both priceless and unreliable. To decide which element of the evidence is what, one have to understand the personality of the witness and the whole situation as deeply as possible.
From this Stukeley’s description, with its direct speech and Newton’s “thought to himself”, one can infer that the author was concerned to tell a good story rather than to be as accurate as possible. Stukeley was neither a physicist nor a historian of science, he was an archaeologist who described himself as a “druid”. When he wrote, many years later, that Newton “was just in the same situation” he apparently forgot that April is a bit too early for falling apples.
Hopefully I am not the only historian of physics for whom Stukeley’s explanation doesn’t make real sense, I am unable to imagine the train of Newton’s thought at the time when the great discoverer hadn’t yet made his amazing discovery. I rather see the explanation which satisfied the archaeologist-druid at the time when “all Europe” knew what was universal gravity.
The only fact that seems to be undeniable is that falling apple somehow triggered the discovery, and a historian of physics may feel free to guess what did happened in that lucky day when Newton saw a falling apple. My guess is that the lucky day was windy and the wind was gusty. So Newton saw the apple falling in a parabolic way. He could easily grasp that a stronger gust of wind would make the parabola wider, and he could ask himself what if the gust would be strong enough to keep falling apple to stay at the constant distance from the spherical Earth’s surface, that is on a circular orbit. Then he could follow the above described way to the inverse-square universal gravity. Here Newton needed only Galileo’s kinematics, rather than sophisticated mathematics of Decartes.
Newton, just like Galileo, did not like the old-fashioned astrological, non-mathematical idea of planetary “attraction” , but had to accept it as re-invented mathemitized fundamentals under the weight of its successful corollaries supported by empirical evidence, just like Galileo had to re-invent and corroborate the notion of the movement in the vacuum.
Newton’s real way to universal gravity was manifested in his thought experiment in the very beginning of his manuscript ‘A Treatise of the System of the World’ which preceded to his ‘Principia’, but was published posthumously:
“That by means of centripetal forces, the Planets may be retained in certain orbits, we may easily understand, if we consider the motions of projectiles. For a stone projected is by the pressure of its own weight forced out of the rectilinear path, which by the projection alone it should have pursued, and made to describe a curve line in the air; and through that crooked way is at last brought down to the ground. And the greater the velocity is with which it is projected, the farther it goes before it falls to the Earth. We may therefore suppose the velocity to be so increased, that it would describe an arc of 1, 2, 5, 10, 100, 1,000 miles before it arrived at Earth, till at last, exceeding the limits of the Earth, it should pass quite by without touching it.” 
Here “stone projected” could be a pseudonym of his falling apple.
Here we can finish “what-if” and “how-specifically” history of the law of universal gravity and return to a general question why this fundamental discovery as well as the invention of the fundamental physics happened only in European civilization, and whether it was facilitated by the Biblical background of its culture and by biblical theism of the originators of fundamental physics.
The last hypothesis might outrage a typical descendant of Biblical civilization of today, when church is securely separated from state, and religious faith is considered a wholly private issue separated from all mundane affairs including science. However more important are opinions of not so typical physicists who firsthand experienced insights and discoveries in physics which required all the creative resources of a person.
An atheist Boltzmann expressed his admiration for Maxwell’s equations in theistic way by quoting from Geothe’s Faust: “Was it a god who wrote these signs? Which still my inner rage, which fill my heart with joy, and which, in a mysterious way, reveal the forces of nature around me”.
To the mind of Einstein, who was no a churchgoer at all, “Our moral leanings and tastes, our sense of beauty and religious instincts, are all tributary forces in helping the reasoning faculty toward its highest achievements.” 
According to a survey conducted by the magazine “Physics World” about two thirds of its readers think that religion and science are compatible, with half of them being non-believers and one third believing that their faith enhances their appreciation of science.  So, apparently, many contemporary physicists the atheists could join Boltzmann in thanking God for helping Maxwell – as well as Newton and Galileo – to make their fundamental discoveries.
And so why don’t contemporary historians of science, regardless of their (ir)religious affiliations, join Einstein in appreciation of the role of “religious instincts” (rather than official theology), at least when considering the origin of modern physics in the 17th century?
Scientific progress and intellectual freedom in the 21st century
In thinking about the beneficial cultural infrastructure for scientific progress, comparative history might be a good resource, although in the 21st century to promote the Bible might be not the only way to ensure such an infrastructure. Thanks to the amazing advancement of science, nowadays the double postulate of fundamental science is self-evident without biblical support.
Various social forces are working in a society to find out persons endowed with extraordinary curiosity and independent thinking and to provide them with necessary freedom to develop their personal abilities to make new inventions in science and technology. Here, as the history of science shows, the intellectual freedom is the most relevant among all the human rights. Instructive is the comparison of two sciences – biology and physics – against the same totalitarian background of Stalin’s Russia.
In the 1920s and the early 1930s both sciences were doing pretty well in the USSR, until the late 1930s when Stalin’s Great Purge killed millions of innocent people including some of the best physicists and biologists.  However in the post-war USSR the fates of the two sciences were quite different.
An agronomist T. Lysenko, enthroned in the Soviet biology directly by Stalin, effectively suppressed intellectual freedom in Soviet biology to result in its major destruction.
On the other hand, the urgent need for nuclear weapons made Soviet leaders restrain their control over the intellectual freedom of physicists, and the highest level of the freedom was allowed at the closed nuclear center where nuclear weapons were designed.
One of the weapons designers, the theoretical physicist Andrei Sakharov, in 1968, was expelled from this center after his article “Reflections on Progress, Peaceful Coexistence, and Intellectual Freedom” had been published in Samizdat and then in the New York Times.  It transformed the secret “father of the Soviet H-bomb” into a public figure.
His way to publicity was unique. Being a top expert in strategic balance and privy to strategic information in full, in 1967, he became gravely concerned with a problem of strategic antiballistic defense. He sent a secret detailed letter to the Politburo explaining the increased threat of nuclear war. In those days he felt himself a defender of socialism and a non-dogmatic Marxist.
Sakharov saw the fact that the founders of Marxism didn’t foreseen: due to advancement in science and technology humanity was facing the threat of global suicide within half an hour, the travel time for a nuclear missile. Sakharov actions were exercises in intellectual freedom coupled with social responsibility. He was well aware that the real intellectual freedom could thrive only on the basis of respect for the rule of law.
However, the Soviet leaders had no respect for both intellectual freedom and social responsibility of citizens, they did not heed the advice of a top non-dogmatic expert and didn’t allow Sakharov to publish a non-secret version of his analysis. It was only then he found that his intellectual freedom, so essential in his profession, was dangerously restricted. Feeling himself free enough, he went public to prevent nuclear war.
Correcting the official formula, Sakharov wrote that “evolution, not revolution, is the best locomotive of history” and confessed himself to be a “reformer and principled foe of violent revolutionary changes of the social structure, which have always led to the destruction of the economic and legal system, to mass suffering, lawlessness, and horror.”
Soviet leaders failed to make the necessary reforms, and the regime collapsed.
Chinese economic reforms show that it was not the only possible outcome. And if Chinese reformers could also create a beneficial cultural infrastructure for scientific inventiveness it would be the best practical response to the grand question of Needham, who was so sympathetic to Chinese civilization. History hints that respect for intellectual freedom and for the rule of law is the best secular approximation to the Biblical prerequisites for fundamental physics at the time of its origin.
I am grateful to Chia-Hsiung Tze for helping me to appreciate the Needham question, to Lanfranco Belloni for help in checking with the original Italian of Galileo, to Robert S. Cohen, who helped me to appreciate Edgar Zilsel, to Sergey Zelensky and the Methodological seminar at the Institute for History of Science and Technology (Moscow) for stimulating discussions, and to John Stachel for helpful critical remarks.
 J. Bruce Brackenridge. The key to Newton’s dynamics. University of California Press, 1995, p. 27, 35.
 William Stukeley. Memoirs of Sir Isaac Newton’s life. 1752.
 Isaac Newton. A treatise of the system of the world, 1728, p. 5-6.
 A. Einstein. Science and God. A German Dialog // Forum and Century. 1930. V.83. P.375.
 Robert P Crease. Religion explained // Physics World, Jul 31, 2009
 G. Gorelik, and V.Ya.Frenkel, Matvei Petrovich Bronstein and Soviet Theoretical Physics in the Thirties, Basel-Boston: Birkhaeuser Verlag, 1994; Springer Basel AG, 2011 (e-book)).
G. Gorelik, ‘Meine antisowjetische Taetigkeit…’ Russische Physiker unter Stalin, Transl. H. Rotter. Braunschweig/Wiesbaden: Vieweg, 1995.
 G. Gorelik, with A. W. Bouis, The World of Andrei Sakharov. Oxford University Press. 2005.
See all three parts of this essay:
How the Modern Physics was invented in the 17th century, part 1: The Needham Question
How the Modern Physics was invented in the 17th century, part 2: source of fundamental laws
How the Modern Physics was invented in the 17th century, part 3: Why Galileo didn’t discover universal gravitation?