Magdalena Kawalec-Segond: Leonardo da Vinci’s Universal Gravity

We are witnessing the 550th anniversary of the birth of Nicolaus Copernicus and – rightfully so – lifting to heaven this “Renaissance man”, who was a mathematician, physician, astronomer/astrologer, Catholic priest, and doctor of canon. Another “Renaissance man”, whose countless works today deserve a scientific journal dedicated to him, was Leonardo da Vinci, more than 20 years older than Copernicus. Modern science – sometimes with extraordinary results – looks at their work and makes new discoveries.

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Almost another century would have to pass since Isaac Newton, one of the few greatest scientists – and post-Renaissance “Renaissance men” – ever bore the earth. He developed, not necessarily as in the anecdote about the apple falling on the head, the law of universal gravitation. That is why he, like many English monarchs, is buried in Westminster Abbey. Because it also gave us, for the next 250 years, a basically complete view of how and why things move. It took Einstein and his theory of relativity to show that Newtonian dynamics is a good approximation of a slice of reality when the objects are microscopic, neither supermassive black holes nor subatomic. This is a section that we go through mainly every day, so the Newtonian approximation is enough for us in everyday life (and in physics lessons at school).

universal law of gravitation

In modern physics, gravity is described by general relativity, where gravity is not an interaction, but a consequence of the curvature of space-time by matter. Newton, who formulated the law of universal gravitation (every body attracts every other body with a force directly proportional to the product of its mass and inversely proportional to the square of the distance between their centers) not only had truly accurate clocks at his disposal, but also – as the history of physics – their predecessors pondering the same issue and building Its foundations were, namely, Galileo and Descartes (which eventually rejected Aristotle’s ideas on motion, and ended the Middle Ages in physics once and for all).



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So the news will be published recently in the scientific journal “Leonard”, dedicated to researching the works of this painter, sculptor, musician, architect, inventor, engineer, mathematician, anatomist, geologist (father of paleontology), philosopher and writer, a study of physicists from the California Institute of Technology (CalTech) on some notes Da Vinci. It places Leonardo in the role of not only one of the researchers of gravity, but also one who understands it as a form of acceleration. Thus, more than half a century before Galileo who noticed it The distance traveled by the falling body is proportional to the square of the elapsed time.

Codex Arundel

As you can read in MIT experts’ discussion of this research, da Vinci’s experiments with gravitational interactions were first noted by Maury Gharib, a professor in the Department of Aeronautics and Medical Engineering, in a collection of articles Da Vinci wrote about science. and Art and Personal Subjects, called “Codex Arundel”. Available online courtesy of the British Library. There, the researcher noticed a series of schematic drawings of triangles caused by fine pebble-like particles falling from a pitcher.

To analyze these drawings showing schematic diagrams of grains or drops falling from a jug and right-angled triangles, where Leonardo wrote (or rather encrypted with his famous left-mirror writing) On the hypotenuse of one of the schematic triangles – the one that was an isosceles right triangle – the words “De Moti’s Equation”. It means “to line up (balance) the movements,” which is what the professor thought deeply about. weird.



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Now we have to imagine this experiment (I would encourage physics teachers to do it in class!). The sandpit will move in a straight line, losing grains along the way. It is clear from Leonardo’s observations that he was aware that it was not falling at a constant speed, but rather accelerating. Also, matter stops accelerating horizontally over time, because it is no longer affected by the motion of fate and only accelerates downwards due to gravity.

When the pitcher is moving at a constant speed, the line formed by the falling sand is vertical, and when the pitcher is accelerating at a constant speed, the falling matter forms a diagonal line, which then forms the hypotenuse. The main diagram from observations shows that the movement of the jug, from which sand is poured, is accelerated at the same rate as the gravitational acceleration of the fallen matter. A right-angled triangle is isosceles, that is, the path is the diagonal of the square. However, in the absence of accurate time-measuring instruments, Leonardo did not have the opportunity to make the calculations correctly and notice the “square of time”, which appears in the school in the definition of all acceleration, including acceleration due to gravity, as 9.81 m / s 2 .

Leonardo’s “principle of equivalence”.

Today, serious physicists from the California Institute of Technology and the University of Applied Sciences and Arts in Geneva, as a result of studying Italian observations and computer modeling of his experiment, and Applications of Newtonian dynamics developed more than a hundred years later, and confirmed Leonardo’s “principle of equivalence”.



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There have not been many so-called “Renaissance people” in the history of mankind, because it is in no way true that Leonardo da Vinci was the model of his era. The aforementioned Copernicus, still deeply “medieval” in his mentality, the great Albert (teacher and friend of Thomas Aquinas), Hildegard of Bingen, Aristotle, Pythagoras, and after Leonard even Galileo, of course Newton and his great rival Leibniz (the last “know-it-all” man ), and finally Einstein.

The history of human thought shows that it is about some central questions—such as that of what is at the center of it all, and why sand spills from a pot drawn along the same road at different speeds along different paths, and from which a giant censer is suspended. The movement of the pendulum over the head leads, the apples falling on our heads, how the chariot actually descends on the inclined plane, what material it is made of and whether it exists at all, how the human body works – many researchers have focused their minds. Some of them, like Leonardo, were actually a century ahead in their thinking and attempts to answer, sometimes a few.

The point is not always to be able to accurately calculate something. Appropriate measuring tools or mathematical methods may not be available. The point is that we must think of sand flowing from a jug that has been dragged across the table. This amazement is the beginning of learning, not arithmetic.



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