A Doodle Reveals da Vinci’s Early Deconstruction of Gravity

When Leonardo da Vinci wasn’t painting a masterpiece or dreaming up flying machines, he was pondering the mysteries of gravity. The Renaissance thinker considered himself as much a man of science as an artist and spent untold hours exploring how the “attraction of one object to another” could affect such things as the flight of birds and the fall of water.

Now, three scientists at the California Institute of Technology have discovered that Leonardo did detailed experiments that sought to illuminate the nature of gravity a century before Galileo and some two centuries ahead of Newton’s making its investigation an exact science. The scientists’ study of his gravitational ideas and experimentation was published earlier this month in the journal “Leonardo.”

“Nothing could stop him,” Morteza Gharib, an author of the paper and a professor of aeronautics at Caltech, said in an interview. “He was far ahead in his thinking. It could not wait for the future.”

Z. Jane Wang, a professor of physics at Cornell University who has studied some of da Vinci’s pioneering analyses, said the new paper revealed a man determined to find an iron law of nature that would shed light on the overall dynamics of falling objects.

“It’s not enough” to call the polymath an artist, Dr. Wang said. More accurately, she added, he was “a quintessential” man of the Renaissance, which gloried in the revival of not only art and literature but also science and explorations of nature.

Leonardo has long been famous for his technical ingenuity and versatility, for his sketches of flying machines and fighting vehicles. He also made advances in geology, optics, anatomy, engineering and hydrodynamics, the arm of science that explores the behavior of fluids.

Walter Isaacson, in his biography of da Vinci, reports that as a close observer of nature, he gave much attention to how birds shift their center of gravity as they twist, turn and maneuver in the wind. He also said that Leonardo realized that gravitational attraction kept the seas from falling off the earth.

Dr. Gharib said he learned of Leonardo’s gravity experiments while examining an online version of The Codex Arundel, named after a British collector, the Earl of Arundel, who acquired it early in the 17th century. Da Vinci composed the collection of hundreds of papers between 1478 and 1518 — that is, between the ages of 26 and 66 — the year before his death. The papers now reside in the British Library. The collection features his famous mirror-writing as well as diagrams, drawings and texts covering a range of topics in art and science.

What caught Dr. Gharib’s eye is what he calls “a mysterious triangle” near the top of Page 143. Its strangeness lay in how Leonardo’s sketch showed an adjoining pitcher and, pouring from its spout, a series of circles that formed the triangle’s hypotenuse. Dr. Gharib used a computer program to flip the triangle and the adjacent areas of backward writing.

Suddenly, the static image seemed to come to life. “I could see motion,” Dr. Gharib recalled. “I could see him pouring stuff out.” It was a eureka moment that unveiled Leonardo’s precocious experiment.

The effects of gravity are typically seen as causing something to fall straight down — be it a dropped ball or Newton’s apocryphal apple. In gazing at Leonardo’s drawing, Dr. Gharib realized that he had managed to split the effects of gravity into two parts that revealed an aspect of nature normally kept hidden.

The first effect was the natural downward pull. The second was added when the holder of the pitcher moved it along a straight path parallel to the ground, pouring out sand or something else along the way. In the drawing, Leonardo noted where the movement of the pitcher had begun, labeling it with the capital letter A. Then, to show the falling material, he added a series of vertical lines going down from the triangle’s top line, the series getting longer as the pitcher moved farther and farther from its starting point. Their growing lengths defined the hypotenuse.

The setup turned gravity’s hidden nature into visible increments. The pitcher experiment, Dr. Gharib said, revealed that gravity was a constant force that resulted in a steady acceleration — a steady gain in speed. Leonardo illustrated the gain as the pitcher’s contents falling lower and lower over time. He succeeded in deconstructing gravity.

The researchers say Leonardo wrote in the codex that he witnessed fast-moving clouds from which pellets of hail had fallen, which they believe inspired the experiment.

Dr. Gharib said “the fascinating part” of Leonardo’s feat was that it let him estimate a constant of nature, the gravitational constant, represented today in physics by the letter G. The constant quantifies the exact strength of gravity’s pull and thus how quickly it can accelerate an object.

Despite the crudeness of his experimental setup 500 years ago, da Vinci, Dr. Gharib said, was able to calculate the gravitational constant to an accuracy within 10 percent of the modern value.

“It’s mind boggling,” Dr. Gharib said. “That’s the beauty of what Leonardo does.”

The researchers say that Galileo and Newton could better address the gravitational question because they had better tools of mathematics and better ways of measuring time precisely as objects fell.

Dr. Gharib agreed with Dr. Wang in seeing da Vinci as far more than an artist and suggested that his fame as a pioneering scientist could skyrocket if more technically knowledgeable experts probed The Codex Arundel and other sources. In his biography, Mr. Isaacson reports that more than 7,200 pages of Leonardo’s notes and scribbles survive to this day.

Dr. Gharib said that he hesitated to peer more deeply into The Codex Arundel lest he find himself tempted to focus exclusively on the mind of Leonardo da Vinci. “I’m like a kid in a toy store,” he said. “I’m afraid of even looking at it.”

He said many art historians had examined The Codex Arundel — but not scientists. “It’s an open book they haven’t looked at yet, haven’t spent time exploring,” he said. “There are so many other things to be discovered.”