# Leonardo da Vinci and gravity

## Notes from the genius reveal amazingly advanced understanding of gravity

**Far ahead of his time: Leonardo da Vinci had an astonishingly modern understanding of gravity. More than 500 years ago he recognized that gravity corresponds to acceleration – and devised experiments to prove this. This is revealed by da Vinci’s drawings and calculations, which researchers discovered on a manuscript page of the Codex Arundel. Da Vinci even tried to calculate the gravitational constant and was 97 percent correct.**

Leonardo da Vinci was a real universal genius: He created unique works of art , conceived and developed buildings , machines and amazingly modern aircraft and dealt with mathematics, medicine and astronomy. Da Vinci was way ahead of his time in many of his ideas, even though he never studied. To this day, the extensive work of da Vinci, which has by no means been fully researched, arouses admiration and is part of the cultural world heritage.

### Chance find in da Vinci’s sketches

Morteza Gharib from the California Institute of Technology and his colleagues have now uncovered a hitherto unrecognized achievement of da Vinci – by accident. Gharib actually wanted to find some of da Vinci’s drawings on fluid dynamics for his aeronautics students when he came across a series of sketches in the Codex Arundel – a collection of da Vinci’s notes and drawings from the period 1480 to 1518 – that puzzled him.

On the sketch sheet, Da Vinci drew vessels from which round particles fell to the ground at an angle. Triangles next to the particles seemed to indicate angles. “What struck me was the label ‘Equatione di Moti’ next to the hypotenuse of one of these triangles – a right triangle,” reports Gharib. “I wondered what exactly Leonardo could have meant by that.” The researcher, together with colleagues, therefore took on the text on these sketch sheets, which was written in da Vinci’s typical mirror writing.

### Gravity as a form of acceleration

The analyzes revealed something surprising: Leonardo da Vinci apparently developed experiments and considerations on gravitation more than 500 years ago that were far ahead of their time. Because he recognized that gravity corresponds to a form of acceleration. In his notes, da Vinci described an experiment that proved this: if you move the vessel depicted in the sketches parallel to the ground while water or sand is trickling out, they will not fall to the ground at a steady rate—gravity accelerates the fall.

Da Vinci realized that this experiment can also be used to find out what the acceleration caused by gravity is: If you accelerate the vessel at exactly the rate that corresponds to the acceleration of gravity, the motion of the sand pouring out should follow a right triangle with two equals Pages match–that image was what Gharib had noticed.

Da Vinci’s inscription “Equatione di Moti” means something like equivalence of movement. “Da Vinci therefore recognized the equivalence of the two orthogonal movements – one is influenced by gravity, the other by the experimenter,” say the researchers.

### Da Vinci’s formula was just off the mark

However, this means that Leonardo da Vinci had already understood an essential property of gravity around 1500 – and even tried to determine the gravitational acceleration. In the mathematical calculations based on this, the Renaissance autodidact managed to get as close as 97 percent to the gravitational constant, as Gharib and his colleagues explain. The mathematically correct description of gravity only succeeded around 100 years later, when Galileo Galilei described the acceleration of a falling object in a formula in 1604.

But da Vinci also understood the principle of the effect of gravity on falling bodies, but he still used an incorrect formula. “He described the distance traveled by the falling object as proportional to the time it fell rather than the square of the time it fell,” explains co-author Christ Roh of Cornell University. With this, however, da Vinci came relatively close to real connections. In any case, he had realized that gravity accelerates falling objects uniformly.

### “Far ahead of its time”

Using Da Vinci’s sketches, Gharib and his team have also determined the reason for his miscalculation: The experiments he depicts cover exactly the period in which his formula and the correct formula give almost the same results. According to the researchers, the limited technical possibilities – for example for measuring time – contributed to the fact that the ingenious thinker and inventor did not come up with the right equation.

“But the fact that da Vinci dealt with this problem as early as 1500 and got this far demonstrates how far ahead of his time he was,” says Gharib. (Leonardo, 2022; doi: 10.1162/leon_a_02322 )