22 Thinking about Motion (Graded Reading)

When he was a mathematics professor at the University of Pisa, Galileo Galilei might (or might not) have dropped two balls of the same material and different weights from the top of the Leaning Tower of Pisa. If they were heavy enough to overcome air resistance on their way down, the two masses would have fallen side by side, striking the ground at the same time.  Such an experiment would have disproved the long-prevailing claim by the Ancient Greek philosopher Aristotle that the speed at which an object falls is proportional to its mass.  That is, that an object that is ten times heavier falls ten times faster.  (While Galileo’s experiment might have only been a proposition or thought experiment, a few years prior two scientists in the Dutch city of Delft dropped identically-sized lead balls of different masses off of a tower and onto a wooden board. The two balls were heard to hit the board at nearly the same time.)

In another famous but apocryphal story, Galileo, after being found guilty of heresy by the Catholic Church and forced to renounce his heliocentric views, stomped his foot and muttered Epur si muove (And yet it does move). When the younger Galileo challenged popular ideas about motion and falling, he was challenging ideas that underpinned a geocentric view of the universe.

Aristotle, who lived in the 4th century BCE, proposed a set of intuitively reasonable ideas about motion that were generally assumed to be true up until Galileo’s time.  During Galileo’s lifetime many natural philosophers (whom we would call scientists today) were questioning Aristotle’s ideas. They used a combination of real and imagined experiments to argue that these ideas did not describe the real world.

Aristotle held that heavier objects will fall faster, and, more specifically, that an object that is twice as heavy will fall twice as fast.  This would explain, for example, why a hammer falls faster than a feather. Galileo argued that the hammer falls faster than the feather only because they are falling through the air.  As the feather falls through the air, the air pushes up on it, slowing its motion.  Galileo proposed that if the two objects were dropped side by side in the absence of air, they would instead fall at the same rate, hitting the ground together.

Galileo could only image conducting this experiment, but during the Apollo 15 mission to the Moon, Commander Dave Scott conducted a brief physics demonstration showing that Galileo was correct.

The following video repeats this experiment (with a bowling ball in place of the hammer) in a vacuum chamber on Earth using high-speed (slow-mo) video.

Falling objects accelerate.  Their velocity changes as they fall; specifically, they speed up.  Objects thrown upward also accelerate, they slow down.  The scientific definition of acceleration is any change in motion, including speeding up, slowing down, or changing direction. Galileo proposed that, in the absence of air resistance, dropped objects share the same acceleration due to gravity regardless of their mass. So if two objects are released at the same time, they will accelerate together, and fall side by side.  Unless, of course, air gets in the way (air resistance is why the feathers fell more slowly when there was still air in the chamber). This happens despite the fact that heavier objects are heavier… they are pulled more strongly toward the ground.

Galileo thought deeply about the difference between motion and changes in motion (accelerations).  He argued that motions (for example, Earth traveling through space) cannot be felt and that it requires no force to keep an object moving. Instead, it is changes in motion that require a force (and that we can feel). This directly opposed Aristotle’s idea that moving objects naturally come to a stop.

We observe that if you start an object moving, it typically comes to a stop after you stop pushing it. Aristotle stated that this happens because being stationary is an object’s natural state and that, in the absence of an applied force, an object will naturally return to rest (it will stop).  Galileo instead proposed that moving objects only stop because there are forces opposing their motion.  Today we call these forces friction and drag (or air resistance).  When, for example, you slide a pen across a desk, the pen comes to a stop because friction between the pen and the desk acts against the pen’s motion, slowing it down.

The misconception that objects in motion naturally come to a stop is still common today because it seems to explain what we see in everyday life. For example, if you are pushing a box across a floor, and you stop pushing it, the box will stop moving. Galileo argued that friction between the box and the floor causes the box to slow and stop. Only by applying a force against friction can you keep the box moving. Instead of imagining a box being pushed along a floor, imagine you are pushing it across smooth ice. If you stop pushing the box, it won’t immediately stop. Its inertia (its tendency to keep moving) will carry it across the ice for some distance. Of course, there is still some friction between the box and the ice and the box will eventually come to a stop.

One reason that some early astronomers resisted the heliocentric model of the solar system is that they couldn’t imagine a force large enough to push the Earth around the Sun. Tycho Brahe, for example, could see the mathematical simplicity of a heliocentric model, but resisted the idea that the Earth (“that hulking, lazy body, unfit for motion”) is moving. (Instead of accepting Copernicus’s model, Brahe instead proposed his own in which the planets orbit the Sun while the Sun orbits the Earth.)

It probably isn’t difficult to imagine a box sliding across ice after it has been pushed, but it is hard to think about the Moon and Earth sailing through space without any force pushing them along their orbits (gravity doesn’t propel planets along, but instead tethers them to the Sun). Galileo’s answer to this objection is simple. No matter how massive an object is, no force is needed to keep it moving. Just like smaller objects, absolutely no force is needed to keep the Moon, Earth, or other planets moving.  (Students often ask what started the Earth moving. This is a good question and hints at the process of star and planet formation.)

Isaac Newton built on the ideas of Galileo and others to formulate his three “laws” of motion and his “law” of universal gravitation. Newton used his laws of motion and gravitation (plus integral calculus) to explain the orbits of the planets around the Sun.  This essentially ended the debate between heliocentric and geocentric views of the solar system (in favor of heliocentrism). These same laws also help us understand the interiors of stars and planets, the evolution of planetary atmospheres, and the orbits of stars within galaxies. They are also a first step in understanding general relativity (our modern theory of motion and gravity), black holes, and the evolution of the Universe itself.