What do a falling apple and an orbiting moon have in common?

by The Insights

If you drop an object, it will fall. It’s a motion we’ve all seen hundreds of times. We’ve also all seen a lot of the moon, which makes a full orbit around our planet every 27.3 days (as seen from Earth). Dropping and Orbiting may seem like radically different types of movement, but they’re not! The same physics explains them both.

There is a famous story about Isaac Newton making the connection through a falling apple. (That’s probably not true, but it’s could be.) Still, its achievement is quite amazing, so I’ll walk you through the process. This includes some concepts that people living today might take for granted, but constructing knowledge like this is not trivial, and Newton didn’t figure it all out on his own. He drew on the ideas of Galileo, who studied the motion of falling objects, Robert Hooke, who explored the effects of things moving in circles, and Johannes Kepler, who produced ideas about movements of the planets and the moon.

falling objects

Let’s start with what happens to an object when it falls. In the third century BC, Aristotle asserted that a massive object would fall faster than a low mass object. Sounds reasonable, right? This seems to match what we’re seeing – imagine dropping a rock and a feather at the same time. But Aristotle was not good at testing his theories with experiments. It seemed right give a meaning that a heavier object falls faster. Like most of his fellow philosophers, he preferred to arrive at conclusions based on armchair logic.

Aristotle also believed that objects fall at a constant speed, which means that they neither slow down nor speed up as they move forward. He probably came to this conclusion because fallen objects fall quickly and it’s really hard to spot changes in speed with the naked eye.

But much later, Galileo Galilei (who went by his first name because he thought it was cool) found a way to slow things down. His solution was to roll a ball down a ramp instead of dropping it. Rolling the ball at a very slight angle makes it much easier to tell what’s going on. It could look like this:

Video: Rhett Allin

Now we can see that as the ball rolls down the track, its speed increases. Galileo suggested that during the first second of motion the ball will increase in speed by a certain amount. It will also increase by the same amount of speed in the next second of movement. This means that during the time interval between 1 and 2 seconds, the ball will travel a greater distance than it did in the first second.

He then suggested that the same thing would happen when you increase the slope of the angle, as this would produce a greater increase in speed. This must mean that an object on a completely vertical ramp (which would be the same as a falling object) would also increase in speed. Boom, Aristotle was wrong! falling objects don’t fall at a constant speed, but instead change speed. The rate at which velocity changes is called acceleration. On the Earth’s surface, a dropped object will accelerate downward at 9.8 meters per second per second.

We can mathematically write acceleration as change in velocity divided by change in time (where the Greek symbol Δ indicates change).

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