As the legend goes, Isaac Newton was inspired to develop his ideas on gravity by taking notice of an apple falling from a tree.
This is how William Stukeley who visited Newton a year before his death recounts a conversation with him, “After dinner, the weather being warm, we went into the garden and drank tea, under the shade of some apple trees … he told me he was just in the same situation, as when formerly the notion of gravity came into his mind …1”.
Historians have expressed their skepticism on whether this event actually happened. To be fair, no really knows whether this story is true.
Read: Did an apple really fall on Isaac Newton’s head.
But Newton did reside in Woolsthorpe between 1665 and 1666 when Cambridge closed due to the Bubonic plague. There were apple trees on his family’s property, and Newton is sure to have witnessed an apple or two falling during that brief stay in Woolsthorpe. Whether an apple did really hit him on the head or not is debatable.
But I like to picture it that way – makes for a good dramatic story.
This article revisits such a story and attempts to offer a dramatized chain of thought that may have inspired Sir Isaac Newton to develop the Law of Universal gravitation. Enjoy!
Disclaimer
This is a highly dramatized version of a story based on a controversial plot. It is intended for clarification purposes and should not be taken as it is.
Background
A young Isaac Newton is forced to briefly postpone his studies at Cambridge University due to the Bubonic Plague. Newton retreats to his family home in Woolsthorpe, England to wait out the plague. With not much to do, the young Newton embarks on an incredible mental journey that would forever change our understanding of the physical world.
The Falling Apple
It is the year 1665 in Woolsthorpe, England.
Apple and Blackberry are fruits, Windows mean windows, nobody knows what Brexit means, and you … well, you are Isaac Newton!
On this boring autumn afternoon, you are sitting in the backyard of your home, reading a magazine from 3 days ago.
The magazine details how the ongoing plague could be one of the worst pandemics to ever hit England with some 7000 people dying every day in London. Seen nothing of interest, you fold the magazine and absentmindedly, as it has occurred to you a thousand times before, you begin to daydream.
You wonder what would happen when this pandemic finally comes knocking on your door.
Your mother could have you and your sister pack and go to your uncle living in the countryside, further away from the wave of the plague. Or you could stay put and “wait out the storm”. The magazine you are holding reckons the plague could last a while, perhaps a few more months. Things aren’t looking so rosy right now.
What will happen when –
Duff!
Your chain of thought is interrupted by a clout to the head by a falling apple.
You were so lost in thought there that you forgot you were under a tree.
You are brought back to reality as the apple rolls a few feet away from you and comes to rest on the ground. As you sit there and watch the apple that hit you rolling away, eventually coming to a stop on the ground. You know exactly why it rolled and then stopped.
From your knowledge of natural philosophy in college, you can provide this explanation: the interaction between the rolling apple and the ground gives rise to a resistance (friction force) that undermines the motion of the apple, bringing it to rest eventually.
No surprises there.
What bugs you is this: What caused the apple to fall from the tree in the first place?
Many scholars and philosophers have grappled with this sort of question throughout history. From the early Greeks philosophers to the recent likes of Descartes and Galileo.
But no one has given a definitive answer about this mysterious force that brings everything back to Earth.
“What is the nature of this force?” You ask yourself.
As you contemplate further, your thoughts seamlessly shift to the motion of the Moon around the Earth and those of planets around the Sun.
“What is the cause of these motions?” You wonder.
As you lean back in your chair, the plague now a complete backdrop, you begin to wonder about the universe. And about the forces responsible for such an awesome realm that encapsulates not only the Earth and the Moon but also the planets, the Sun, and plenty of stars beyond.
“Surely, there has to be an explanation…”
What your school of philosophy says
As an undergraduate student in mid 1660s England, you are well acquainted with ideas taught by the great Greek philosopher, Aristotle. He too weighed in on this mysterious force. Aristotle believed that all matter in the universe is a blend of only four classical elements: water, air, fire and earth.
He taught that if these elements we left to settle, they would form layers simply by virtue of their inherent nature. Solid earth would sink through water and air forming the base, water would sink through the air to settle on top of the earth (or conversely air would move up through the water, as do bubbles), with fire would exist at the top of the arrangement because it tended to move up through the air.
He taught that objects fall back to Earth spontaneously in an attempt to seek their natural place in the universe.
For example, the fall of the apple would be explained this way:
Because the watery and earthly material that make up the apple are both in a lower rank than air in the classical hierarchy of order. Then they would naturally descend through air, to attain their place in the universe, which is at the ground (Earth).
He also taught that objects are intrinsically heavy or light and fall at different rates due to their differing tendency to seek their natural place in the universe2. In essence, heavy objects fall faster than lighter objects.
Problems with the Aristotelian philosophy
Personally, do not subscribe to this philosophy.
Recently, contemporary philosophers have found inconsistencies with this philosophy. For example, 75 years ago an Italian philosopher by the name of Galileo was able to experimentally prove that heavy objects and lighter objects both fall at the same rate. He also showed that falling objects trace out parabolic paths as they fall, contrary to Aristotle’s view that “natural motion” is vertically down.
In addition, this Aristotelian philosophy doesn’t fit with your own convictions about the motion of bodies.
Read: What is motion (article).
You have been captivated by the motion of bodies yourself for the past year or so. Back at Cambridge College, you have studied several publications on motion of bodies by celebrated scholars and philosophers. Building on these studies, you have embarked on a journey to unravel the mystery of motion of bodies, including planets. This has seen you develop over 100 axioms about motions of bodies in your notebook3. And these axioms don’t exactly fit with Aristotle’s view of motion.
For example, you do not believe that an external agent is necessary to maintain the motion of an object as popularised by Greek philosophy. You are rather convinced that objects in motion possess an innate tendency to remain in motion and to keep moving in a straight line – unless influenced by an external agent. You also don’t believe that objects are “intrinsically” heavy or light by nature, but rather it is to do with the quantity of matter packed into them.
Turning your attention back to the mysterious force of gravity, here is everything you know about it.
Characteristics of the mysterious “Force of Gravity”
Although you are not convinced with Aristotle’s explanation, you do not have a better theory; no one has given a better alternative explanation of why things tend to fall back to Earth. Contemporary philosophers and scholars have studied the properties of this force, but they still can’t explain it4. Here are some strange characteristics of gravity that you know about:
- It doesn’t make contact with an object in order to pull it. It pulls through everything: air, water, solid, and space5 – it knows no boundaries.
- Gravity pulls everything downwards at the same rate of fall. Contrary to common sense and Greek philosophy, which suggests heavier bodies, ought to accelerate faster than lighter ones.
- Bodies falling freely under gravity have trajectories perpendicular to the surface of the Earth. In other words, gravity seems to pull everything towards the center of the Earth.
Emergence of the centrifugal force
The days after your apple incident are filled with plenty of contemplation, speculation, and reasoning with plenty of scribbling math equations in your notebook that you have savagely titled “Waste Book”6. Locked alone in your attic room, you wonder, sometimes late into the night of questions surrounding that incident.
“Why does an apple fall down … and not sideways or even up”
While this might seem like a ridiculous question, you can make a very good sense of it:
You know that the Earth is a spherical body rotating on its axis at a speed of 1500 ft/s (expressed in modern values) at the equator. Everything on the surface of the Earth also rotates along with the Earth at that astounding speed.
But this picture is incomplete. It immediately reminds you of a scene that you have seen a hundred times before: a ball of wet cloth thrown so that it rotates about its axis has water droplets leaving tangentially from its surface. Anything attached to a rotating sphere should experience a tendency to pull it away from the sphere so that it tends to fly off.
“But why aren’t we feeling that?” You ask yourself.
You are not the first one to ask yourself of this.
Galileo did ask himself of this several decades prior7. He theorized that the force of gravity keeping a body on Earth must greatly overwhelm this other force. In fact, he attempted to determine the relative strengths of the force keeping an object on Earth (gravity) and the tendency of the same body to fly off tangentially out to space. He did not succeed in determining the actual relative strengths between the two forces, however, he went as far as to postulate that gravity must be much, much stronger than the other force.
You reckon if you must embark on a journey to figure out the force of gravity, a good place to start will be to follow Galileo’s pursuit. You call this apparent tendency of a body in a circular motion to pull away from the circle and fly off tangentially, centrifugal force.
Isaac Newton and the Centrifugal force
You are inclined to believe Galileo that the force of gravity must largely outweigh the centrifugal force of the objects on the Earth’s surface; otherwise, we should be flying off pretty cheaply. The best way to prove this hypothesis is by expressing your result in terms of a ratio: between the force of gravity of an object on Earth and the force borne out of the tendency of the same body to fly away tangentially.
You expect to find a big numerical value if Galileo is right.
The problem is, you don’t know where to start. Which is what stopped Galileo as well. He couldn’t find a way to quantify the centrifugal force. If you have to solve his problem, you’ve got to figure out how to determine the centrifugal force and relate it to the force of gravity – something no one has ever done before.
Isaac Newton and a particle in a box
Several weeks later, you still can’t figure out the problem.
Running out of paper, you have scribbled some diagrams and calculations on the walls of your home, at the slightest inspiration, hoping not to lose an insight8.
Eventually, you able to deduce a brilliant thought experiment. Here it is:
A body moving in a circle may be thought of as originally moving in a confined square by bouncing off the walls. If the collision with the interior walls of the square is perfectly elastic (i.e. without losing energy), then the ball will keep bouncing off the walls indefinitely following a trajectory shown below.
In this case, the tendency of the body to pull away from the “square-like” motion is felt as impacts on the walls as the ball collides with them.
In one revolution, these walls will experience a total force of four “impacts”, which will be equivalent to the “centrifugal force” required to keep a body moving in the square-like motion in one revolution.
If the number of sides of the square is increased to six so that it is now a hexagon with sides of equal lengths. The particle will move in a somewhat smoother trajectory. And if the number of sides keeps increasing in this manner, then the polygon will eventually inscribe a circle.
The body will now attain a circular motion where the original impacts on the walls are now felt as a smooth continuous push against the walls. This “push” is the centrifugal force exerted by the body in a circular motion against the walls of the circle.
If you can determine this “push” against the walls, then you can determine the centrifugal force.
Calculating the Centrifugal force
Following the same line of reasoning coupled with your recent developments in calculus mathematics, you are able to eventually deduce the centrifugal force9, the tendency of a body to fly off tangentially from a circular trajectory. The expression is (expressed in modern terms)
Where m is the mass of the body, v is the velocity and r is the radius of the circle10.
From this result, you are able to deduce that the force of gravity is about 300 times stronger than the centrifugal force for objects on the Earth’s surface. In essence, this result tells you that in one second, gravity will make a body descend 16 feet, whilst the centrifugal force will make it travel over just half an inch11.
This result, not only confirms Galileo’s hypothesis, but it also makes sense. If the force that’s keeping everything on planet Earth doesn’t greatly outweigh the force causing us to fly off tangentially due to the Earth’s rotation, then planet Earth would be such a lonely place indeed!
All the way to the Moon
Motivated by your own success in figuring out the centrifugal force problem, you quickly apply your newfound insight to the motion of the moon around the Earth.
The Moon is revolving around planet Earth, once every 27 days. And just like any object subject to a circular motion, it experiences a force that pulls it off the circular path – centrifugal force.
But it doesn’t fly off. You are convinced that there ought to be another force responsible for keeping the moon in her orbit, preventing it from flying off into space.
“What could that force be?” You wonder.
“Could it be gravity?” You debate yourself.
“But if it is gravity, where is this gravity coming from?” You ask yourself.
“The Earth?” You wonder.
But the moon is so far away from the Earth. You have no reason to suggest that the force of gravity reaches that far out in space. You keep reasoning with yourself.
But then it occurs to you that if the power of the force of gravity can be felt on the tallest buildings and on top the tallest mountains with the same intensity, how much further away from the center of the Earth does it go? – Why not all the way to the Moon?
With this argument, you formally extend your analysis of gravity to the Moon.
The Force of Gravity and the Moon
You theorize that the force of gravity extends all the way to the Moon. But you are faced with another immediate problem, if the force of gravity is pulling on the moon, then why doesn’t the moon come crashing down to Earth?
This is a huge question. In fact, according to your calculations the moon should crash into Earth in about 2 hours and 15 minutes!
What if the Moon is indeed “falling” to Earth
Well, after several weeks of fresh air, long walks, deep contemplation, sketches, scribbles, and self-debating. You have, at last, devised a thought experiment that has literally given you the chills as you rolled in your bed thinking about the moon. Here it is:
If gravity is responsible for the motion of the moon around the Earth, then it must diminish as one travels further away from the center of the Earth. Otherwise, there wouldn’t be a moon.
You figure that the moon is indeed falling towards Earth, but the centrifugal force pushes it through a distance large enough to coincide with the curvature of the Earth so that the moon ends up revolving around the Earth rather than crashing into it.
If this is true, then it is not only the moon that can be made to travel around the Earth, literally, anything can be made to travel around the Earth given a velocity large enough to push it over the edge of the Earth without crashing into it.
And why stop at the moon?
What if all planets revolving around the sun follow the same principle?
Sitting alone in your attic room in Woolstrope, you believe you glimpsed the secret of the universe!
From the Author
I think Isaac Newton’s time in Woolstrophe between 1665 and 1666 was one of the most important times in his life. I have written a short-story fiction book that builds on the idea of this article and dramatizes other aspects of Newton’s life while in Woolstrophe during the plague period. You read a free PDF version of the book by following the link below.
The Tale of Sir Isaac Newton and Gravity (PDF).
It is an extensive 9-chapter drama that, from the second-person perspective that if you enjoyed reading this article, then you’ll definitely love reading this as well. As for the e-book, feel free to support my work on Amazon. Here’s a link below.
- Memoirs of Sir Isaac Newton by William Stukeley (1750)
- See Isaac Newton: The Last Sorcerer by Michael White
- See Newton: A Very Short Story by Rob LLiffe
- There were other alternative theories, such as Descartes’ theory of vortices. It wasn’t so successful at explaining phenomena though
- Newton might have probably used the word ether in place of space though
- Isaac Newton really had a notebook titled “Waste Book” that he used in part to develop his theories on mathematics and physics. Read Three Things You Didn’t know about Isaac Newton
- In his “Dialogue of the Two Chief Systems of the World” published in 1632, some 34 years prior
- Several sketches believed to be of Isaac Newton have been found in his childhood home, historians believe they date around the mid-1600s when Newton was home due to the Plague
- The derivation of the result is beyond the scope of this article
- Christiaan Huygens formally published this result in 1673; Newton, however, had already used the result years ago but hadn’t yet published his work. Furthermore, the Moon follows an elliptical path rather than a circle, but still, this formula gives decent results
- As described on page 27 of IIiffe’s Book, Newton: A Very Short Story
