When I took my first mechanics class in college,
the professor related a story that I'll never forget. He said that on a recent
trip to Europe, he had visited this scientist's grave. And as he stood near
the grave, along with other visitors, his knees buckled. He fell to the ground and
started to weep uncontrollably...not because he was hurt, but because he was
overcome with emotion, standing in such close proximity to the scientist whose
work he had devoted his entire life to, and whom he considered the father of
modern science itself. In a poll taken many years ago, 50 of the most respected
scientists of the world were asked to list their choice of the greatest
scientists of all time. Of course, the usual suspects were on these lists -
Maxwell, Bohr, Einstein, Darwin, Galileo, Tesla, Curie. But only one man was on
every single list at or near the top. The late Nobel laureate Subrahmanyan
Chandrasekhar, famous for the "Chandrasekhar Limit," once said: "it is fashionable
today to think of Einstein as the epitome of scientific genius, and
compared to us ordinary mortals, Einstein was indeed a giant. But compared to this
man, he runs a very distant second. Even Einstein had said that his work would
have been impossible without this man's discoveries. You might have guessed by
now that the man I'm talking about is Isaac Newton. But what makes him a giant
amongst Giants? He had many major discoveries, but perhaps his
most significant united the earth with the heavens. What was this discovery and
how did it change our paradigm? The explanation is coming up right now...
What you have to understand about Newton's accomplishments is that this was the mid
to late 1600s. These were the dark ages of science. Everything was a miracle.
People believed in magic, curses, astrology, and spells. It was commonly
thought that the earth was 6,000 years old, and they had other crazy ideas too.
People believed insects like roaches, could be born from dirt and garbage. Evil
spirits could occupy people's bodies. Sickness could be cured by draining your
blood. You could make it rain by plowing land. And that tiny human babies lived
inside sperm cells. These were all common beliefs during the time of Newton's
birth. 20th century scientists like Einstein and Bohr, and even 19th century
scientists like Maxwell, had a body of scientific work that they could build
upon. They could stand on the shoulders of other great scientists. Newton in the
17th century, had almost no shoulders to stand on. There were some prior ideas
from scientists like Galileo and Kepler, that Newton used, but there was no
rigorous mathematical basis to develop the ideas that he had. the math to
express the dynamics of velocity and acceleration, for example, had not been
invented yet. Newton invented the mathematics to
express his laws. That mathematics is called "calculus" today. In the process
Newton changed the way that science was done. He outlined a way to decide the
true nature of reality. And he invented the modern rigorous mathematical way of
looking at the world. Newton had four major accomplishments. One, he developed
calculus. Virtually all modern scientific analysis relies on this. Two, he
discovered many of the laws of optics including the composition of light and
the nature of color. Three, he developed the laws of motion, including a clear
definition of what a force is. And four, he defined the law of
universal gravitation. Any one of these accomplishments would be a feat worthy
of a modern-day Nobel Prize, and would have put Newton among the greatest
scientists who ever lived. But to have done all four, is staggering! But I left
out an even more amazing fact. Newton came up with the theoretical basis of
all these accomplishments in a period of only eighteen months! Let me repeat that,
eighteen months, between 1665 and 1667,
at the ripe old age of 25. Interestingly, he did this while he was in isolation at
home because his university was closed due to an epidemic called the bubonic
plague, that was ravaging England at the time. This is eerily similar to the Covid-19
pandemic that's going on right now. Can you imagine that some genius student
today, with time on his or her hands, might be coming up with the theory of
everything, right now, in isolation at home because of Covid-19? We can hope
can't we? And the crazy thing is, Newton may have never published any of his
works had it not been for the prodding of Edmund Halley,
for whom Halley's Comet is named, who convinced Newton to publish it. But
Newton published it 20 years later in 1687, in an epic landmark book of physics
called "Philosophiae Naturalis Principia Mathematica," or mathematical
principles of natural philosophy, which is considered the greatest single
written work in the history of science, no contest. By the way, this greatest
scientific work of all time, sells only a few hundred copies a year. I believe
Newton's greatest discovery may very well be number four, the law of universal
gravitation, which brought together all his other laws of motion. Now you may
have heard the legend that an apple fell on Newton's head, causing a Eureka moment
of discovery. But that's probably not what actually happened. According to
Newton himself, one fall day on his farm during those plague years, an apple fell at
his feet. As he looked at the Apple, and looked up at the tree, from where it fell,
he asked himself what is it that caused the Apple to fall. It must be some kind
of force from the earth acting on the Apple, without
touching -- an action at a distance. How high does this force reach, he thought? If
I climbed to the top of a mountain, and dropped an apple, it would also fall to
the ground. Could it reach even higher perhaps as high as the moon? He had a
brilliant insight that it may be the same force acting on the moon, but just
with a different magnitude. He reasoned that whatever the force is, it may be
proportional to the total amount of stuff in the object, that is, all the
atoms -- in other words, its mass. So for example, the pull of the earth would be
proportional to its mass. And the pull of the Apple would be proportional to the
mass of the Apple. Since Newton's third law says that forces are equal and
opposite, the force exerted by the Apple on the earth, is equal in magnitude to
the force exerted by the earth on the Apple. This force must be proportional to
the product of the two masses. Newton also guessed that whatever gravity is,
since it emanates from all parts of the earth, it must spread out like a sphere
in all directions. And if that's the case, then it must decrease in magnitude
proportional to the surface area of a sphere. Because surface area is
proportional to the radius squared, using this formula, and since the surface area
gets bigger the further away from Earth you are, then the magnitude of this force
must decrease by r-squared as well. This means that the r-squared must be in the
denominator. This is similar to the way that light dims the further away you are
from the source of the light. As this graphic shows, when light is two units
from its source, it has to go through four times as much surface area. When it
is three units from its source, it has to go through nine times as much surface
area. So it dims proportionately. Gravity decreases the same way. So this completes
the formula for the law of universal gravitation. The force is proportional to
a constant now called the gravitational constant, "G" times the product of the two
masses divided by the distance between the two masses squared. So if gravity is
pulling the moon towards the earth, why doesn't the moon hit the earth?
This is the part where Newton had a huge insight and made a crucial connection
between the forces on earth and the forces in the cosmos. He did a thought
experiment, if you have an object moving at a constant speed with no force, like
friction or gravity, acting on it, Newton's first law says that it will
just continue moving in a straight line, at a constant velocity V. There's no
acceleration. If, on the other hand, you drop that object from rest near
something with gravity like earth's, it will accelerate towards the earth. This
means it's velocity will start off at zero, but continue to speed up at a
faster and faster velocity, as it falls. Acceleration means its velocity will
increase according to the formula Delta V divided by delta T - change in velocity
divided by a change in time. Since this is a continuous process over
infinitesimally small changes, acceleration is written in calculus as
dV/dt, or the derivative of velocity. Now, if we take an object traveling at a
constant velocity, while at the same time it experiences an acceleration due to
gravity of Earth, it will have a different kind of motion. It will no
longer move in a straight line, but will experience a pull towards the earth,
while also continuing to travel in the direction that it had been traveling. It
will not slow down or speed up because the force it experiences is in a
direction perpendicular to its original direction of motion. Its trajectory will
now be a direction towards the earth. So it will move both down as well as
across. Now, as it keeps going, it will continue to move in this same kind of
direction, towards the earth, as well as in the direction it was initially moving.
So, although we're making a polygon in this illustration, you have to imagine
that these changes in direction of the object will be infinitesimally small. And
if you take the tiny movements of the object towards Earth continuously, as it
moves, calculus tells you that the real trajectory of this object will be
circular. It will form an orbit. This is how the moon forms an orbit around the
Earth. So it's in this way the moon is also falling towards the Earth. But don't
worry, it will not hit the earth. Another way to visualize this is to use
another famous thought experiment that Newton used. Imagine a cannon on top
of a mountain, that fires a cannonball at a certain speed.
The Cannonball will land at some distance away from where it was fired, as
it gets pulled towards the earth due to gravity. Now if you shoot it at a faster
speed, it will land further away from where it was shot. If you keep going up
in speed, it will land further and further away. And if you fire it at a
sufficiently fast speed, Newton said it will go all the way around the earth, and
hit the back of the cannon. Now if the cannon wasn't there, and if there was no
friction in the air, the cannonball would continue to go around the earth in an
orbit. It is actually falling towards the earth but never hitting the earth. This
is the same way that the moon is also falling towards the earth. Newton also
showed that if you fire the Cannonball at a somewhat higher speed than needed
to just make it orbit in a circle, it will orbit in the shape of an ellipse.
The planets orbit the Sun in a similar elliptical shape. Newton went further and
reasoned that this law of gravitation might be universal, not just limited to
the earth, and the Apple, and the moon. He knew about the moons of Jupiter, for
example, and clusters of stars. And there's no reason his laws wouldn't
apply to them as well. The heavens were now connected to everyday motion on
earth. There were no unique forces affecting the rest of the cosmos, or in
outer space, that was not also going on right here. The idea that everything can
be understood using the same principles of motion on earth, as well as outer
space, changed the paradigm that earth was
somehow special. So now our place in the universe was just another planet that
behaved like any other planet in the solar system. Now I think it's important
to note that Newton did not explain what gravity is. He only described what
gravity does, and how it behaves. But what exactly is gravity? Why do massive
objects attract other massive objects? Why don't they repel each other? Or not
have any effect on each other at all? Einstein provided a little bit of
insight by showing that space-time bends like a trampoline
in the presence of a mass. But we still have to ask, "why does mass or energy bend
space-time?" What is the connection between mass and space-time? This is a
question we really haven't answered? And that will probably take another
intellectual giant. But if humanity can produce an astounding intellect like
Newton, I have no doubt that we can produce another. And I hope I'm still
alive to read the paper written by the next Newton that changes our paradigm
once again. I'd like to thank my supporters on Patreon and Youtube.
Post your questions below. I'll try to answer all them. If you like this video,
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