We have learned a lot recently about how the Universe evolved in 13.7 billion years since the Big Bang. More than 80% of matter in the Universe is mysterious Dark Matter, which made stars and galaxies to form. The newly discovered Higgs-boson became frozen into the Universe a trillionth of a second after the Big Bang and brought order to the Universe. Yet we still do not know how ordinary matter (atoms) survived against total annihilation by Anti-Matter. The expansion of the Universe started acceleration about 7 billion years ago and the Universe is being ripped apart. The culprit is Dark Energy, a mysterious energy multiplying in vacuum. I will present evidence behind these startling discoveries and discuss what we may learn in the near future.
This course is offered in English.

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From Daily Life to the Big Bang

Understanding the Universe in which we live and how to probe it can begin with simple daily life experiences such as night and day and the four seasons. Starting from these observations, we will take a journey from our local Earth at the present time all the way to the edge of the universe and back to its birth, learning the techniques and findings in modern physics that provide us this understanding.

MacAdams Professor of Physics, University of California, Berkeley Professor, Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), Todai Institutes for Advanced Study (TODIAS)

Okay.

So today we started talking about the why we have

days and nights every day, and we have four seasons.

And we wanted to understand the four seasons based

on the revolution of the earth around the sun.

But then we came to the point that

we couldn't quite understand how the orbiting actually works.

and then came back to this idea that we have to think about this

elliptical orbits that we are following around

the sun, not like complete circular orbits

but elliptical.

So unless we understand why we follow this

elliptical orbit, we haven't quite completed the story.

Right?

So, how do we understand that individual planets move about

the sun in an elliptical orbit instead of a circular orbit.

And that answer was given by Newton.

So when he talked about this universal theory of

gravitation, then he came up this this formula That

the force of gravity goes with so called inverse square law.

The farther you go, the gravity becomes weaker.

If you go twice as far, then gravitational force becomes four times weaker.

So that's what this equation is telling you,

and this equation turns out to be the key.

And as the legend goes, Newton discovered this law of universal

gravitation by watching an, an apple falling from the tree, and

then realized that exactly the same force is

also letting the moon revolve around the Earth.

And sort of the inspiration came from this kind of thinking.

So if you actually throw a planet from

the tree down, it ju, just goes straights down.

But if you actually start about, giving a little thrust to the apple,

then you would fly for all the distance, but eventually falls on the ground.

But once you know that earth is round, if you actually put enough thrust, then

you might actually go pretty far along

before it actually falls down on the earth.

And if you actually put you know, really sufficient thrust

that way, then it might actually go around the Earth once.

And that's exactly what the moon does.

So, depending in this the initial thrust, you may

find that something just falls, or something can go around

the earth based on exactly the same idea of this universal gravitation.

So, that's the way we understand that things

can actually about an object, based on the

same idea that something is being pulled by

a mass due to the univ, universal gravitation.

I learned that this, this legend that Newton was observing an apple

falling from the tree was just a legend, that's probably not a fact.

But apparently Newton did

have an apple tree, and at the University of Tokyo we

wouldn't have a descendant of Newton's tree in our botanical garden.

So if you happen to have a chance to visit

Tokyo, don't miss out on this descendant of Newton's apple tree.

But this law of universal gravitation wasn't quite enough, because

that only tells you how much an object is being pulled.

But what you also need to know is that how the object is influenced by the pull.

And that is given in terms of this another famous equation called F equals ma.

Which you might have actually studied in high school physics class.

So, in this equation, m stands for mass.

And, and this idea is called inertial mass.

Namely that if you are given a force, and

if the mass is bigger, you get less acceleration.

So a stands for acceleration.

Namely, that the mass is a measure of how

difficult it is to change the motion of an object.

And that I think is plainly clear just by comparing these two objects.

So, suppose you provide the same push on a tank and on a little kid on this tricycle.

And with the same push, you can hardly move this tank at all.

Right?

Because it's so massive.

But with the same little push that little poor kid may fall down.

So you can really change the, the course of his motion.

So, which one is easier to move is really determined by how massive the object is.

Heavier it is, it is very difficult to change the course of the motion.

So, m in F equal ma really stands for how

difficult it is to change the motion of an object.

So, as you see in this animation the sun is not at

the center, because the orbit is an ellipse, not a complete circle.

And as the planet moves around the Sun, it

gets pulled more strongly when it's closer, but gets

pulled less forcefully when it's farther away, so that

changes the course of motion at the same time.

The most important thing about this is that

by combining the two equations we talked about.

F equals ma,

that tells you how the motion gets affected by the pull.

And how big the pole is, and that's the Universal Theory of Gravitation.

If you put these two equations together, you

can fully explain this elliptical orbit of individual planets.

And to work it out with Algebra, it's a little

complicated, I'm not going to actually show that, precisely my lecture.

But you're welcome to solve one of the

problem sets where you can verify that this elliptical

motion really comes out from these two equations.

So, by combining these two equations, F equals ma and F goes like the Gmm over r

squared, that's the square law of gravity, then you

can fully understand this elliptical motions of individual planets.

And therefore, you'll fully understand the origins of four seasons.

So that's the way physical theory is suppose to give

you a deep understanding of what's going on in our universe.

And it actually, happens at incredible speed.

If you measure how fast the earth revolves around the

sun, it's at the speed of 30 kilometers per second.

You might feel dizzy about this.

It's incredibly fast, but nonetheless we're not throwing away from

the earth, because again we're bound tightly by the gravity of

the earth towards the earth, and we're not we don't have

to worry about this, it's flung outside from, from the planet.

And the individual planets are also moving you know, as fast.

And the closer it is, like Mercury, it's moving at a much faster speed.

The farther away it is, it's moving at the slower

speed, because the, the pull of the gravity is weaker.

And they fall on a very simple curve as you can see.

So, as function from distance, the orbital speed goes down.

And it goes like one over the square root of the distance.

So, that's something that you can verify right

away by knowing these equations that we talked about.

So, we make an approximation.

And we make a lot of approximate methods in, in physical theories.

Let's assume that it's not quite ellipse, let's say it's a complete circle instead.

It's a pretty good approximation for this purpose.

So, if it is a completely circular orbit,

then the distance from the sun doesn't change.

So r is just a number

for each planet.

On the other hand, when things are moving about, then the pull by the gravity should

be balanced by so called centrifugal force that

is trying to pull us away from the sun.

And there's a formula for that too. So, mv squared over r.

Where v is the velocity of an object. M again, is the mass of the planet here.

So, this pull by the sun due to gravity, and the centrifugal force that is trying

to pull us away from the sun should balance against each other.

So we set them equal.

And here's the pattern, read the power of having an equation.

By setting them equal to each other, you can solve for the velocity of the planet.

And that goes like this.

And this big M is the mass of the sun, that's common to all the planets.

We experience the same force of gravity due to the same sun.

G is Newton's constant, that tells you how strong

the gravitational force is.

So these two numbers are fixed for all the same planet in the solar system.

The only difference is this r, distance from the sun.

So that gives you a very precise prediction, that the velocity of an

individual planet goes down like one over square root of the distance from the sun.

And that's exactly what this data show, they follow on the same smooth curve.

The velocity

goes down like one of a square root of the distance.

So outer planets go much more slowly, inner planets goes much faster.

And we're, we can understand all of these planets

on the same equation, same curve, on a single footing.

That's the power of this Newtonian gravity.

So a question to you then, is that is there anything else we can

do about this theory of gravity, and,

and you might start asking some simple questions

that's the subject of our next clip. Now, why do all these objects follow the

same idea of Newtonian gravity when their masses are so different from each other.

Mercury is pretty light, Jupiter is among us, they differ a lot in their masses, but

they still seem to follow the same curve. Do you have any idea what's going on here?

So we'll talk about that next.

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