Uploaded by vmargoniner on 16.09.2009

Transcript:

Welcome back to the Cosmic Classroom.

So this week I heard a lot of questions

about Kepler's Laws. Mostly, many of you had

questions about the understanding of what

Kepler's Law means. And also how can you memorize

the the different laws. There're also some questions

regarding Newton's version of Kepler's Law, which we'll

treat somewhere else. So lets review Kepler's

Law, so they are three laws, and I think that much

you probably remember. So there're three laws.

The first law, first law,is the one that says that

planets orbit in elliptical orbit around the sun,

with the sun in one of the focus of the ellipse.

So let me try to draw an ellipse here,there,let's

put the sun in one of the focus, and of course I'm

exaggerating the ellipse. Right?

The real, if you were to really draw this to scale,

it would look like a circle. Right?

You wouldn't be able to see it, how elliptical it is.

That's just to make a point here. So there's the sun and

there is a planet here and the first law says

that the planet orbits in this elliptical orbit, that's it.

Now the Second Law draws on it.

The Second Law, adds something else to it.

So the Second Law, Second Law, I'll use the

same drawing here. What the Second Law

is, says is that the time that it takes the

planet to move from this position here.

Let's say it's here, August first, and it takes

two months to travel here, and it would a day

in September first, yeah. So it says that while

traveling the planet covers an area here and that,

that area is constant. So if it takes two months

to go from here to here, there is another place in

this orbit that it will also take two months to go

to, from there to there. Because the area

here is the same. So it says, the Third Law says

that planets sweep equal areas and equal amount

of time in the orbit. Now it's often not clear how

is it possible that this area here is equal to this one.

How do I know that? So of course in this case

I just drew it approximately, but you could convince

yourself that this a very similar by getting something

for which you know the area and see how many

you can fit in there. So for example you get

some pennies see how many you can fit in there.

And you'll see that you'll be able to fit about

as many in this side. The pennies are a little bit

too big to demonstrate here, but that's the idea of area.

Right? So it's the same real state in

both, in both places the same real state is covered, but the

shape is different that's Newton's that's Kepler's Second Law,

excuse me, Kepler's second law. Alright?

So Second Law builds on the third one.

The third one gets more confusing. The third one is the one that

adds an, another planet to it. Ok?

So the Third Law now deals with comparison between

two planets orbiting the sun. The first and second law

are talking about one planet and thus,and the

third law lets add another planet here, in another orbit.

Alright? Around the sun. There.

So the Third Law states that the period of, that's

period the amount of time that it takes for a planet

to go around the sun square is proportional to

the average distance from the planet to the sun cube.

And this is an empirical relationship and Kepler didn't

know why it was that way. He just notice that, that

was a relationship... Notice that

it makes sense. If 8 increases lets, lets

imagine that this is Earth at one astronomical unit.

If you're now at two astronomical units of

course it's going to take longer to go around

because the path is longer. But not only it takes

longer because the path is longer but actually

the planets are moving slower further from the sun.

You can think about it as they attracted less to the

sun, so they slowed down. So a planet an outer planet

here is moving up to certain velocity while the inner planet

is moving at a faster speed. A faster velocity.

And it's got really busy. But I hope you followed.

Just to give you a little bit more on, on Kepler's

third law, which is the more complicated one.

It dares to have an equation in there,which you

really don't like I know. Kepler's third law, so I

would like to give you one more specific example.

So lets imagine, so we have the sun here,

right there, and then there is the Earth going

around the sun in something that should look more

or less like a circle,you shouldn't be able to say

that the sun ellipse. So here is the Earth,

here is the sun and you now that the

Earth is at the distance of one astronomical

unit from the sun. That's the definition of an

astronomically unit and it takes one year for the sun

to go around, for the Earth to go around the sun, one year.

Now at about three astronomical units from

the sun we have something called the Asteroid Belt.

So I'm going to try to draw something that's

three times further away. Alright?

Here, its called the Asteroid Belt it doesn't have any

planets on it, but it has a lot of little rocks there.

No planet was formed in there because Jupiter is nearby and

keeps, you know, messing them up. But they are a bunch of,

you know, little rocks in here, and those little rocks

are also orbiting the sun. The rocks are at three

times the distance,three astronomical units from the sun.

So let's see how long it takes for the Asteroids to

complete one full orbit. Right?

According to Kepler's third law we know the relationship

between that period and the distance from the sun.

We know that "P" squared equals "A" cubed. So if the distance is three,

so I have that "P" squared equals 3 cubed meaning "P" squared equals about 27.

And if you take the square root of this, P is

square root of 27, P is approximately, this design

for approximately, 5 years. So it takes 5 years for the

Asteroids to complete one orbit, but notice that they are only

traveling a distance that it's three times greater than Earth.

Right? The radius is three times

the distance is just three times greater, but it's taking 5

times as long to go around. Which leads us back to

the conclusion that the Asteroids are traveling at

the slowest speed than earth. And that's it for Kepler's Law.

I hope it helped. See you next time.

So this week I heard a lot of questions

about Kepler's Laws. Mostly, many of you had

questions about the understanding of what

Kepler's Law means. And also how can you memorize

the the different laws. There're also some questions

regarding Newton's version of Kepler's Law, which we'll

treat somewhere else. So lets review Kepler's

Law, so they are three laws, and I think that much

you probably remember. So there're three laws.

The first law, first law,is the one that says that

planets orbit in elliptical orbit around the sun,

with the sun in one of the focus of the ellipse.

So let me try to draw an ellipse here,there,let's

put the sun in one of the focus, and of course I'm

exaggerating the ellipse. Right?

The real, if you were to really draw this to scale,

it would look like a circle. Right?

You wouldn't be able to see it, how elliptical it is.

That's just to make a point here. So there's the sun and

there is a planet here and the first law says

that the planet orbits in this elliptical orbit, that's it.

Now the Second Law draws on it.

The Second Law, adds something else to it.

So the Second Law, Second Law, I'll use the

same drawing here. What the Second Law

is, says is that the time that it takes the

planet to move from this position here.

Let's say it's here, August first, and it takes

two months to travel here, and it would a day

in September first, yeah. So it says that while

traveling the planet covers an area here and that,

that area is constant. So if it takes two months

to go from here to here, there is another place in

this orbit that it will also take two months to go

to, from there to there. Because the area

here is the same. So it says, the Third Law says

that planets sweep equal areas and equal amount

of time in the orbit. Now it's often not clear how

is it possible that this area here is equal to this one.

How do I know that? So of course in this case

I just drew it approximately, but you could convince

yourself that this a very similar by getting something

for which you know the area and see how many

you can fit in there. So for example you get

some pennies see how many you can fit in there.

And you'll see that you'll be able to fit about

as many in this side. The pennies are a little bit

too big to demonstrate here, but that's the idea of area.

Right? So it's the same real state in

both, in both places the same real state is covered, but the

shape is different that's Newton's that's Kepler's Second Law,

excuse me, Kepler's second law. Alright?

So Second Law builds on the third one.

The third one gets more confusing. The third one is the one that

adds an, another planet to it. Ok?

So the Third Law now deals with comparison between

two planets orbiting the sun. The first and second law

are talking about one planet and thus,and the

third law lets add another planet here, in another orbit.

Alright? Around the sun. There.

So the Third Law states that the period of, that's

period the amount of time that it takes for a planet

to go around the sun square is proportional to

the average distance from the planet to the sun cube.

And this is an empirical relationship and Kepler didn't

know why it was that way. He just notice that, that

was a relationship... Notice that

it makes sense. If 8 increases lets, lets

imagine that this is Earth at one astronomical unit.

If you're now at two astronomical units of

course it's going to take longer to go around

because the path is longer. But not only it takes

longer because the path is longer but actually

the planets are moving slower further from the sun.

You can think about it as they attracted less to the

sun, so they slowed down. So a planet an outer planet

here is moving up to certain velocity while the inner planet

is moving at a faster speed. A faster velocity.

And it's got really busy. But I hope you followed.

Just to give you a little bit more on, on Kepler's

third law, which is the more complicated one.

It dares to have an equation in there,which you

really don't like I know. Kepler's third law, so I

would like to give you one more specific example.

So lets imagine, so we have the sun here,

right there, and then there is the Earth going

around the sun in something that should look more

or less like a circle,you shouldn't be able to say

that the sun ellipse. So here is the Earth,

here is the sun and you now that the

Earth is at the distance of one astronomical

unit from the sun. That's the definition of an

astronomically unit and it takes one year for the sun

to go around, for the Earth to go around the sun, one year.

Now at about three astronomical units from

the sun we have something called the Asteroid Belt.

So I'm going to try to draw something that's

three times further away. Alright?

Here, its called the Asteroid Belt it doesn't have any

planets on it, but it has a lot of little rocks there.

No planet was formed in there because Jupiter is nearby and

keeps, you know, messing them up. But they are a bunch of,

you know, little rocks in here, and those little rocks

are also orbiting the sun. The rocks are at three

times the distance,three astronomical units from the sun.

So let's see how long it takes for the Asteroids to

complete one full orbit. Right?

According to Kepler's third law we know the relationship

between that period and the distance from the sun.

We know that "P" squared equals "A" cubed. So if the distance is three,

so I have that "P" squared equals 3 cubed meaning "P" squared equals about 27.

And if you take the square root of this, P is

square root of 27, P is approximately, this design

for approximately, 5 years. So it takes 5 years for the

Asteroids to complete one orbit, but notice that they are only

traveling a distance that it's three times greater than Earth.

Right? The radius is three times

the distance is just three times greater, but it's taking 5

times as long to go around. Which leads us back to

the conclusion that the Asteroids are traveling at

the slowest speed than earth. And that's it for Kepler's Law.

I hope it helped. See you next time.