Archive | February, 2016

What Newton showed D.3.1

29 Feb

What Newton did was he showed that Kepler’s first two laws were not magnetism, as thought by Kepler, as thought by Galileo, but instead they were a consequence of the conservation of angular momentum.

Angular momentum is a mass times a speed times a distance, and that has to equal to a constant.

That is what we mean by conservation.

Two classes of orbits D.2.29

28 Feb

Newtonian gravity shows us that not only can you have nearly circular orbits, and not only can you have nearly elliptical orbits, but it admitted two new classes of orbits.

One is called a parabola, so it can go on a parabolic orbit. It comes in, let’s say, from the Oort Cloud or from the Kuiper Belt. It comes on in, it circles the sun once, and then it goes back out, never to be seen again.

You can also have hyperbolic orbits. And maybe you remember some of these terms from geometry. So you have parabolas and hyperbolas. And so, you can have a comet or an asteroid come in on a hyperbolic orbit.

Again, it comes in, goes around the sun once, and then goes on out back to the Kuiper Belt and infinity, never to return again.

So we have two types of orbits. One is called bound orbits, where it’s caught in the gravitational field, and bound orbits are things like ellipses or circles.

Unbound orbits are the parabolas and the hyperbolic orbits. They’re called this because each of the types of orbits can be taken strictly geometrically

When two objects orbit each other D.2.28

27 Feb

Newton showed that when two objects orbit each other, they orbit about their common center of mass. So it’s not like Jupiter orbits the Sun or Earth orbits the Sun.

They orbit about their common center of mass. So if I have two stars or two planets that are exactly the same mass, then much like a see-saw, that center of mass point is exactly in the middle if both masses are the same.

If one of the masses is twice as big, so for example you may have a light star and a heavy hot Jupiter type of planet, then that center of mass moves closer to the heavier object. And if you continue that process, so you have something like the Sun, and then you have the Earth, or you have Jupiter, then that center of mass point actually moves inside the Sun.

Close to the center of the Sun, but not at the center of the Sun. And so both objects are going to orbit about the common center of mass, and not one around the other.

Gravity D.2.27

26 Feb

Newtonian gravity is something that Newton made up to describe the force of gravity between two objects.

Every object in the universe attracts every other object in the universe through what he called a gravitational force that is proportional to the product of the two masses.

So it is the mass of one and the mass of the other, and it declines, gets smaller and smaller, with the square of the distance between the two objects.

And so it’s codified in the formula that the gravitational force is equal to some constant called G, which is a fundamental constant of nature. It’s like c, the speed of light or h, the Planck’s constant, this one is G. It’s the universal constant of gravitation.

Air Molecules D.2.26

25 Feb

In room temperature, most of the air molecules are colliding at about 1,000 miles an hour, 500 meters a second.

So your skin is constantly being bombarded by particles that are hitting your head, your arms – everything else and are going 1,000 miles an hour.

So if you got hit by some microscopic object at 1,000 miles an hour like a train or an airplane – well that is different you would feel it.

But because there are so many molecules and they’re coming at all different angles, we don’t perceive the impact of one. Instead we feel what is called the air pressure. And we’re quite used to this air pressure of about 15 pounds per square inch due to particles moving around at about 1000 miles an hour – characteristic of a comfortable room temperature of about 70 degrees Fahrenheit.

What is temperature? D.2.25

24 Feb

What do you mean by a temperature? When you measure the temperature of something, what do you mean? So the temperature is a measure of the kinetic energy of the molecules within a substance.

So when you record a temperature, when you measure a temperature, you are actually measuring how fast the molecules are moving within that substance.

So for example, you’re measuring how fast, how many particles are moving at a particular speed!

The conservation of angular momentum D.2.24

23 Feb

Angular momentum is a mass times the speed times the distance. And that means that a planet’s orbit cannot change unless it transfers angular momentum with other objects.

So the planets in our solar system do not exchange significant angular momentum with each other or anything else – their orbits remain steady.

In other words, it doesn’t take anything for the planets to keep orbit. They don’t need to tap energy from the Sun. They go around in the orbits simply because the conservation of angular momentum, the orbit of a planet going around elliptical orbit.

Conservation of momentum D.2.23

22 Feb

Conservation of momentum is just a mass times a velocity. This means that an object’s momentum cannot change unless it transfers momentum to or from another object.

When there’s no force present, no momentum can be transferred, so that an object must maintain its speed and direction.

A billiard table and ball is a great example. There is the one ball sitting on the table. Then there is the cue ball. And you take your stick and you pop the cue ball just right and that cue ball will go down and will impact the other ball, and the cue ball will stop and the other ball will keep going. That’s a good example of the conservation of momentum. Because initially when you hit the cue ball it has all of the momentum a billiard ball table the ball that your hitting originally has none. It is just sitting there; its speed is zero so it has no momentum.

And then afterward the cue ball stops and the other ball goes off with the same amount of momentum, the same combination of mass times speed.

Conservation Laws D.2.22

21 Feb

Conservation states that there is a certain quantity which we call energy that does not change within the manifold of changes that nature undergoes. So this is a most abstract idea. It says that there’s this numerical quantity which doesn’t change when something happens. It’s not a description of a mechanism or how something works or anything concrete.

It’s just this strange fact that we can calculate some number. And when we are done watching nature go through the tricks and trades and all the things that she does, and we calculate that number again, it’s the same.

So energy is conserved. It cannot be created and it cannot be destroyed. And objects have whatever energy they have from exchanges of energy with other objects.

But the laws do not contain explicitly time so that there is a symmetry in time, that the same laws apply here, they apply in the past, they’ll apply in the future. That symmetry of not having time in those laws means that energy is conserved.

Conservation D.2.21

20 Feb

Conservation laws and why they exist! The word conservation is generally understood to mean preventing a wasteful use of a resource, to save, to protect.

If we were speaking casually, we could use one of these meanings for the word conservation and each of us would know what the other one meant.

But conservation, the term has a different meaning when used in a technical way. It means the total value of a quantity is a constant. So there is in fact, a law governing all natural phenomena and it is exact as far as we know.

There are no known violations of this fact. And this fact, this law if you like is called the conservation of energy.