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Gravity
Notes de l'éditeur
- Let’s talk about gravity in terms of Newton’s laws. When I hold the apple like this, what is its velocity?ZERO. And when I let go, what is its velocity? FASTER!So there has been a change in the speed of the apple, and the direction, because now it is moving toward the Earth, and before it was moving nowhere. So there is definitely an acceleration here. Here is a little review from Newton’s laws. There is an acceleration of this mass, speed and direction has changed, so by definition, there must be a force! Where there is acceleration there is ALWAYS a force. The two are NEVER APART from one another. They always go together. What is putting the force on this apple? What is the force??GRAVITY. Gravity is the force on this apple. It is a very special force, that always pulls an object in the exact same way. It always pulls an object toward another object. In this case, the apple is being pulled by what? The Earth.
- So lets look at gravity through Newton’s laws. Gravity is something that changes somethings velocity, so if the apple is floating through space and it gets near a planet, the gravity of that planet will change the objects velocity, maybe even pull it in.Gravity makes a mass, like this apple, accelerate toward the object with the gravity.And finally, every action has an equal and opposite reaction….so if the Earth is pulling on this apple, the apple must be pulling on the Ear th! And it IS. We are each pulling on the Earth with the same force of gravity it is pulling on us. So gravity is a force between 2 objects, ANY two objects.
- How much gravity something has depends on its mass. So the apple doesn’t have a lot of mass, and neither do we really, so even though we have gravity, the apple is not really attracted enough to move toward us. But the Earth has a LOT more mass than we do. So both us and the apple move toward the Earth, always. It is the most massive thing around.
- So here comes themathiest part of this whole course. Let’s go back to Newton’s second law. F = m *a. When the acceleration is due to gravity, we show that by writing it as little g. This was somethingGalileo famously postulated, and the story is that he dropped some stuff off of the leaning tower of Pisa to demonstrate, but I’m pretty sure that is a myth. Because the thing is, it is very hard to prove this on Earth, because once again, the pesky air gets in the way. Remember that air made stars twinkle and was annoying for astronomers? Air is also very annoying for physicists working with gravity, because when things are falling, like for example this ball, it is being PUSHED UP at the same time. What is pushing up on this ball? AIR MOLECULES! And even though gravity treats everything exactly the same, air molecules do not treat everything the same. Air molecules have a lot more surface area to push on a piece of paper, for example, and the paper is light, so it is pushed easily. Same with a feather. But if there was no air here, there would be NO DIFFERENCE!If you don’t believe me, check out these videos!http://youtu.be/_XJcZ-KoL9ohttp://youtu.be/5C5_dOEyAfk
- So if we take Newton’s second, F = m times a, and we remember that the acceleration due to gravity is little g, we get this equation F sub g = mass times little g. And I told you already that for the surface of the Earth, little g is always the same. But how do we know how much this is? How do we know what the acceleration due to gravity is for me right now? It turns out that you can figure out g based only on two things, the mass of the object you are dealing with, in this case the mass of the planet Earth, and how far away you are from the center of that object you are, in this case, how far am I from the center of the Earth? Mass of the Earth is 5.97E24KgRadius of the Earth is 6.37E6m(6.67E-11N(m/kg)2 * 5.97E24kg) / (6.4E6m^2) = 9.72165527m/s2 which is about 10 m/s2So the acceleration due to gravity on Earth, at least at sea level, is about 10 m per second squared. Which means that if you drop something, ANYTHING, lets say I dropped this ball from the grand canyon, every second it will fall 10 meters/second faster than the second before. So the first second I drop it, it will be going about 10 meters per second. Then the next second it will be going 20 meters per second. And the next second it will be going 30 meters per second. Remember that acceleration describes how the velocity of something is CHANGING, not how fast something is going. Velocity is how fast something is going.
- Check out this cheat sheet I am passing out. It is the most math intensive thing we will do. The equation at the top is called the Universal Law of gravitation. This law is very important, because it dictates almost every motion we see in Space. This law dictates the gravitational interaction between the Moon and the Earth, for example. Also the Sun and the Earth. Also the Sun and the Milky Way center. You could make big M and little m ANY TWO OBJECTS in the Universe, and this law would hold true. Always. That’s why it is called the Universal law of gravitation. We are going to do a group activity right now, about this. Don’t worry, this is the most math we will ever do.(Pass out gravity worksheet 2).Independent worksheet afterward.
- So lets get back to Newton and the apple. What is the difference between the Moon, and an apple falling from a tree? Are they both governed by the same force? He decided that THEY ARE! They are both governed by gravity. What Newton realized is that both the apple and the Moon are in free fall.
- When a rocket is sent into orbit around the Earth, it does not crash into the Earth. But it is still affected by the gravity of the Earth, everything is. It falls toward the Earth, just like this apple does. But it is going fast enough, that every time it falls a little, it moves forward just enough to keep it in orbit. The Moon is doing this too! We don’t call it falling and moving, we call it oribiting. So when astronauts are on the space shuttle, they are falling toward the Earth, and so is the space shuttle. You know how when an elevator goes down, you feel slightly weightless? Has anyone ever been on a freefall ride at an amusement park?
- When people are in free fall, they feel weightless. Imagine if these skydivers were inside of a box, that was falling at the same speed as them. They wouldn’t even know they were falling! They could not feel the wind. ALL they would know would be that they felt weightless, and they were floating. This is what is going on in space, when astronauts are weightless in the space station. Here is a cool video showing what happens when water is in free fall on the space shuttle. http://youtu.be/gTqLQO3L4KoPretty cool, huh.
- Keep in mind, that there is never such thing as NO GRAVITY. EVER. Every object always has a gravitational pull on everyt other object, its just that sometimes this is so small it doesn’t make a difference. That’s why we never say that in space when there are no other massive objects there is ZERO GRAVITY. Instead we say there is MICROGRAVITY.
- So remember what we said about orbiting, that in fact when something is attracted by the gravity of something much larger, but is also moving through space, it actually can fall toward it and never hit it, just circle around it. This is what the Earth is doing around the Sun. So gravity is what shapes our solar system. Without it, we would have no solar system! All the planets are being pulled around the Sun by gravity. Remember the scale of this picture! If the Earth were a peppercorn, the Sun would be a balloon that is all the way across the courtyard downstairs, 33 meters away.
- So gravity is responsible for the Earth going around the Sun. In this case, take a look at your cheat sheet, the Earth is the little m, and the Sun is the big M. So that Universal law dictates how much force is between the Earth and the Sun. It is the reason why the Earth is circling around the Sun.
- In exactly the same way….
- In fact, gravity is the reason that there are galaxies and stars at all! Stars are formed when gas is attracted to other gas by gravity, and galaxies are formed when stars are attracted to each other, and to black holes, and to more gas, all by gravity!