 Greetings and welcome to the Introduction to Astronomy. In this lesson, we will go through and talk about more of the more understanding motion and how things work and how orbits work, and in this case we're going to specifically talk about Isaac Newton and our understanding of gravity. And this was something that had been missing for a long time. We did not have that understanding of what gravity was. Even if you look at some of the early thoughts as to how the orbits worked, you had things orbiting around nothing. So we had epicycles and what was at the center of the epicycle was really nothing. There was nothing there. Now, if you didn't have an understanding of gravity, that might make sense, but once you begin to understand gravity, we can see the big problems with those types of models. So let's look at what we know about gravity and some of the early ideas going back to Galileo's time. And Galileo gave us some of the ideas of motion. So we looked at Galileo before and we talked about his telescope, but Galileo also gave us some ideas on study of motion and gave us an idea of the concept of inertia. Inertia just means that things are reluctant to change their motion. And he also found that all objects fall at the same rate in a gravitational field. So it doesn't matter what two objects you drop. In a gravitational field, they will always fall at the same rate. It can be a hammer and a feather, as we'll see here in the Apollo 15 video. And this was done back in the 1970s by the Apollo 15 astronauts on the moon where they took a hammer and a feather and you'll watch the astronaut drop them and see that they fall at the same rate. So watch that they fall at the same rate, but also watch how slow they fall. If you can imagine dropping that hammer here on Earth, it would fall much faster. And that's because we're also seeing that the gravity is much less on the moon. So let's watch this video clip here. Here's a picture of a man and a 10-atometer drum in the ETB. I'll watch this. A good picture there. Beautiful picture, Dave. I guess one of the reasons we got here today was because of a gentleman named Galileo a long time ago who made a rather significant discovery about falling objects in gravity fields. And we thought that where would be a better place to confirm his findings on the moon. And so we thought we'd try it here for you. The feather happens to be appropriately a falcon feather for our falcon. And I'll drop the two of them here and hopefully they'll hit the ground at the same time. How about that? Mr. Galileo was correct in his findings. So hopefully what you noted there as you watch those two objects fall was not only did they fall at the same rate and that the hammer and the feather hit the ground at the same time but they also fell a lot slower because of the reduced gravitational field of the moon. So let's see what else we have here. And we want to look at a couple of definitions. We want to define a couple of things here in terms of two terms that we want to use and that we'll use at various times that are important for this. One is velocity and the other is acceleration. Now these are terms that you've heard of but we want to look at them here in a physical sense. And when we look at velocity and acceleration in a physical sense, they are vector quantities which means they not only have a magnitude, a size, so you might relate velocity to speed. Speed is how fast you are going but velocity has a direction associated with it. So your speed could be 50 miles per hour. That might be your speed but your velocity would be 50 miles per hour east. And it's very important that velocity has a specific direction associated. A velocity of 50 miles per hour east is different than a velocity of 50 miles per hour north. Yes, you're traveling at the same speed but your velocity is different. And acceleration is what happens when your velocity changes. Now we typically think of an acceleration as going faster and that is one example you can speed up. However, you can also have an acceleration when you slow down. We sometimes call this a deceleration here on Earth but in reality it is just another form of acceleration. Now one of the differences the other things that you can have is you can also have a changing direction is also an acceleration. So if you went from traveling 50 miles an hour east and turned to go 50 miles an hour north even though you went 50 miles an hour the entire time you were accelerating. Your speed wasn't changing but your direction was changing. Your changing direction can also give you an acceleration and we'll see that that means that there is a force needed here and when we look at that in terms of orbits that's what we'll understand as gravity. So let's look at what Newton, a little bit about what Newton gave us and here is Sir Isaac Newton and he gave us a number of different things. So what we're looking at here is his understanding of gravity but let's look at a few of the different things that he did. Not only did he give us universal law of gravitation and give us our first really good physical understanding of gravity that could then apply this to understand Kepler's laws so the laws that Kepler gave us for planetary motion can now be explained based on Newton's laws of gravitation. We'll also look at his three laws of motion. These are very general laws unlike Kepler's laws which applied very specifically to the planets orbiting the sun. Newton's three laws of motion apply anywhere and we know that Sir Isaac Newton also developed calculus to solve some of the problems of motion and gravity that he was working on. The mathematics was not sufficient and he needed something else to be able to solve that and he developed calculus as a way of being able to do that. So let's take a quick look at Newton's three laws of motion here and we'll start with his first law and Newton's first law of motion is what we call the law of inertia. So the law of inertia simply means and we'll state it here an object at rest or in a state of uniform motion continue in that motion unless acted upon by an outside force. What does that mean? That means that if you are moving you want to keep moving. If you are standing still you want to keep standing still and that applies to a person or any other object. An example of this could be riding in a car. When you are traveling down the road at a constant speed and you slam on your brakes the car comes to a stop but what happens to you? You end up lunging forward until something stops you whether it's the seat belt or an airbag or a steering wheel or the windshield something will eventually stop your motion. But why did you do that? Because you were moving forward you had inertia and you did not want to stop it as a property of all objects that if they are moving they want to continue in that motion. You can also look at the opposite point if you're stopped or if you're on a roller coaster perhaps one of the ones that starts and accelerates very quickly at first you feel yourself pushed back. Well, you were sitting still all of a sudden this roller coaster car starts moving forward and therefore you are pushed backward because you did not want to move until the roller coaster accelerates you up to that same speed. So that's an example of Newton's first law of motion that things at rest will remain in rest and objects in a state of uniform motion will continue unless there is an outside force acting on them. What that also means is that if an object is not at rest or in a state of uniform motion there must be a force that is acting on it. So there must be a force if it is not at rest or if it is not in a state of uniform straight line motion. So anything that is accelerating has to have a force acting on it and that can mean things speeding up, slowing down, or moving in a curve such as an orbit. So let's look at Newton's second law. Newton's second law tells us that f equals ma most concisely written as an equation here although what it also says in words if you want to write it out is that the acceleration of a body is proportional to and in the same direction as the net force acting upon it and inversely proportional to the mass of the object. What does that mean? Well it means that if you apply the same force to two objects the more massive one is going to be harder to move. That would be an example for if you have a car, a small car and it breaks down and you need to move it you can put it in neutral and one person can generally push it and move it off the road. You can get it moving and you're applying some amount of force to that it has a small mass. However if it's a fully loaded semi truck that breaks down and you want to push that with the same amount of force then what you have is you have the same force so this is the same this is larger you have a much larger mass and that means that the acceleration is going to be smaller and in fact you probably won't be able to even push with enough force to get that truck moving. With a car you'd have a much smaller mass even though you're still using the same force you're going to be able to then get a larger acceleration and get that smaller object moving whereas you could not move a larger object. So we can use this to say that if there is an acceleration if the velocity is changing and remember that velocity has a magnitude in a direction then there must be a force acting on that object. Now let's look at Newton's third law here Newton's third law tells us that for every action there is an equal and opposite reaction and for every force there is an equal and opposite force so that forces and action-reaction come in pairs. An example of this would be launching a rocket when you launch a rocket you are throwing material out in the exhaust downward and that causes the object to accelerate upward so material being pushed downward as one action and then the reaction is pushing this upward so continually doing that will launch the rocket upward into space. So those are Newton's three laws of motion that really explain how things move and they're applicable to anything moving in the universe they do not apply in just specifically talking about the orbits of the planets and they do not apply just to things here on Earth they apply everywhere. Now the other thing that Newton gave us was the universal law of gravitation let's read that out here and that says that the gravitational attraction of any two bodies is proportional to the product of their masses and inversely proportional to the square of their distance so Newton's law of gravity is shown here it depends as I said on the product of the two masses M1 and M2 you multiply those together you look at the distance between the two objects and divide it by the square of that and then there is a gravitational constant G that gives us the value of the force so for any two objects whether it be the Earth and the Moon or the Moon and the Sun you can then figure out the force between those as long as you can know the masses and the distance between them this is what we call a universal law it applies to any two objects in the universe that have mass and it is always an attractive force it is never something that is repulsive and we often put that in that the force is negative just to imply that it is always an attractive force you can never get to know two masses will ever repel each other if we look at other types of forces they can be attractive or repulsive gravitation is always an attractive force so let's look at an example here and we can look at some examples here what would happen if we were to do various things with the to change the masses now let's re-put up the Newton's gravitational it equals G M1 M2 over R squared so let's look at the first example what if we double the mass of one of the objects in that case we have we have G 2M1 M2 over R squared and the force is going to be two times greater if we double the mass of both objects we have G 2M1 2M2 over R squared and now we have that's going to be two times two is four times the increase in the force so the gravitational force will change very significantly let's clear this and look at our last two examples so if we increase the mass we increase the force if we were to decrease the mass we would have decreased the force so let's look if we triple the distance now the mass is the same so we have G M1 M2 but now we have 3R the quantity squared while 3 squared is nine so that means that the force is going to be nine times less and that is decreased because we have increased the distance between the objects and our last example here we can look at is we again G M1 M2 those don't change but now we're going to bring them four times closer together so it's now one fourth of R squared one fourth squared is one sixteenth and that's going to come to be 16 times greater we've brought the objects closer together so now it is going to be 16 times the force between them if nothing else has changed you could also change masses and radii together and get even a little bit more complicated values to try to work with so let's look at what Newton did what this did for Kepler's third law as we get towards the end here Newton was able to revise this Kepler gave us that P squared equals A cubed so the period squared is equal to the cube of the semi-major axis Newton revised this he actually gave us a slightly more complicated version of this but simplified it says that P squared equals the sum of the masses of the objects times A cubed this is very important because it allows us to determine the mass of objects if you know P and you know A you can then solve and then say that M1 plus M2 is equal to A cubed over P squared if you know the semi-major axis or the distance of the objects and you know how long it takes them to orbit you can then determine the mass of the central object this is something very important is how we can actually determine masses out there in the universe so let's finish up and summarize here and what we learned and looked at in this lesson we looked at a couple of things we looked at first of all all objects will fall at the same rate in a gravitational field the amount of mass does not matter it doesn't do that here on Earth because on Earth we have air resistance so there is a force that pushes things back up as you try to drop something light like a feather or piece of paper that does not occur on the moon Newton gave us the three laws of motion and we looked at those and he gave us the law of universal gravitation which eventually led to a modification of Kepler's third law which would allow us to determine the mass of objects in the universe so that concludes our summary of Newton and our understanding of gravity and we'll be back again next time for the next lesson so until then, have a great day everyone and I will see you in class