 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about Isaac Newton and gravity and how that has then applied to orbits as we understand them. So we looked previously at Kepler and his ideas of how things can orbit and his laws of orbital motion for the planets and now we want to look at Newton and gravity and how we can understand where those laws come from. So let's go ahead and get started and we want to go back a little bit first and we want to talk about Galileo. Now we talked about Galileo and his telescope in a previous discussion, however we also know that Galileo gave us a couple of other things including the concept of inertia and the idea that all objects fall at the same rate in a gravitational field and what that means is that if you drop a hammer and a feather at the same time that they will land at the same time. Heavier objects do not fall any faster than lighter objects, in fact they fall at exactly the same rate. Now we don't notice this here on earth because we have air and air resistance will keep the feather from falling as fast as the hammer but if we do this experiment on the moon we will see that they do fall at exactly the same rate and in fact we can look at that with what was done with the Apollo mission with the and we will go ahead and watch a video of that mission and listen to what was done with the Apollo 15 mission where they did this exact experiment on the moon. Uh, Jim we copied a bow shoulder wind and a 10-eutometer drum in the ETB. And yes I will. Beautiful picture, Dave. It 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 uh where would be a better place on the moon and here for you. The feather happens to be appropriately a Falcon feather. Now what we saw there with two different things first of all we noticed that the objects fell at the exact same rate. The hammer and the feather hit the ground at the same time but you may also have noticed that they fell at a much slower rate than they would here on earth. You know how fast something like a hammer might fall when you drop it on earth and here we're able to see that it was much slower showing the lower gravitational field of the moon. So let's go ahead and take a little bit of an aside here and also introduce a couple of concepts and those are the concepts of velocity and acceleration. And what we have with those is that they're a little bit different. They're actually what we call vector quantities. A vector quantity has a magnitude, a size, and a direction. Now this means that velocity is not the same thing as speed. Speed is how fast you are going. It does not have a direction associated with it. So you could be going 50 miles per hour for example and that would be your speed. In order to make it a velocity we need a direction. So 50 miles per hour say east. And if you're that would give it a direction and that would be different than 50 miles per hour west. So those are different velocities even though the speeds are the same. Now we also look at acceleration. In acceleration we understand in everyday language as speeding up going faster. That is when you are accelerating. However in reality an acceleration occurs whenever a velocity changes. So that can be speeding up. It can also be slowing down. We often call that a deceleration. But in physics terminology it isn't an acceleration. It is just not a increasing in velocity. It is a decrease in velocity. It can also occur when directions change. So if you change direction that is also a change in velocity because you could be going from 50 miles per hour east to 50 miles per hour north. You have changed your direction and therefore accelerated even though your speed has remained exactly the same. So let's move on and talk about Sir Isaac Newton and a little bit about what he gave us. Sir Isaac Newton pictured here gave us a number of things including the calculus as a way of solving his problems of motion and gravity. He gave us three laws of motion that we will talk about shortly and the universal law of gravitation that we will be looking at. So a number of different things done by Newton and those are just a few of the things that he did but the ones we want to focus on for this class. So let's start off looking at his laws of motion and he gave us three laws of motion. His first law sometimes called the law of inertia states that an object at rest or in a state of uniform motion will continue that motion unless acted upon by an outside force. So if an object is sitting there it's going to stay sitting there. If an object is moving at a straight line at a constant speed it will continue doing that. So it also means that any object not doing these things any object that changes its motion so any object that accelerates is must have an outside force acting upon it. So a car crash could be one example of this pictured here. If the car is stopping then it is changing it is accelerating and you'll note that the person or in this case the crash dummy inside is being accelerating is still moving forward even though the car stopped. So while the car stops the person will accelerate forward. And you're familiar with this if you have to slam on your brakes you will feel yourself lunging forward. Well that's because of the law of inertia that you want to keep moving forward but the car is then going to stop you. So Newton's first law the law of inertia. We also apply this to planets. If a planet is moving in a circular orbit it is accelerating. Remember that acceleration is a change in velocity so they are accelerating as well because even if they're moving at a constant speed they are changing direction and therefore being accelerated and a force must be exerted on them. Newton's second law of motion states in two ways we can state it in an equation which is f equals ma and that means that the acceleration of a body we can also write that a little differently the acceleration is proportional to the net force acting on the body so it equals force and inversely proportional to the mass. So this is really the same equation just rewritten to solve for acceleration here but this is what Newton's law tells us that there is a relationship between the force the mass and the acceleration. So how can we see how this works? Well we look at the examples here of a person pushing a ball with what the force and then pushing a car with the same force. Well because of the math the force is the same so we have identical force here on both cases where push the ball and the car with the same amount of force. Well the masses are different so if you have a much smaller mass you are going to get a larger acceleration. If you take that constant force and divide it by a very small mass the acceleration will be larger than if you divide it by a large mass. So the ball will then accelerate and we see a one here much larger than a two but the forces are identical it is the masses that are different so the acceleration depends on the force acting on it if you push with more force you will accelerate something more but it also depends inversely on the mass the greater the mass the harder it is going to be to accelerate that object. All right let's go ahead and look at the third law then the third law sometimes called action and reaction for every action there is an equal and opposite reaction so launching a rocket is one example of this the material is expelled downward at a very high speed and the reaction then pushes the rocket up and launches it into space so it is an example of Newton's third law of motion that if one you do some push something in one direction it's going they're going to have motion in the other direction as well so it's a way of again looking at the rocket launch as one example of Newton's third law. Now the other thing we wanted to look at for Newton was his law of gravitation his universal law of gravitation states and here it is stated in words that the gravitational attraction between any two bodies is proportional to the product of their masses and inversely proportional to the square of their distance let's write that as an equation f equals and it's a negative g m1 m2 that's the product of the masses divided by the square of the distance g is the gravitational constant that is in there it has a specific value we really don't need to worry about for our class here we consider it universal because it applies to any two objects in the universe with mass so you could figure out the force of attraction between yourself and the moon all you need is the distance between you and the moon and the masses of the moon the mass of yourself and the gravitational constant and you could calculate that force the negative sign is because it is always an attractive force pulling things together you will never get a repulsive force out of gravity because everything here has to be positive we will always get a negative value here because g is positive masses cannot be negative and the radius squared the distance cannot be negative so it is always an attractive force gravity never pushes things away now we could look at a couple of examples here and we're going to look at a couple here what happens if with this equation if we do a few things so these are some of the things that are reasonable to expect i don't you don't need to do the calculations to calculate the exact force for my class but we can look at things like what happens if you double the mass of one or both objects what if you triple the distance between them or bring them four times closer together let's look at those examples briefly and what you find first of all what if we double the mass of one of the objects well all we've done is replaced m here by 2m so when we multiply everything out we get just a factor of two in front of the force and that this new force is twice the value so if we double the mass of one of the objects the force of attraction will be twice as much what if we double the mass of both objects well now we have the mass there twice 2m and 2m and two times two being four everything else is still the same we will get the force being four times as much so if we double the mass of both objects the force would be four times as great what if we look at the distance what if we triple the distance between the object so what was r becomes three r well three r squared is nine r squared is nine becomes nine and the r squared so three squared is nine r squared become is still r squared and we will get that the force will now be one ninth so we have tripled the distance they are further apart and the force is going to be one ninth as much and this is the inverse square law so it doesn't just drop off as the distance so you don't double the distance and that doesn't mean half the force it actually if you triple the distance it is one ninth the force and the same thing can happen if you increase and bring the object closer together in this case we are bringing them four times closer together so the distance is now one fourth of what it was and that is going to be one fourth squared which is one sixteenth but that's one sixteenth in the denominator which means 16 in the numerator so the force will now be 16 times the original force by bringing those two objects four times closer together so those are just a few examples of some of the things you can do with Newton's law of gravitation without actually going through detailed calculations now what does this apply for Kepler's third law remember Kepler gave us p squared equals a cubed Newton revised this in a simplified version to give us p squared times m1 plus m2 equals a cubed so m1 is the mass of one object m2 is the mass of the other object the what this means now is that we can determine the mass of a system by measuring its semi-major axis axis the average distance between the two and the orbital period of the system so if we determine those orbital period we can determine the mass we're going to find this very useful for determining masses of stars and galaxies further when we get further out into studying other parts of the universe so let's go ahead and finish up with our summary and what we've looked at we looked at a couple things we looked at the video that showed that all objects fall at the same rate regardless of mass we briefly looked at Newton's three laws of motion and looked at his universal law of gravitation and some examples and how that can be applied to a modification of Kepler's third law so that concludes this lecture on Newton and gravity we'll be back again next time for another topic in astronomy so until then have a great day everyone and i will see you in class