[BLANK_AUDIO] So, imagine we've used a giant telescope to survey the whole sky every few nights. We've used CCD detectors in order to record the light that those telescopes have collected and we've used computers in order to analyze those petabytes of data from the CCDs in order to detect objects that are moving. We've collected all that data. How are we now going to find out if those moving objects are going to crash in to planet Earth? All right, let's imagine that we've tracked an asteroid for seven days. And in that time, it's moved an angle of half a degree on the sky. Now let me draw you a quick diagram. So you get a sense of how far that it is. I am sure you have all seen the constellation of Orion. So, in those seven days our asteroid has moved roughly half way between two of the stars in Orion's belt. Another the frame of reference is half a degree is about the size of the full moon on the sky. Okay, so our asteroid has moved that far in seven days. So, how long is it going to take it to complete a full orbit around planet Earth. Well, in physics, we always start off with the simplest model, and the simplest model is to assume that the asteroid is orbiting planet Earth in a perfect circle. And I'm also going to assume that it's sufficiently far away that I can ignore the fact that the earth's going around the sun and just think that the earth and the sun are in the center of this diagram. Okay, so in seven days, it's moved half a degree on the sky. I'm exaggerating that on this diagram just for you to see it. How long is it going to take to complete a full orbit all the way around? Well, a full orbit is going to be 360 degrees. That's just how many degrees there are in a circle. So, the time that it's going to take to do a full orbit and I'm calling it capital P there because it's a time period, to complete the full orbit, that's just going to be 360 degrees times the time that it's taken to do that angle on the sky. Now, if you put in the numbers, that gives you 5,040 days, which is 14 years. Okay, so our asteroid that we've tracked is going to take 14 years to orbit the Earth, in our model that it is orbiting in a perfect circle. So, how far away is the asteroid from Planet Earth? Well, to answer that question, we are going to use some of the formula that we've used already in this course, our trusty friend speed is distance over time. Call the speed v. The distance is the distance it takes to go one full circle, so that's the circumference of the circle is 2 pi R. And the time we calculated here, call that capital P. All right, we're going to need some other formulae. Remember back to when we were thinking about the black hole. You've got that the force of gravity is keeping this asteroid going around our sun. And the force of gravity is given by GMm/R^2, G is gravitational constant, M here is the mass at the center and little m is the mass of our asteroid. And let's not forget the distance, GMm on r squared. Now, it's gravity that is keeping our asteroid in orbit. But it's experiencing centripetal force and the equation for that is mv^2/r. So, I think we have all of the ingredients that we need now, in order to be able to calculate the distance that our asteroid is away. But to do that, I'm going to need another piece of paper. So, let's equate our force of gravity with the centripetal force. And we did this equation before when we were looking at the black holes. And cancel out the mass of the asteroid. I can cancel out one of these r's. And so, I've got v squared here, the speed squared, and I'm going to put in our equation for speed. 2 pi r on P and it's all squared. Okay, so now I can rearrange this and what I will find is that I get r cubed (r^3) is GM P^2/ 4 pi^2 And I'll leave that as an exercise for you at home, to see if you can rearrange that equation to give you that result. Now, the mass of our sun is 2x10^30 kg. We've calculated the time period. So, you can now calculate the distance to our asteroid and I'll leave that as an exercise for you to do. And you can also calculate the speed. Remember, the speed is just 2pi r on P, so once you've calculated r you can calculate the speed. So, just with our simple model of a asteroid orbiting planet Earth in a perfect circle and some measurements of how fast it moved, or how far it moved in seven days. We can calculate how fast it's moving, and how far it is away. So, we're now inside a very special room in the Royal Observatory of Edinburgh. Because this room hosts our Crawford collection that contains 15,000 ancient manuscripts and books that cover maths and physics and astronomy. And the reason why I've brought you here today is because I wanted to show a first edition of Newton's Principia. Now, this book was first published in 1687 and it is Newton's derivation of the laws of gravity. Now, the page that I want to show you is going to help us improve our model of the asteroid going around the earth. Now, this page shows you a comet going around the sun, and the first thing that I want you to take away from this is that the orbit is elliptical. So, we were making an assumption that the orbit was going to be circular, but actually, most orbits in our solar system are elliptical. Now, the other thing I want you to take away from this picture is that the tails of the comet always point towards the sun. Now, I think a lot of people, when they imagine a comet, and they see the tail coming out of it. They think the tail is because of the motion of the comet. But that's not true. What happens is the sun evaporates some of the icy comet. And, it's the radiation pressure of the sun that pushes out that material to create the tail. Now, if we want to improve our model of an asteroid as it comes toward the Earth, we're going to have to add in an elliptical orbit, as you've seen here in Newton's book. We're also going to have to add in the motion of the Earth relative to the Sun, and indeed, all of the other objects in the solar system that will effect how the asteroid moves as it travels towards the Earth. Now, all of these additional complexities are going to be quite hard to put in just on pen and paper, so you do that with a computational code. Now, if you do discover a moving object with your telescope in your garden, then you can upload those positions and the time that you took those observations. You can upload that to the minor planet center, it's an online tool, and they add that data in with all of the other data that's been taken about moving objects and compute those orbits for you with that detailed computer code. And they'll also be able to tell you whether you've discovered something that's really new. Now, the final thing that I want to talk to you about today is how we would model what happens to the Earth if an asteroid did hit. And to do this, we're going to have to think about energy. Specifically, kinetic energy, which is the energy that happens if something is moving. Now, the asteroids are going to be moving towards us very fast, and so, the kinetic energy that they are going to impact into planet earth has a formula which is E =1/2 mv^2. Now, m there is the mass of the asteroid and v is the speed or the velocity that it's moving at. Now, intuitively, this formula will hopefully make some sense to you. Imagine that a ten ton truck is coming toward you, at a really, really high speed. You're going to be much worse off if that collides with you, than say, a small toddler, toddling along on a trike. Now, the detailed modelling of the orbit of the asteroidal comet will give us quite an accurate measurement of the speed or velocity with which that object is going to crash into planet Earth. But what we don't really have a good feeling for is the mass of these asteroids. And so, we're very excited because the NASA Rosetta mission is going to be landing on a comet in May this year, and we're recording this in 2014. And that's going to really tell us about the composition of these objects which will really help us find out what's going to happen to planet Earth if something like that crashes into it. So, we've told you how we can use telescopes, CCD detectors and computers in order to find potential killer rocks. I've told you a little bit about the physics of how we can then use that data to work out really whether these rocks are going to crash into planet Earth and with future technology, we're going to be able to find out exactly what's going to happen when these rocks potentially collide. Well, let's hope we don't suffer the same fate as the dinosaurs.
