 Okay, this is the test problem that I gave in class. And I've already set up part of the thing just to save some time. So here I have a spacecraft going near an asteroid, okay? So they give this distance is 1200 kilometers, they give the speed of the satellite, and they give the volume, oh I raised part of it, oh I didn't, I squared. The volume of the asteroid and the mass, well they give the density, so I calculate the mass, I don't want to spend time on that. Okay, so then they say estimate the change in momentum. Well first of all, let's just sketch the trajectory, you know this thing is clearly as it comes by it's going to do something like that, right? It's going to get bent towards the asteroid, the asteroid won't move as much because they have the same force on it but it's very massive, okay? So let's estimate that, you know this is an estimate problem and you're going to have to pick some things here. And I know you feel uncomfortable doing that, I know, but you have to do that, okay? And so there's not just one right answer here, there's a right method, but you could do it a lot of different ways. So what I did was I said okay, the spacecraft's going pretty fast. So there's going to, and the, when it's really far away from the asteroid it's not going to be interacting with it very much, only when it's close will be, and the strongest interaction will be when it's within this 1200 kilometers, okay? So if I knew this, I could say f net equals delta P over delta T, can I calculate the net force? Well, I can calculate it right there, it's going to actually change over here but not too much. Can I calculate delta T? I can, well I can get an estimate for it and that's what I'm going to do. So I'm going to say delta P equals f net delta T. And so for the net force I'm going to use the gravitational force right there, okay? Which is not correct, but it's good enough because it's not going to change that much over this whole time. And then for the time I'm going to assume it's going at a constant velocity across this. I'm going to pick, if it's 1200 kilometers far from it, I'm going to pick a distance of 1200 kilometers just randomly mostly, okay? Just so I can say, okay that's the time over which it's going to act. You could pick a shorter interval and that'd be acceptable too. Really we're just getting a rough estimation here and then if we want to do it better we'd do it in a different way. So let's first find this delta T. So if I say the average, the speed is 10 to the fourth meters per second, it's going to be delta S over delta T. And if delta S is 1.2 or 1200 kilometers, so I can solve for delta T, delta T is going to be equal to delta S, 1200 times 10 to the third meters over 10 to the fourth meters per second, so that's going to be 120 seconds. So now I have my time, okay? Now for the gravitational force, let's just calculate this as the gravitational force right here. It's going to be FG equals G mass of the spacecraft mass of the asteroid I'll call Matilda over R squared and then it's going to be in this case 0, negative 1, 0, right? Because it's going in the negative x direction but that's not too important here. Okay, so I have everything I need right there. So I can just say 6.67 times 10 to the negative 11th Newton's meter squared, I'm sorry, kilogram squared meter squared, that's G. The mass of the spacecraft is 805, I gave that. The mass of Matilda I just calculated before is 8.75 times 10 to the 17th kilograms. And then R is going to be 1.2 times 10 to the third, fourth, sixth meters squared, okay? And then that's the magnitude, I'll write it as FG because it asked for, estimate the change momentum, okay? So it doesn't say not as a magnitude, so I'll give it the real way, okay? Let's see, let me put this in my calculator, 6.67 times 10 to the negative 11th times 805 times 8.75 times 10 to the 17th divided by 1.2 times 10 to the sixth quantity squared and I get 0.033 Newton's. Now go ahead and leave that, 0 negative 1, 0, that makes it a vector, okay? So I don't have to do that. So now delta P is just going to be this times delta T, delta T is 120, I should be able to do that in my head but you know we're in a hurry, you just can't do these things, 3, 3, so I get 3.96, so delta P is going to be 0 negative 3.96, 0 kilogram meters per second. So that's my change momentum as it passes by here, okay? So and just look at the initial momentum, the initial magnitude momentum is 8 times 10 to the sixth kilogram meters per second and the change is a small amount here. So this assumption is okay, right? Because it's not going down that much compared to the way it was going before, so I'm probably okay. So it's a small change momentum but really this is important because if we know, if we can actually measure the change momentum of the spacecraft, one of the things that can do is give us an estimate for the mass of the asteroid. So, okay.