And so we're going to be looking at gravitational potential energy as it relates to great distances. Now near the Earth, gravitational potential energy was relatively easy to figure out. It was just M times G times 8. And so if I were to look at my skater as I pick him up, his gravitational potential energy would increase, as you can see. And it would change into kinetic energy depending on his position. Now I can also do things like I can move this reference line, for example. And I can see his potential energy here is shown as being negative, up until I get him up to the reference line. And then when I drop him, potential energy declines. And I consider it negative just because I've chosen that as a reference line. But what happens when something is coming from a long way from the Earth? So for example, an asteroid or a rocket is approaching the Earth. How do we consider that gravitational potential energy? Because the force of gravity can no longer be considered to be just 9.8 times the mass. And that has to do with the inverse squared nature of the relationship, predicting the force between two bodies relative to the Earth. And so as I can see, force declines as these things get further and further apart or as they get closer together, force increases and rather dramatically. So that has implications about how gravitational potential energy works when you're not near the Earth's surface. Now it's a little bit beyond the scope of the course, but I'll include a link. Here's the formula for calculating gravitational potential energy between two bodies based on their mass. And there's separation. And as you can see, it doesn't look a whole lot different than Newton's law of universal gravitation. We use you to represent the gravitational potential energy. And you'll notice the nature of the curve is like any negative inverse relationship. Now we consider potential energy to be zero at infinity. And so any object, for example, an asteroid would have zero potential energy. And it would just continuously lose that potential energy as it gets closer and closer to Earth. That potential energy is going to get transformed into kinetic energy. And it's going to be moving faster and faster and faster as it gets close to the Earth. As you can see, initially it's not losing a lot of energy when it's a great distance away. And of course, that's because the force is much, much less. But the closer it gets Earth, the more potential energy it loses. And of course, it's going to be accelerating at that point. And we're going to see a lot of kinetic energy get produced as it gets closer and closer to the Earth. You'll notice as well that this is all considered relative to the center of the Earth. And so nothing is ever going to get closer than what the radius of the Earth is. So this line is demonstrating that you're not ever going to get closer than the radius of the Earth when you're dealing with this equation. So just a quick reiteration for reference potential energy is given by that equation. You'll notice that there's a negative in front of it. And the zero reference is set at infinity. And so something starts with zero potential energy and just loses it from there. Now we're also interested in what we're going to do. Now we're also interested in what happens with rockets, not things coming towards the Earth, but things leaving the Earth. As they take off from the Earth, we give them a lot of kinetic energy. And of course, they have a bit of potential energy because they're not sitting at the center. And what happens is time for grip is they gain potential energy as they lose kinetic energy. And so as you can see, this rocket starts off fast, lots of kinetic energy. And it's going to be slowing down unless, of course, it's applying thrust all that way. So kinetic energy gets converted into potential energy. And so looking at our conservation of energy equation, potential energy plus the kinetic energy when the rocket's just sitting near the Earth or on the surface of the Earth is equal to the potential energy when the rocket ultimately reaches its maximum separation from the Earth. Now we talk about escape velocity. And escape velocity is the point at which that rocket can ultimately make it to infinity. In other words, completely leave the Earth's gravitational field. In which case, potential energy plus kinetic energy at the surface of the Earth has to add up to that potential energy when it gets at infinity. And then the rocket's potential energy plus kinetic energy has to be equal to zero in that rocket makes it all the way out to infinity.