 Now, instead of sheep, let's think about a mass, a lonely, solitary mass sitting in empty space. How would this mass want to move? Well, we know from Newton's first law that if there's nothing else to apply any forces, the mass will never change its velocity, and if it wasn't moving to start with, it'll sit there forever. What would we expect to happen if a second mass appeared? Newton's law of universal gravitation predicts that there would be a force between these two masses, so mass one would want to accelerate towards mass two. And what would happen if we moved mass one up above mass two? Well, this time mass one would want to accelerate downwards, and if we place mass one closer to mass two, it would feel a stronger pull, and if we put it much further away, it would feel a much weaker pull. Just like with the sheep and the hay, we can draw out a vector field showing how much mass one wants to move. But there's one small issue. If we just use Newton's law of universal gravitation to get the gravitational force at every point, it will depend on the mass of mass one and mass two. But the field we've drawn represents the attraction towards mass two. Surely we could quantify how intrinsically attractive mass two is without needing mass one, just like we can consider the size of the hay bale without needing to worry about how hungry the sheep are as well. So how can we control for the mass of mass one? Well, if we divide the force experienced by the mass of mass one, we get the acceleration that mass one would experience. And as you can see, the acceleration that mass one experiences only depends on the mass of mass two. Mass one could be anything, and it would still accelerate the same amount towards mass two. We call this field describing how objects would accelerate the gravitational field of the source object, in this case mass two. This is another equivalent way of looking at gravity. Instead of gravity being a force between objects with mass, every object with mass generates a field, and that field applies a force to any other masses in the field. As we guessed out earlier, the field generated by a mass with mass m comes directly from Newton's law of universal gravitation. The gravitational field strength is equal to the universal constant of gravitation multiplied by the mass divided by the distance from the center of that mass squared. For multiple objects, we can vector sum the field from each object individually, and we end up with the total acceleration that an object would experience at any point. Alternatively, you could imagine flying around in a spaceship and measuring the acceleration at every point in space without any knowledge of the size or position of the masses generating the field. Fields are very useful when you have lots of masses and you want to visualize how another object would react to all these masses. They're also very useful when you have a small object, such as a spaceship or a satellite, which is small enough that it has a very small impact on the other objects. When this is the case, we can treat the field like it's static, so we don't have to worry about the sun moving due to a satellite because the sun is so much bigger than this satellite. In this way, we can look at how a small object moves and interacts within a field.