 So, we now know that Newton's Law of Universal Gravitation takes the form f equals g multiplied by m1, m2, divided by r squared, but you've previously probably learnt about gravity on Earth as being equal to f equals mg. Well, don't worry, because this equation is actually an approximation of Newton's Law of Universal Gravitation on Earth. While you can derive the equation for gravity on Earth from Newton's Law of Universal Gravitation, and indeed we will do this later in the course, this gravity on Earth equation can, like many things in physics, also be determined through observation by measuring how things fall on Earth. So, we'll explore this simpler equation to understand a variety of situations on Earth. Let's unpack the equation f equals mg for gravity on the Earth. Just note here that when we talk about gravity in physics, we're actually talking about gravitational forces on objects. You may remember that when we look at forces on objects, we're interested in three defining characteristics, the forces' strength and direction, which together make up the vector quantity of a force, and finally, where the force actually interacts with an object. We typically get around this last point by modelling many objects and problems as point objects located at the object's centre of mass, and then the forces simply apply to this point. It's the point where all the mass is balanced, so for something with uniform density, like a bar of gold, the centre of mass is in the exact middle of the object. However, for something like a light bulb, the centre of mass will be closer to the bottom of the light bulb, because there's more mass at the base than at the top. So we now have the point at which the force is applied, but where is the direction? While the direction in which gravity is exerted on an object near Earth is pretty clear if you drop any object, it points vertically downwards. There is no horizontal component to gravity as it doesn't push things sideways, it just pulls them down towards the centre of the Earth. So any object at the Earth's surface experiences a gravitational force downwards. But what is the magnitude of the force? The magnitude of the gravitational force near the Earth's surface is given by our equation, F equals mg, where F is the gravitational force, m is the mass of the object, and g is called the acceleration due to gravity. In this equation, we need to note that the force is the force due to gravity only, so if there are many forces acting on an object, it can be especially useful to place the g subscript referring to gravity on our force parameter. Interestingly, no matter the mass of the object, all objects on the Earth's surface will experience the same acceleration due to gravity. We know from Newton's second law, which is that the force on an object is equal to mass times acceleration, or F equals ma, that in our equation for the force due to gravity, our g is equal to our acceleration. This g is often known as little g by physicists to distinguish it from big g, which is the universal constant of gravitation that occurs in Newton's law of universal gravitation. Importantly, this little g tells us that an object's acceleration does not depend on mass. This contrasts with most physical situations where we would typically expect that greater forces are required in order to have the same effect on acceleration of a larger mass. For example, if you tried to pull a piece of iron with a magnet or push an object across a table, it would be more difficult to do with a heavier object. The reason you don't see the same effect with gravity is that while heavy objects are pulled more strongly by the Earth, they also require a bigger push to cause them to accelerate. Finally, we'll look at little g, which we know is the acceleration due to gravity near the Earth's surface. Now little g has a constant value being 9.8 meters per second squared. Later in the course, we'll look at exactly how well this value fits with Newton's law of universal gravitation. As we saw with mass before, the mass of objects doesn't affect the acceleration due to gravity. So if you drop a chocolate bar and a gold bar at the same time from the same height, they'll accelerate at the same rate and fall next to each other at the exact same moment, even though the objects experience different gravitational forces. In this video, we've discussed the force due to gravity on Earth, where it's applied, in what direction it acts, and what its magnitude is. Now, we'll look at some examples.