 Now we'll discuss gravity near the Earth's surface. So far, most of the examples we've looked at have involved gravity in space, with big masses generating strong gravitational fields. The strength of these fields depends on the distance between the two bodies, with acceleration due to gravity equal to big G times the mass divided by the distance between the objects squared, and the fields point radially inwards towards the mass. However, the gravity we interact with every day doesn't seem to be changing direction. As I move around, gravity keeps pointing downward, and it doesn't seem to have any dependence on distance either. And Apple seems to weigh just as much on the ground as it does when I step onto a table. In fact, last year you were explicitly taught that the force due to gravity is f equals mg, where g is constant and points downward. So how do we square that with Newton's law of universal gravitation? Let's look at our specific situation on Earth. The Earth is big, really, really big, and we're small. Let's say you were standing on the ground, and the ground was exactly 6,400 km from the centre of the Earth. How much would the strength of the gravitational field change one metre above the ground? Let's calculate this. Well, on the ground we can find the strength of the field using the gravitational field strength equation, with the distance being 6,400 km. If we plug in these numbers, we get an answer of 9.770508 metre per second squared, being the acceleration due to gravity. If we now use a distance of 6,401 km from the centre of the Earth, and we plug in our values, we get an acceleration due to gravity of 9.7705 metres per second squared. So the difference in gravitational field strength when you move 1 metre above the ground is 3 times 10 to the minus 6 metres per second squared, or 3 millionths of a metre per second squared. As you can see, this is a very small difference. So for most purposes, we can treat the strength of the gravitational field like it's constant for problems on the surface of the Earth. But what about the direction? Well, we know that the gravitational field points radially towards the centre of the Earth, and therefore perpendicular to the surface of the Earth, which is, roughly speaking, a sphere. Since the Earth looks flat for physics problems on the surface of the Earth and the field points perpendicular to the ground, the field looks like it points straight downward. So there you have it. We can treat the strength of the gravitational field near the surface of the Earth as a constant of 9.8 metres per second squared, pointing directly downwards. This is the constant value you should use to solve problems, unless you're specifically asked for more accuracy.