We know that Earth’s gravity is attracting the Moon, but why doesn’t the Moon fall down on Earth. Even worse, why does it keep moving from Earth almost 4 centimetres each year?
Newton pondered this question when he formed his laws of motion. Just as he did, imagine standing on a cliff and having a canon and a few cannonballs. If you took one cannonball into your hands and dropped it from the cliff, it would fall straight down to the ground. Earth’s gravity would pull it. Keep in mind that only force affecting this cannonball is gravity.
Now, imagine putting the second cannonball in the cannon and firing it from the cliff. This cannonball has two forces influencing it - gravity and momentum it gained when it got fired by the cannon. It will travel horizontally at first, but as it loses momentum, gravity takes over and sooner or later it falls down to the ground. It loses momentum partially because the momentum wasn’t big enough to start with and gravity takes over and partially because of the friction between it and the atmosphere, but we’ll ignore this third force in this example. Cannonball’s trajectory is a parabola and by the time it touches ground, vertical distance it has traveled is greater than that of the first cannonball.
Reason for this is curvature of the Earth. If your second cannonball traveled 1 kilometre horizontally, by the time it hit the ground, Earth was another 12.6 centimetres farther down compared to the cliff you’re standing on. This extended the second cannonball’s path by just a bit.
The more momentum a body has, the less influence gravity exerts on it. So, if you had a more powerful cannon, you could theoretically fire the third cannonball with so much momentum, it never touches the ground. This is called an orbit. The cannonball is losing momentum at such rate that it falls 12.6 cm for every km, but by that point, Earth’s curvature made sure the ground is exactly 12.6 cm farther down and the cannonball keeps orbiting the planet forever because gravity and its momentum are at balance, so it never falls down at stays at the same distance from the surface.
Take even more powerful cannon, put the fourth cannonball in it and fire it from the cliff, it will have so much momentum that it will break Earth’s orbit and not only never fall down on the ground, but leave Earth altogether. Speed needed for this is over 10 km/s at Earth’s surface and it is called escape velocity. At this speed, gravity is not strong enough to ever pull the cannonball down to the ground. This is what is happening with the Moon. It is escaping Earth’s gravity!
The Moon has orbital speed of 1022 m/s, ten times less than escape velocity at Earth’s surface, but it is over 400,000 km away from Earth, so it needs smaller escape velocity. This implies that the Moon was much closer to Earth in the past, which you can read about in another post.