How do orbits work?

We might take it for granted, but why do stars, moons, planets or any celestial bodies constantly move around one another?

 What an Orbit Really Is

The drawings at the right simplify the physics of orbiting Earth. We see Earth with a huge, tall mountain rising from it. The mountain, as Isaac Newton first envisioned, has a cannon at the top. When the cannon is fired, the cannonball follows its ballistic arc, falling as a result of Earth's gravity, and it hits Earth some distance away from the mountain. If we put more gunpowder in the cannon, the next time it's fired, the cannonball goes halfway around the planet before it hits the ground. With still more gunpowder, the cannonball goes so far that it never touches down at all. It falls completely around Earth. It has achieved orbit.
If you were riding along with the cannonball, you would feel as if you were falling. The condition is called free fall. You'd find yourself falling at the same rate as the cannonball, which would appear to be floating there (falling) beside you. You'd never hit the ground. Notice that the cannonball has not escaped Earth's gravity, which is very much present -- it is causing the mass to fall. It just happens to be balanced out by the speed provided by the cannon.   

How do orbits work?

Although we don’t encounter orbits day to day, it’s common knowledge that in space, satellites, asteroids, moons, planets and even stars move around other celestial bodies in a seemingly perpetual dance. With the right conditions, anything will fall into orbit around Earth. But what are those conditions?

A terrestrial orbit is actually a freefall along the curve of the Earth’s gravity that never touches down. The basic physics is the same for any planet or star, no matter its size. For an Earth-like planet, if an object is at the right altitude so that the thinner atmosphere doesn’t drag too much – around 160 kilometres (99 miles) up – and the acceleration is enough – about 28,080 kilometres (17,450 miles) per hour – it will continue to tumble around the planet.

To put a satellite or shuttle into a circular ‘high’ orbit, the craft makes use of boosters to go from low orbit into a transfer orbit to achieve the required height, technically known as its apogee. Left to its own devices, the spacecraft would fall into an elliptical orbit, so an additional rocket motor called an ‘apogee kick’ (AKM) fires at the appropriate point. This gives the vessel the extra boost it needs to remain at that specific altitude in a high orbit.