# Movement in Three Dimensions

Part of the Astronomers' Universe book series (ASTRONOM)

On the Earth we usually only move in two directions, forwards and backwards or left and right. These directions are known as degrees of freedom. Unless we have access to some form of aircraft, we have a limited third degree of freedom, the ability to move up and down. In space, everything has six degrees of freedom. There are the three degrees of freedom in a straight line, left, right, up, down, forwards and backwards, but things can also rotate or spin. One end of a spacecraft can rotate up or down with respect to the other end, this is known as pitch and can cause the spacecraft to spin like a cartwheel. The spacecraft can also rotate along its long axis like a rolling pin, which is known as roll, or around its vertical axis like a merry-go-round, known as yaw. These degrees of freedom are shown in Figure 4.1. On the Earth, even in a vehicle, these degrees of freedom are usually restricted, such as by the wheels only turning on one axis and by gravity keeping the wheels in contact with the ground.

Moving around on the Earth is relatively simple. In a car, for example, to change the speed you either accelerate or brake, and to change direction you turn the steering wheel. You are normally in complete control of where the car goes by using the friction between the tyres and the ground. If you are travelling on ice, however, and make a sharp turn, the car is likely to carry on in its original direction. Travelling in space is like being in a three-dimensional ice rink. Even if the direction the spacecraft is pointing, called its attitude, is changed, it will still carry on following the path it was on. Over short distances, this appears to be a straight line, but over a longer time, the path curves as it is pulled by gravity towards the Earth, Moon, Sun and planets. On the Earth the effect of gravity is usually ignored as it keeps us on the ground, although we do notice it when we climb a hill or if we fall over. In space, however, the force of gravity changes with the distance away from the body the spacecraft is orbiting and must be taken into account.

## Keywords

Circular Orbit International Space Station Elliptical Orbit Geostationary Orbit Lagrangian Point