### special relativity

## Length versus Velocity

*length contraction is real*

### animation

The relationship between your velocity and length is simple. All you need is Pythagoras's theorem.

There are two lengths to consider. The length of something on the spacecraft. In this example we will consider a ruler on the spacecraft of unit length that lies in the direct of travel. The length of the ruler when stationary is called the *proper length*. The other length is the length of the ruler as measured by an observer for which the spacecraft is moving.

The following are a list of points to be mindful of when studying the animation.

- The proper length is the length of a ruler when stationary.
- The orange line is the length of a moving ruler laid in the direction of motion. Called the observed length.
- Note the similarity with the time velocity plot.
- With a spacecraft speed of less than 0.1c the difference in the two lengths is very small.
- Above 0.9c a small change in velocity results in a big variation in observed length.
- At 1.0c the observed length is 0.

### animation controls

There are two text boxes

observed length : enter a length less than, or equal, to 1.0. The graph will update to show the corresponding spacecraft velocity.

velocity : enter a spacecraft velocity as a fraction of c. The graph will update to show the observed length of the proper length.