## Time versus Velocity

relativity is a geometric effect.

### animation

The relationship between your time and spacecraft time is simple. All you need is Pythagoras's theorem.

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

• A time interval of 1 second in your frame of reference is represented by the blue line.
• The orange line is the time interval passed on the spacecraft for 1 of your seconds.
• With a spacecraft speed of less than 0.1c the difference in the two times is very small.
• Above 0.9c a small change in velocity results in a big variation in spacecraft time.
• At 1.0c the time passed on the spacecraft is zero seconds for each of your seconds. Time has stopped on the spacecraft.

### animation controls

There are two text boxes

spacecraft elapsed time : enter a time interval 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 elapsed time in the spacecraft.

### Origin of Triangle

The triangle originates from the photon path in the time dilation animation.

The triangle in the illustration is for a spacecraft velocity of 0.866c. The same as the example triangle above.

Scale the hypotenuse to 1 and the green length is the velocity of the spacecraft. The length of the orange line is the spacecraft time interval for 1 second of your time.

### time dilation equation

Pythagoras to the rescue.