Relativistic Length Contraction

A GIF Animation

One of the peculiar aspects of Einstein's theory of special relativity is that the length of objects moving at relativistic speeds undergo a contraction along the dimension of motion. An observer at rest (relative to the moving object) would observe the moving object to be shorter in length. That is to say, that an object at rest might have be measured to be 200 feet long; yet the same object when moving at relativistic speeds relative to the observer/measurer would have a measured length which is less than 200 ft. This phenomenon is not due to actual errors in measurement or faulty observations; the object is actually contracted in length as seen from the stationary reference frame. The amount of contraction of the object is dependent upon the object's speed relative to the observer.

The animations below depict this phenomena of length contraction. In each animation a spaceship is moving past Earth at a high speed. The spaceship would be measured to be 200 feet in length when at rest relative to the observer.

 

Spaceship Moving at the 10 % the Speed of Light


 

Spaceship Moving at the 86.5 % the Speed of Light


 

Spaceship Moving at the 99 % the Speed of Light


 

Spaceship Moving at the 99.99 % the Speed of Light


Note that the length contraction is only significant when the object is moving at relativistic speeds - i.e., speeds which are a significant fraction of the speed of light. Furthermore, note that the contraction only occurs in the dimension of the object's motion. That is, if the object is moving horizontally, then it is the horizontal dimension which is contracted; there would be no contraction of the height of the object. This information is summarized in the table below.

Speed of Spaceship

Observed Length

Observed Height

At rest

200 ft

40 ft

10 % the speed of light

199 ft

40 ft

86.5 % the speed of light

100 ft

40 ft

99 % the speed of light

28 ft

40 ft

99.99 % the speed of light

3 ft

40 ft

 

More information on the physics of special relativity is being developed and will soon be available at The Physics Classroom.

Other animations can be seen at the Multimedia Physics Studios. Other useful resources regarding the physics of motion is available through the Glenbrook South Physics Home Page.

This page was created by Tom Henderson of Glenbrook South High School.

Comments and suggestions can be sent by e-mail to Tom Henderson.

This page last updated on 1/26/98.