Relativity of Length

Imagine that your spaceship is lying on a truck bed, waiting to be hoisted into position on the launch pad. You and some friends measure its length while it’s lying motionless (which is called its rest length, L0), and you find that it’s 10 meters long.

But then you fly off to the party at 86.6 percent of the speed of light, or 0.866c. Your friends, who’ve been following your progress with telescopes, decide to try to measure your ship while it’s in flight. They find that its length, L, is shorter than its rest length. It turns out that it’s shorter by a factor you can calculate if you know the speed v of the ship. This factor is known as gamma (): 

                 

If you do the calculation, you’ll find that when v = 0.866c, = 2 .

Once you know the value of gamma, you can solve the equation for length contraction, L = L0/.

                  L = 10 m/2

                  L = 5 m

To your friends on Earth, then, your ship appears to be half its rest length, or 5 meters long.

Try This!

Enter two values into the calculator—a fraction of the speed of light (from 0 to 0.999 999 999) and the rest length of an object of your choice. You’ll find out what fraction of its rest length the object would be at that speed.

Speed
(1 = speed of light
= 299792 km/sec)

 
Rest Length
meters  

 

Moving Length
meters  

 


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