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How did the distance of the light year get calculated?

Lesson 1: Relativity - What is it?

  1. Fermilab's Time Dilation Challenge.
  2. The Basics of Relativity (6 seconds)
  3. The Relativity Game - Challenge what you know!

Note: For Fermilab's Time Dilation Challenge and The Relativity Game, you need Shockwave. You may painlessly Download Shockwave here if you do not have it.

Lesson 2: Time Dilation

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the basketball analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Lesson 3 : Relativistic Mass

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the space pool analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Lesson 4 : Length Contraction

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the pole and the barn analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Since distance is equal to speed multiplied by time (I want to review that), we can make some simple conclusions about how far the ship travels as it travels from earth to Alpha Centuri:

We know the speed of light and we know from the reference frame of the earth, light takes about 4 years to travel the distance. Since there are 31,557,600 seconds in one year (I want to see that calculation), according to the earth's reference frame, Alpha Centuri is:

Therefore, if we see the space ship travel at 50% c, according to us, it should take the space ship 8 years to get to Alpha Centuri.

Link below to its own page.

This would be different for the mover in the space ship, because the mover would measure a different time predicted by the time dilation equation.Would this time measured for the mover by the mover be more than, less than or the same as the time measured for the mover by the stationary frame?

In fact the time would be about 6.9 years. So according to the mover, the distance traveled was only 3.46 light years (I want to see that calculation), not 4 light years as was registered by the stationary frame. Therefore, space has been contracted for the mover.

In general, distance is calculated by knowing time and velocity.

d = vt

Here we will refer to the distance measured for the mover by the stationary frame as length, lo.

Consider a 3 x 108 meter stick traveling past us at half the speed of light (50% c). We want to measure the length of this stick in the mover's frame of reference and the stationary frame of reference.

To accomplish this, we will time how long it takes the 3.0 x 108 meter stick to pass a set point in space.

According to the mover for the mover, the meter stick is 3 x 108 metes long. Since it is traveling at 50% c, the mover measures a time of 2.0 seconds (I want to see that calculation) to pass by the time both ends of the meter stick pass the point in space.

See animation. (add animation and link)

According to the stationary frame, the mover's stick takes a longer time to pass the point. Instead of 2 seconds, the stick, traveling at 50% c, takes 2.3094 seconds to pass the point in space.

Since the mover was moving at 50% c, and the stationary frame timed the stick to take 2.3094 seconds to pass the point in space, the stationary frame calculates the stick's length to be 3.5 x 108 meters.

Here, we need to make some distinctions. The stick is 3.0 x 108 meters in the frame that sees it at rest, its own. In the frame that sees it moving, it is longer!

The above is wrong! Check out how to say it correclty and break this page up into parts b, c, and d for lesson 3. Also remember to consider calling this Level 3 and remember the game is a game of hunting for a ship headed toward different stars with a convict...you are a bounty hunter and you must arrive before convict to collect your bounty.

Also remember to set of a table of contents for this site.

 

 


© Brian Wegley, 1998
Comments and suggestions can be sent by e-mail to
Brian Wegley of Glenbrook South High School..
This page last updated on 7/23/98.