You wish to make a trip to Remulac, which is 30 light years away from Earth. If
ID: 1518474 • Letter: Y
Question
You wish to make a trip to Remulac, which is 30 light years away from Earth. If your ship can quickly accelerate to O.999c, how long will it take you to get there according to your friends back on Earth, and how long does it take according to your clock? 9. ANS: According to the Earthlings, the time it takes is just 30 ly /0.999 30.03 years. (Just a bit more than light would take, so that makes sense.) The value of gamma is = 1/sqrt(1-0 999)- 22.4. So, according to Earthlings, your clock will run slow by this factor and so only 30.03 yr/22.3 = 1.34 years should pass. You will agree, because y shrink by that same factor to 30 ly/22.3 = 1.35 ly ou will see the Earth to Remulac distanceExplanation / Answer
Here, value of gamma = 1/sqrt(1 - v2/c2)
=> where, v = speed of ship
=> In the theory of relativity, time dilation is a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from a gravitational mass or masses.
=> A clock in a moving frame will be seen to be running slow, or "dilated" according to the Lorentz transformation. The time will always be shortest as measured in its rest frame. The time measured in the frame in which the clock is at rest is called the "proper time".
=> value of gamma = 1/sqrt(1 - 0.999c2/c2)
= 22.4
=> clock will run slower by 22.4 times .
=> according to Eartlings time measured = Distance/speed
= (30 ly/0.999)
= 30.03 years
=> according to your clock time measured = (30 ly/0.999) * (1/22.4)
= 1.3406 years
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