Time dilation and interstellar travel

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SUMMARY

The discussion focuses on calculating the minimum speed required for a spacecraft traveling to a star 10 light-years away, considering time dilation effects. The correct speed for the spacecraft to ensure the crew survives the trip, given a one-year life support system, is determined to be approximately 0.707c, while the erroneous reference from the textbook states 0.99c. The second part of the problem, which involves time dilation, reveals that the speed should be 10c, but this was corrected to reflect the one-year time frame rather than ten years. The participant confirms that their method of using the time dilation equation was valid.

PREREQUISITES
  • Understanding of time dilation in special relativity
  • Familiarity with the time dilation equation
  • Basic knowledge of relativistic speeds (e.g., c as the speed of light)
  • Ability to manipulate equations involving length contraction and relativistic time
NEXT STEPS
  • Study the time dilation equation in detail
  • Learn about relativistic velocity addition
  • Explore the implications of traveling at speeds close to the speed of light
  • Investigate practical applications of time dilation in modern physics
USEFUL FOR

Students of physics, particularly those studying special relativity, aerospace engineers, and anyone interested in the theoretical aspects of interstellar travel and time dilation effects.

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Homework Statement


Plans are made to send a spaceship from Earth to a nearby star 10 light-years away and at rest with respect to Earth. The light support systems within the spacecraft will last for a year. (a) what is the minimum speed of the spacecraft relative to the Earth-star system if the crew is to survive the trip? (b) If time we mot dilated, what minimum speed would be necessary for the trip?

Homework Equations


the time dilation equation

The Attempt at a Solution


a)From an observer on Earth, the velocity of the ship is the rest length (10 ly) divided by the relativistic time corresponding to the 10 years of life support.
v=L0/\gammaT

v=10 ly/\gamma10y

Solving, I get v=0.707c

The back of the book (which has had two mistakes this chapter) says v=0.99c for part a.

Is my initial equation in error?

b) It looks to me like the answer is v=10 ly/y=c. The book's answer is 10c.
 
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Never mind: it was a stupid mistake. I transcribed the problem correctly, but I got into my head that the rest time was 10 years, not the given 1 year.

It is good to know my method worked. It was kind of cool to need to substitute a rest length and a relativistic time into a classical equation.
 

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