Relativity: Spaceship travel times and distances

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SUMMARY

The discussion focuses on calculating the travel time and distance for a spaceship traveling to a star 95 light-years away at a speed of 0.96c. The calculations yield a time of 99 years from Earth's perspective, while the spaceship's perspective shows a contracted travel time of 27.7 years. The equations used include t = L/v for time calculation and Lr = L * sqrt(1 - v^2/c^2) for length contraction. The participants clarify the application of these equations to ensure accurate results in relativistic physics.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation and length contraction.
  • Familiarity with the formula t = L/v for calculating time based on distance and speed.
  • Knowledge of the Lorentz factor, represented as Lr = L * sqrt(1 - v^2/c^2).
  • Basic comprehension of the speed of light as a constant (c) in physics.
NEXT STEPS
  • Study the implications of time dilation in special relativity using various speeds approaching the speed of light.
  • Explore the concept of the Lorentz factor in greater detail and its applications in different scenarios.
  • Investigate the effects of relativistic speeds on mass and energy as described by Einstein's theory.
  • Learn about practical applications of special relativity in modern physics, such as GPS technology and particle accelerators.
USEFUL FOR

Students of physics, educators teaching special relativity, and anyone interested in the implications of high-speed travel in the context of astrophysics.

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Homework Statement


A star is 95.0 year lights away from Earth. How much time does it take to a cosmic ship, which moves with speed 0.96 c, to reach the star, if it is measured from a watcher from a) Earth a)ship c)What si the distance of trip, based on the viewer from the ship?

Homework Equations


t=L/v
Lr=L*sqrt(1-v^2/c^2)

The Attempt at a Solution


a) t=L/v=99 years
c) Lr=L*sqrt(1-v^2/c^2)=26.6 years
b) tr=Lr/v=27.7 years.
I'm not sure if for this I should use tr=t/sqrt(1-v^2/c^2). Which one is the best to use because the results are different. But if I use tr=t*sqrt(1-v^2/c^2) it has the exact same result. If 27.7 years is the correct answer, then why should the length contract and time not dilate?
 
Last edited:
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Is your problem description complete ?
In part a) , what do you use for L and what do you use for v to get 99 y ?
 
BvU said:
Is your problem description complete ?
In part a) , what do you use for L and what do you use for v to get 99 y ?
I had forgotten to put the speed. it is 0.96 c
 

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