Understanding Time Dilation: How Do Clocks Differ in Space Travel?

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SUMMARY

The discussion centers on the concept of time dilation as it pertains to a rocketship traveling at 0.800c relative to Earth. Observers on the rocketship and Earth agree on the initial time of 3 pm, but due to relativistic effects, the time experienced on the rocketship differs from that on Earth. Specifically, when the rocketship clock reads 3:40 pm, calculations reveal the corresponding Earth time and the distance from Earth to a space station. The problem illustrates the practical implications of Einstein's theory of relativity in a space travel context.

PREREQUISITES
  • Understanding of Einstein's theory of relativity
  • Familiarity with the concept of time dilation
  • Basic knowledge of Lorentz transformations
  • Ability to perform calculations involving relativistic speeds
NEXT STEPS
  • Study Lorentz transformations in detail
  • Learn how to calculate time dilation using the formula Δt' = Δt / √(1 - v²/c²)
  • Explore the implications of time dilation in GPS technology
  • Investigate real-world applications of relativistic physics in space travel
USEFUL FOR

Students of physics, educators teaching relativity, and anyone interested in the effects of high-speed travel on time perception.

DespicableMe
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Homework Statement




At 3 pm a rocketship passes extremely close to the Earth with a speed of 0.800 c. Observers on the ship and on Earth agree that it is 3 pm. At 3:40 pm, as indicated on the rocketship clock, the ship passes a small space station that is fixed relative to the Earth and whose clocks read Earth time.

a) What time is it on the station clocks when the ship passes?
b) How far from Earth (in Earth coordinates) is the station?
c) At 3:40 pm rocketship time, the ship reports by radio back to earth.
When (by Earth time) does the Earth receive the signal?

I'm confused on time dilation. I've read the section several times but I'm still a little puzzled. At the concept and at this problem.

I'm not sure where to start. :confused:
 
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Hi DespicableMe! Welcome to PF! :smile:

Call the rocketship's measurements x and t, and the Earth measurements x' and t'.

You know that, for the rocketship, both the Earth and the space station are moving with speed v = 0.800c, and that they go past the rocketship at positions x = 0 and t = 0 and 240 (I'm measuring t in seconds, starting at 3:00pm :wink:).

(And the answers you need are all in x' and t')

Carry on from there. :smile:​
 

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