Hyper asked in Science & MathematicsPhysics · 5 months ago

Physics Problem - Time Dilation?

You leave on a mission to a distant star. Your craft accelerates at a 0.65 g for 30 days. From your point of view, you spend the next 1000 days moving at this speed.

What is the difference between the period of this steady travel from your point of view and from the point of view of an earth observer?

I need to know how to SOLVE this. DO NOT GIVE ME THE ANSWER, PLEASE GIVE ME A FORMULA!! I know there are many professors out there who scold people who want answers, so what I want is to know how to solve this. THANK YOU.

Update:

Also, the problem does not state 0.65 c, the problem states 0.65 "g". I don't know if it's talking about gravity, or some other variable I have yet to learn about.

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  • 5 months ago
    Best answer

    v = v₀ + at

    t = 30 day x 24 hr/day x 3600 sec/hr = 2592000 s

    0.65g = 0.65 x 9.8 m/s² = 6.37 m/s²

    v = at = 6.37 x 2592000 = 1.65e7 m/s, which is relativistic, but I think (?) that the equation is still valid, just that as mass increases, the force needed to maintain that acceleration increases.

    time dilation

    t' = t/γ

    γ = 1/√(1–(V²/c²))

    γ = 1/√(1–(1.65e7/3e8)²) = 1.0015

    time slows down for the traveler

    so the 1000 days is seen to an external observer as 1000 x 1.0015 = 1001.5 days

  • 5 months ago

    I think the wording is in error--the 0.65g should read 0.65c.

    • sojsail
      Lv 7
      5 months agoReport

      0.65g makes sense. That would be acceleration - as it says.

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