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Gravitational Time Dilation Problem

  1. Feb 3, 2016 #1
    1. The problem statement, all variables and given/known data

    A person lived 75 years in a city located 3.1km above sea level. How much longer could they have lived at sea level? (Times are measured by an observer at infinite distance).

    2. Relevant equations

    tr/t∞ = {1 - [ (2GM) / (r(c^2)) ]}^(1/2)

    Rc (Radius at city) = Rearth + 3.1km

    ∴ t(sea-level)/t∞ = {1 - [ (2GMe) / (Rearth(c^2)) ]}^(1/2)

    and ∴ t(city)/t∞ = {1 - [ (2GMe) / (Rc(c^2)) ]}^(1/2)

    3. The attempt at a solution

    t(sea-level) / {1 - [ (2GMe) / (Rearth(c^2)) ]}^(1/2) ≈ t(city) / {1 - [ (2GMe) / (Rc(c^2)) ]}^(1/2)

    Having made the the two t∞ equal to each other.

    Knowing t(city) = 75 years this gave t(sea-level) as 74.99 years.

    Where have I gone wrong as shouldn't t(sea-level) be longer?
     
  2. jcsd
  3. Feb 3, 2016 #2

    PeroK

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    What gives you that idea?
     
  4. Feb 5, 2016 #3
    I was just using the fact that the question says "How much longer could they have lived at sea level?" so assumed t(sea-level) should therefore be longer?
     
  5. Feb 5, 2016 #4

    Bandersnatch

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    Ask yourself, which of the two has longer until his 76th birthday according to your calculations.
     
  6. Feb 5, 2016 #5
    Ah, so the t(sea-level) has longer until his 76th birthday so the person could have lived 0.01 years longer at sea level according to my calculations?
     
  7. Feb 5, 2016 #6

    Bandersnatch

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    You got it.
     
  8. Feb 5, 2016 #7
    Thanks!
     
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