- #1
J_M_R
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Homework Statement
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).
Homework 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)
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?