A clock sits on the ground floor of a tower of height m and an identical clock sits…
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry
The Geometry of Gravity, Ch Redshift, local inertial frames and the failure of flat spacetime
Problem
A clock sits on the ground floor of a tower of height ℓ=828 m and an identical clock sits at the top. Both are at rest in the Earth's weak, static field, with Φ=g⊕ℓ over this height, g⊕=9.81ms−2.
((a)) Find the fractional rate difference between the two clocks.
((b)) After one year (3.156×107 s) of continuous running, by how much time (in microseconds) has the top clock gained on the ground clock?