A caesium clock is carried in a helicopter that hovers at rest above the ground

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Atomic, Molecular & Optical Physics · The equivalence principle and gravity as geometry

Relativity and Gravitation, Ch Experimental foundations: free fall, Lorentz invariance and clock tests

Problem

A caesium clock is carried in a helicopter that hovers at rest above the ground, at height

h = 3.00\ \mathrm{km}

, for

6.00\ \mathrm{h}

, and is then compared with an identical clock left on the ground directly below. Take

g = 9.81\ \mathrm{m\,s^{-2}}

, constant over

3.00\ \mathrm{km}

, and

c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}

; the Earth's rotation carries both clocks alike and is ignored throughout, and all work is to first order in

gh/c^{2}

and in (speed)

^{2}/c^{2}

. ((a)) Compute the offset accumulated by the airborne clock, in ns, and say whether it gains or loses. ((b)) The flight is repeated at the same height and for the same

6.00\ \mathrm{h}

, but the helicopter now flies a closed circuit at a ground speed of

70.0\ \mathrm{m\,s^{-1}}

relative to the Earth's surface. (The Earth-rotation cross term averages to zero round the circuit and is to be ignored.) Compute the offset now, in ns. ((c)) What does an accelerometer carried in the hovering helicopter read, and what would it read if it were released and left to fall freely? ((d)) Which pillar of the Einstein equivalence principle does the height term of parts (a) and (b) test?

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