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Hafele & Keating
Experiment: Effect of Latitude, Altitude and Velocity on the rates of two
clocks in a round the world trip.
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Clock
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degrees
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minutes
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Earth radius at lat. (m)
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altitude of clock (m)
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clock v east (m/s)
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v in ECI frame
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latitude
1 (East)
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latitude
2 (West)
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Clock Drate at altitude h, latitude f, velocity v
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hours in trip
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cos(lat)
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sin(lat)
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Earth radius at pole (m)
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Clock
Lat. 1
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Clock Lat. 2
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East
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Height
term
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Height term
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West
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a*a*cos(lat)
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b*b*sin(lat)
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Earth radius at equator (m)
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gh/C^2
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gh/C^2
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seconds in trip
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East
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a*cos(lat)
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b*sin(lat)
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Earth W average
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speed term
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speed term
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West
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v^2/2c^2
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v^2/2c^2
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cos(lat)
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sin(lat)
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Earth Velocity RW
(m/s)
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Earth Circumference
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Sagnac
term
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Sagnac term
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at latitude 1 (m)
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a*a*cos(lat)
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b*b*sin(lat)
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vWRcosf/c^2
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vWRcosf/c^2
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East
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at latitude 2 (m)
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a*cos(lat)
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b*sin(lat)
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Dt for clock (ns)
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Dt for clock (ns)
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West
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East
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West
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height term
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The
conditions of the Hafele & Keating Experiment are pre-loaded. The
simulator calculates
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speed term
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the time
gained or lost by each clock carried by a plane straight around the world's
equator once
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Sagnac term
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either
east or west at the heights and speeds reported. Since the actual paths
were not straight
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total kinematic
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or at constant
height and velocity, the final integrated Hafele & Keating result was a
little different
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Net Dt
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then
that shown here, at -40 ns for the eastbound clock and +275 ns for the
westbound clock after
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returning
to the starting point. The Dt
is the time gained or lost with respect to a clock that remained
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stationary at
the starting point. Other values for hours in trip, latitude of each clock,
and altitude
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of each clock,
can be entered to see how it would affect the result by pressing
calculate.
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