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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.

Clock

degrees

minutes

Earth radius at lat. (m)

altitude of clock (m)

clock v east (m/s)

v in ECI frame

latitude
1 (East)

latitude
2 (West)

Clock Drate at altitude h, latitude f, velocity v

hours in trip

cos(lat)

sin(lat)

Earth radius at pole (m)

Clock
Lat. 1

Clock Lat. 2

East

Height
term

Height term

West

a*a*cos(lat)

b*b*sin(lat)

Earth radius at equator (m)

gh/C^2

gh/C^2

seconds in trip

East

a*cos(lat)

b*sin(lat)

Earth W average

speed term

speed term

West

v^2/2c^2

v^2/2c^2

cos(lat)

sin(lat)

Earth Velocity RW
(m/s)

Earth Circumference

Sagnac
term

Sagnac term

at latitude 1 (m)

a*a*cos(lat)

b*b*sin(lat)

vWRcosf/c^2

vWRcosf/c^2

East

at latitude 2 (m)

a*cos(lat)

b*sin(lat)

Dt for clock (ns)

Dt for clock (ns)

West

East

West

height term

The
conditions of the Hafele & Keating Experiment are pre-loaded. The
simulator calculates

speed term

the time
gained or lost by each clock carried by a plane straight around the world's
equator once

Sagnac term

either
east or west at the heights and speeds reported. Since the actual paths
werenot straight

total kinematic

or at constant
height and velocity, the final integrated Hafele & Keating result was a
little different

Net Dt

then
that shown here, at -40 ns for the eastbound clock and +275 ns for the
westbound clock after

returning
to the starting point. The Dt
is the time gained or lost with respect to a clock that remained

stationary at
the starting point. Other values for hours in trip, latitude of each clock,
and altitude

of each clock,
can be entered to see how it would affect the result by pressing
calculate.

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