8-23
The following expression accounts for relativistic effects, provides
for clock rate accuracies of better than 1 part in 1014,
and allows for global-scale clock comparisons of nanosecond accuracy, via satellites:
Where
Dt = time difference between spacecraft clock and ground clock, tS-Tg
VS = spacecraft
velocity (<<c), Vg = velocity of ground station
FS = gravitational potential at the spacecraft
Fg = gravitational potential at the ground station
w = angular velocity of rotation of the
earth
AE = the projected area on the earth’s
equatorial plane swept out by the vector
whose tail is
at the center of the earth and whose head is at the position
of the portable
clock or the electromagnetic signal pulse. The AE is taken positive if the head of the
vector moves in the eastward direction.
Within 24 km of sea
level, F = gh is accurate to 1 x 10-14 where g = (9.780 + 0.052 sin2Y
)m/s2, Y = the latitude, h = the distance above sea level, and
where the sin2Y term accounts for the centrifugal
potential due to the earth's rotation.
The "Sagnac effect," (2w/c2)AE = (1.6227 x 10-21s/m2)AE, accounts for the earth-fixed
coordinate system
being a rotating, noninertial reference frame.
Relativistic Time Corrections