[ntp:questions] A Suggestion For Abolishing the Leap Second

jlevine jlevine at boulder.nist.gov
Tue Jun 5 14:08:07 UTC 2007

> In my ignorance of these matters, I would have thought that if the Sun
> were the immovable center of the Universe, and the Earth were
> revolving around it in a perfect circle, time (at least at the poles,
> assuming no axial tilt) would progress at a uniform rate on the Earth
> as viewed from the Sun, just changed by a *fixed percentage* due to
> relativistic effects.

   Not quite. The SI second is defined on the rotating geoid, and
that are not on the geoid run at a different rate. For example, the
frequency standard operated by NIST in Boulder, Colorado is about 1700
meters (5300+ feet) above the geoid. Although this standard realizes
definition of the SI second with an uncertainty of about 2e-15, its
is offset from the definition of the second by about 2e-13 because of
gravitational blue shift. This systematic correction is about 100X its
and it is included when the data from the primary frequency standard
are reported to the International Bureau of Weights and Measures. If
correction were not included, there would be an enormous (relative to
capabilities of the device) frequency offset between the primary
standard operated here and a nominally identical device operated by
colleagues at other standard laboratories in Europe, since they are
closer to the geoid reference height.
    The clocks in the GPS satellites, which fly at an altitude of
about 4.2
earth radii, have a much larger version of this effect: the frequency
in that case is about 4e-11 relative to identical clocks located on
the geoid.
This offset is incorporated into the GPS satellites by offseting the
oscillator before the satellite is launched so that its frequency
to be correct when it is observed by an observer on the geoid. The
ellipticity of the satellite orbit adds an additional smaller
correction which
is done in the receiver based on the orbital parameters of the

Judah Levine
Time and Frequency Division
NIST Boulder

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