GPS relies on principles of special and general relativity to account for relativistic effects that would otherwise cause errors. The Sagnac effect, which results from light traveling in opposite directions around a rotating object, must be considered and can cause time differences of hundreds of nanoseconds depending on satellite and receiver positions. An experiment in 1984 precisely measured the Sagnac effect using GPS satellites and atomic clocks at three locations, finding results that matched relativity predictions to within 5 nanoseconds.

1. Relation GPS and relativity theory
S1150048 Takefumi Ogata

2. Outline
●Introduction
●GPS
●Sagnac effect
●How to calculate
●Consideration
●Result and Conclusion

3. Introduction
The Global Positioning System (GPS) uses accurate, stable atomic
clocks in satellites and on the ground to provide world-wide
position and time determination. These clocks have gravitational
and motional frequency shifts which are so large that, without
carefully accounting for numerous relativistic effects, the system
would not work. This paper discusses the conceptual basis,
founded on special and general relativity, for navigation using
GPS. Relativistic principles and effects which must be considered
include the constancy of the speed of light, the equivalence
principle, the Sagnac effect, time dilation, gravitational frequency
shifts, and relativity of synchronization. Experimental tests of
relativity obtained with a GPS receiver aboard the
TOPEX/POSEIDON satellite will be discussed.

4. GPS
GPS is a space-based global navigation satellite system that
provides reliable location and time information in all weather and
at all times and anywhere on or near the Earth when and where
there is an unobstructed line of sight to four or more GPS
satellites. It is maintained by the United States government and is
freely accessible by anyone with a GPS receiver. In addition to
GPS other systems are in use or under development. The Russian
GLObal NAvigation Satellite System was for use by the Russian
military only until 2007. There are also the planned Chinese
Compass navigation system and Galileo positioning system of the
European Union. GPS was created and realized by the U.S.
Department of Defense and was originally run with 24 satellites.
It was established in 1973 to overcome the limitations of previous
navigation systems

5. Sagnac effect
The Sagnac effect named after French physicist Georges Sagnac,
is a phenomenon encountered in interferometry that is elicited by
rotation. The Sagnac effect manifests itself in a setup called ring
interferometry. A beam of light is split and the two beams are
made to follow a trajectory in opposite directions. To act as a ring
the trajectory must enclose an area. On return to the point of entry
the light is allowed to exit the apparatus in such a way that an
interference pattern is obtained. The position of the interference
fringes is dependent on the angular velocity of the setup. This
arrangement is also called a Sagnac interferometer.

6. Consideration
In the ECEF frame used in the GPS, the unit of time
is the SI second as realized by the clock ensemble of
the U.S. Naval Observatory, and the unit of length is
the SI meter. This is important in the GPS because it
means that local observations using GPS are
insensitive to effects on the scales of length and time
measurements due to other solar system bodies, that
are time-dependent.

7. Result and Conclusion
GPS can be used to compare times on two earth-fixed clocks
when a single satellite is in view from both locations. This is the
¡Ècommon-view É method of comparison of Primary standards,
whose locations on earth¡Çs surface are usually known very
accurately in advance from ground-based surveys. Signals from a
single GPS satellite in common view of receivers at the two
locations provide enough information to determine the time
difference between the two local clocks. The Sagnac effect is very
important in making such comparisons, as it can amount to
hundreds of nanoseconds, depending on the geometry.

8. Conclusion
In 1984 GPS satellites 3, 4, 6, and 8 were used in simultaneous
common view between three pairs of earth timing centers, to
accomplish closure in performing an around-the-world Sagnac
experiment. The centers were the National Bureau of Standards in
Boulder, CO, Physikalisch-Technische Bundesanstalt in
Braunschweig, West Germany, and Tokyo Astronomical
Observatory . The size of the Sagnac correction varied from 240
to 350 ns. Enough data were collected to perform 90 independent
circumnavigations. The actual mean value of the residual obtained
after adding the three pairs of time differences was 5 ns, which
was less than 2 percent of the magnitude of the calculated total
Sagnac effect.