The Sagnac effect influences precise measurements on the Earth when using GPS or GNSS. Perhaps not for the general user, but definitely for high precision geodetic type measurements.

Apart from effects on the GPS clocks such as the gravitational red (blue)-shift and time-dilation effects, the Sagnac effect involves the second postulate of special relativity (the constancy of the speed of light), the fundamental principle on which the GPS (and other GNSS's) is based.

In the Earth-Centred Inertial (ECI) frame, the special relativistic theory is valid to a high level. The ECI frame is basically a freely falling, local, non-rotating inertial frame with its origin at the centre of Earth. Although the Earth is accelerating towards the Sun, in this frame, the speed of light can be assumed to be constant. For the purposes of GPS and in general of satellites with clocks on board, it is most convenient to describe their motions in the ECI frame. This approach makes the Sagnac effect irrelevant although the Sagnac effect on Earth-based (moving) receivers must still be taken into account. It is therefore practical to synchronise clocks in an Earth Centred Inertial (ECI) frame as light does not travel in a straight line in a rotating frame.

It would not be practical in an Earth Centred Earth Fixed Frame (ECEF frame) due to the Sagnac effect. In the ECEF, which is a rotating frame, clock synchronisation is difficult as light travels in a spiral path due to the Sagnac effect. Practically, the ECI is used for the establishment of positions by the GPS and afterwards a rotation to the ECEF is performed.

The Sagnac effect depends on the path and direction travelled by the GPS receiver (rotating frame of reference). The effect basically means that the onboard GPS clock runs fast or slow relative to a clock on the geoid (Earth's equipotential surface).

A stationary GPS receiver located on the equator will have a velocity of ~465 m/s through the ECI frame as the Earth rotates. The corresponding Sagnac correction can be as large as 133 ns (equal to 86 ms signal propagation). This correction is also applied in the receiver. Allowing for the Sagnac effect in the ECEF is therefore equivalent to correcting for the receiver’s motion in the ECI frame.

You can find an explanation of Sagnac effect for GPS in volume 1 of the book by Brad Parkinson and Jim Spilker, et Al. "Global Positioning System: Theory and Applications," AIAA, 1996.  See chapter 18 "Introduction to Relativistic Effects on the Global Positioning System by Neil Ashby and Jim Spilker.

thanks everyone

Dear Ludwig Combrinck ,

Sagnac correction is needed to make the GPS base station work correctly...once they have been treated with the Einstein's synchronization procedure (ESP) they need the Sagnac correction to define a simultaneity in ECIF.

ESP between two clocks set on earth surface fails of the quantity vPH/c2 , where vP is the projection of their velocity v parallel to the tangential speed of the surface of earth W --> E

while H is the distance of the clocks, on the surface of earth, measured with a meter stick.

Yes, considering two clocks A and B which are at maximum distance of half the length of the equator 2*10^4 Km, it is vH/c2 is .5 Km/s * 2*104 Km/ (9*1010 ) Km2/s2

=1.11*10-7 s = 111 ns (quite close to your calculations)

if A and B are in a lab oriented N-->S at a distance of 0.2 Km they can be set in sync since no influence should come from spinning earth.

if A and B are rotated such that they are now EST--> WEST it should be detected a difference of the order of 10-12 s which can be still measurable.