I7    GPS, LRS and Relativity


Atomic clocks, following their introduction in the 50s, quickly became more accurate and smaller. Thus, in 2003, a rubidium atomic clock was successfully built occupying a volume of 40 cm3, consuming 1 Watt of power and having an accuracy of 3 • 10-12 ! Pierre Thomann of the Observatory of Neuchâtel and Gregor Dudle of the Federal Office for Metrology (METAS) in Berne also succeeded in 2003 in increasing the accuracy of the standard cesium clock using a special cooling technique by a factor of 40 to 1 • 10-15.

Starting in 1958 the U.S. military began to combine these clocks with other advances in electronics and satellite technology into a worldwide global positioning system (GPS). The first working system, TRANSIT, was deployed in 1964 and primarily had the function of guiding submarine missiles to their destination. Better well-known was NAVSTAR, which was formally put into operation on July 17th, 1995 and was also available for civilian use. 24 satellites circle the earth in well-known orbits twice a day and continually transmit time signals. Small and cheap receivers can use the tiny time differences of the signals from at least 4 of these satellites to determine their own position to a few meters and also the time (four measurements determine the four unknowns). Recall: 1 nanosecond corresponds to a distance of 30 centimeters. If the receiver itself had a highly accurate and perfectly synchronized clock then two or three satellites would be sufficient to determine its position with an accuracy of a few centimeters. The uncertainty would then be mainly from the imprecise knowledge of the trajectory of the satellites.

A small group at the University of Bern is working at the forefront of this problem: In Zimmerwald laser pulses are sent to reflectors attached to the satellite specifically for this purpose. The orbit of the satellites can be precisely determined to within centimeters from the few photons of the reflected signal that can be captured. The precise orbital data allow the off-line evaluation of the GPS satellite signals with special software from the University of Bern achieving accuracy sufficient for surveying purposes. In this way one can today directly measure the folding of the Alps, the drift of continents or the earth tides. LRS (Laser Ranging Systems) are also available in Germany, in both Potsdam and Wettzell in Bavaria. These stations work together all over the world (http://ilrs.gsfc.nasa.gov/).

The former Soviet Union has also built a military-controlled satellite navigation system (GLONASS). The European Space Agency (ESA) is preparing its own, civilian-controlled system (GALILEO). The first satellites are already in space (the launch could not be delayed because otherwise ESA would have lost a reserved frequency band ...). In addition to the ESA member states China, India, Canada and Israel are also participating on this project. The clocks being used for the Galileo satellites have been developed by the Neuchâtel Institute mentioned above.

All of these satellite-based navigation systems would never work without taking into account the STR and GTR. The corrections for the STR, as well as those of the GTR are not even constant over an entire orbit since the orbits of the satellites are always slightly elliptical. These variations in both altitude and relative speed must be taken into account for high precision measurements  (to within a few millimeters). The influences are exactly those that we discussed in I5 and I6.

Since these Global Positioning Systems have arisen in the www-age, you will find a wealth of descriptions and illustrations in the web. Also the indispensable ‘counterpart’, the LRS, is well documented in the web, although it is much less well-known to the public.


The inconspicuous facility of the Astronomical Institute of the University of Berne in Zimmerwald.

The heart of the facility at Zimmerwald: A laser which delivers ten very intense and sharp pulses per second and which are then sent to the reflector on the satellite through a small telescope (see picture above, domed building on the left). To accomplish this, the approximate position of the satellite must, of course, already be known. The few photons that arrive within the narrow time window and also have the correct wavelength will be recognized as a reflected signal and used to determine the round-trip time with a precision in the range of 0.1 nanoseconds.

Both photos on this page are snapshots taken by the author.