It is the most stable clock ever put in permanent orbit, and is designed to keep time with an accuracy of better than one nanosecond (billionth of a second) in 24 hours.
As well as its atomic clocks (Giove-B carries three clocks), the latest demonstrator will test the generation of signals across the full spectrum Galileo intends to use for its five sat-nav services.
Saturday's launch from the Baikonur spaceport was an important moment for Galileo which has experienced several delays.
Giove-B was held on the ground for a year because of a component failure during the final stages of its preparation for flight; but more generally, the Galileo programme itself has seen its timeline slip on a number of occasions, and has come close to being abandoned.
Europe has already spent 1.6bn euros ($2.5bn; £1.3bn) on the project and ministers have warned that the additional 3.4bn euros ($5.3bn; £2.7bn) recently approved for sat-nav investments will be the limit on expenditure.
GALILEO UNDER CONSTRUCTION
A European Commission and European Space Agency project
30 satellites to be launched in batches by end of 2013
Will work alongside US GPS and Russian Glonass systems
Promises real-time positioning down to less than a metre
Guaranteed under all but most extreme circumstances
Suitable for safety-critical roles where lives depend on service
Galileo is envisaged as being technologically complementary to GPS, and is touted as a key high-technology venture for the EU.
It is designed to improve substantially the availability and accuracy of timing signals delivered from space.
Users should get quicker, more reliable fixes and be able to locate their positions with an error of one metre compared with the current GPS error of several metres.
"One of the short-comings of GPS has been the ability to rely on it for safety-critical applications such as landing aircraft," said Richard Peckham from EADS Astrium.
"Galileo has a safety-of-life service which is basically an integrity, a monitoring service that checks the signal constantly. With this, we should be able to start relying on satellite navigation much more than we can today with GPS."
If all of the technologies in Giove-B work as predicted, engineers will be clear to launch the first four operational satellites in 2010.
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