  As a consequence of gravitomagnetism, which is a fundamental weak-field
prediction of general relativity and ubiquitous in gravitational phenomena,
clocks show a difference in their proper periods when moving along identical
orbits in opposite directions about a spinning mass. This time shift is induced
by the rotation of the source and may be used to verify the existence of the
terrestrial gravitomagnetic field by means of orbiting clocks. A possible
mission scenario is outlined with emphasis given to some of the major
difficulties which inevitably arise in connection with such a venture.
