When relativistic effects become important, synchronization of clocks in Keplerian orbit is formally a problem of synchronization in noninertial frame of reference. Although such a procedure is impossible from basic principles, even the synchronization in approximation has never been treated in the historical literature of relativity. In recent times a number of papers have appeared which touch upon this subject; however, those communications are not entirely in agreement with one another over the procedure. This paper attempts to clarify what each author has done and delineates the differences and questions left open by their individual procedures. Finally, a number of specific questions are enumerated which, if thoroughly researched, could resolve the controversy which appears to surround current attempts at relativistic synchronization of clocks orbiting the earth.