Consider next the process of transferring coordinate time from one satellite clock to another by direct exchange of signals. This will be important when “Autonav” is implemented. The standard atomic clock in the transmitter satellite suffers a rate adjustment, and an eccentricity correction to get the coordinate time. Then a signal is sent to the second satellite which requires calculating a coordinate time of propagation possibly incorporating a relativistic time delay. There is then a further transformation of rate and another “” correction to get the atomic time on the receiving satellite’s clock. So that the rate adjustment does not introduce confusion into this analysis, I shall assume the rate adjustments are already accounted for and use the subscript ‘S’ to denote coordinate time measurements using rate-adjusted satellite clocks.
Then, let a signal be transmitted from satellite nr. , at position and having velocity in ECI coordinates, at satellite clock time , to satellite nr. , at position and having velocity . The coordinate time at which this occurs, apart from a constant offset, from Eq. (38), will be
This result contains all the relativistic corrections that need to be considered for direct time transfer by transmission of a time-tagged pulse from one satellite to another. The last term in Eq. (52) should not be confused with the correction of Eq. (40).
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