Relativistic theory for time and frequency transfer to order c(-3)

Citation
L. Blanchet et al., Relativistic theory for time and frequency transfer to order c(-3), ASTRON ASTR, 370(1), 2001, pp. 320-329
Citations number
26
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Space Sciences
Journal title
ASTRONOMY AND ASTROPHYSICS
ISSN journal
0004-6361 → ACNP
Volume
370
Issue
1
Year of publication
2001
Pages
320 - 329
Database
ISI
SICI code
0004-6361(200104)370:1<320:RTFTAF>2.0.ZU;2-J
Abstract
This paper is motivated by the current development of several space mission s (e.g. AGES on International Space Station) that will use Earth-orbit lase r cooled atomic clocks, providing a time-keeping accuracy of the order of 5 10(-17) in fractional frequency. We show that to such accuracy, the theory of frequency transfer between Earth and Space must be extended from the cu rrently known relativistic order 1/c(2) (which has been needed in previous space experiments such as GP-A) to the next relativistic correction of orde r 1/c(3). We find that the frequency transfer includes the first and second -order Doppler contributions, the Einstein gravitational red-shift and, at the order 1/c(3), a mixture of these effects. As for the time transfer, it contains the standard Shapiro time delay, and we present an expression also including the first and second-order Sagnac corrections. Higher-order rela tivistic corrections, at least O(1/c(4)), are numerically negligible for ti me and frequency transfers in these experiments, being for instance of orde r 10(-20) in fractional frequency. Particular attention is paid to the prob lem of the frequency transfer in the two-way experimental configuration. In this case we find a simple theoretical expression which extends the previo us formula (Vessot ct al. 1980) to the next order 1/c(3). In the Appendix w e present the detailed proofs of all the formulas which will be needed in s uch experiments.