By Neil., . Ashby
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R 31 (h/al)' NB S TECH N ICAL PU B LI CAT10 N S PERIODICALS JOURNAL OF RESEARCH reports National Bureau of Standards research and development in physics, mathematics, and chemistry. I t is published in two sections, available separately: Physics and Chemistry (Section A ) Papers of intercst primarily to scientists working in these fields. This section covers a broad range of physical a i d chemical research, with major emphasis on standwds of physical measurement, fundamental constants, and properties of matter.
Defining we have 26 -+ r , If we apply the above expressions to the case of the moon, the leading term in $00 2-t -+ will be proportional to the ordinary newtonian potential, 4Gm/c Ir - r' I . The leading correction term is due to retardation and will be of order 4Gm 2-t c Ir - The velocity of the moon is such that v/c Y -t r'l - c -6 3 x 10 . 84 x 10" m cm , we obtain 4Gm 2-t -t c Ir - r'I E ;10-18 c This retardation term contributes a term of order lasting to hO0 . In a typical flight 10 hours , such a term would contribute no more than about 4 x the elapsed coordinate time and may, therefore, be neglected.
1 Thus in terms of elapsed proper time on a standard clock carried in the satellite, (dx0l2 = ds2 + 2GMe + and since the orbit is determined by we have dxo = ds [I + 7 1. 31 assuming that + the positions r(xo) of the satellite can be determined and the integral of Equation ( 9 9 ) performed for clock synchronization. Since in 1 ns light travels 30 cm , positional accuracies of the satellite and of the receiving stations must be better than ? 30 cm for 1 n s synchronization accuracy. In addition, variations in propagation time due to dispersion of the electromagnetic waves in the ionosphere must be considered.
AN EARTH-BASED COORDINATE CLOCK NETWORK by Neil., . Ashby