ULTRA-ACCURATE INTERNATIONAL TIME AND FREQUENCY COMPARISON VIA AN ORBITING HYDROGEN-MASER CLOCK

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ULTRA-ACCURATE INTERNATIONAL TIME AND FREQUENCY COMPARISON VIA AN ORBITING

HYDROGEN-MASER CLOCK

D. Allan, C. Alley, N. Ashby, R. Decher, R. Vessot, G. Winkler

To cite this version:

D. Allan, C. Alley, N. Ashby, R. Decher, R. Vessot, et al.. ULTRA-ACCURATE INTERNATIONAL TIME AND FREQUENCY COMPARISON VIA AN ORBITING HYDROGEN-MASER CLOCK.

Journal de Physique Colloques, 1981, 42 (C8), pp.C8-395-C8-413. �10.1051/jphyscol:1981846�. �jpa-

00221742�

JOURNAL DE PHYSIQUE

Colloque C8, suppZdment au n012, Tome 42, ddcembre 1982 page C8-395

ULTRA-ACCURATE INTERNATIONAL TIME AND FREQUENCY COMPARISON V I A AN ORBITING HYDROGEN-MASER CLOCK

2 3 4

D.W. ~llan', C.O. Alley , N. Ashby , R. Decher , R.F.C. vessot5 and G.M. R. Winkler6

National Bureau o f Standards, Boulder, Colorado, U . S. A.

2 University of Maryland, Co ZZege Park, Mary land, U . S. A.

3 University of Colorado, Boulder, Colorado, U.S.A.

4 Marshall Space Flight Center, h'untsvi ZZe, Alabama, U . S. A.

5 Smithsonian AstrophysicaZ Obseruatory, Cambridge, Massachsetts, U.S.A.

U. S. Naval Observatory, Washington, DC, U . S.A.

Abstract. - Hydrogen maser c l o c k s have e x h i b i t e d f r a c t i o n a l frequency s t a b i l i t i e s of b e t t e r than 1 x 10-Is f o r averaging times as l a r g e as 20,000 seconds [l]. T h i s represents an rms t i m e d e v i a t i o n o f about 20 ps f o r day p r e d i c t i o n times [2]. S-band Doppler c a n c e l l a t i o n frequency compari son techniques have been developed w i t h phase s t a b i 1 i- t i e s o f a few picoseconds [2,3]. Laser r a n g i n g systems have been developed w i t h accuracies o f a few cm [4]. Combining t h e v i r t u e s o f these devel opments and choosing a sate1 1 i t e w i t h an a p p r o p r i a t e o r b i t would a l l o w worldwide t i m e comparisons a t t h e subnanosecond l e v e l , and frequency comparison u n c e r t a i n t i e s o f t h e o r d e r o f 1 x 10-16. Such a capabi 1 i t y would open up new horizons t o t h e frequency standards 1 abora- t o r i e s , t o t h e VLBI community, t o t h e Deep Space Tracking Network, and t o fundamental t i m e and frequency (T/F) metrology on a worldwide b a s i s , as w e l l as g r e a t l y a s s i s t i n g t h e BIH i n t h e generation o f UTC and TAI.

I n t r o d u c t i o n . - For t h e u l tr a - a c c u r a t e frequency m e t r o l o g i s t , i t would be u s e f u l b o t h t o have a p e r f e c t reference and a l s o t o have t h a t reference a v a i l a b l e t o o t h e r m e t r o l o g i s t s so t h a t comparisons c o u l d be made w i t h r e s p e c t t o t h e same reference. Though t h e experiments o u t l i n e d i n t h i s paper do n o t p e r f e c t l y achieve these goals, t h e y a l l o w g i a n t steps t o be taken from where we a r e now i n t h e comparison o f remote T/F standards. The c u l m i n a t i o n o f these experiments would r e s u l t i n a system which would be t h e marriage o f f i v e very successful methods t h a t have been developed i n t h e r e c e n t p a s t and whose i n d i v i d u a l accura- c i e s and c a p a b i l i t i e s a r e documented i n t h e l i t e r a t u r e . These are: 1) t h e c l o c k f l y o v e r experiment, o r i g i n a l l y i n v e s t i g a t e d and conducted by Besson, e t a1 [5], and l a t e r by o t h e r s [4]; 2) t h e subnanosecond accuracies a v a i l a b l e u s i n g r e c i - p r o c i t y o f l a s e r pulses (propagation delay times i n b o t h d i r e c t i o n s a r e equal )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981846

C8-396 JOURNAL DE PHYSIQUE

o f f o f r e t r o r e f l e c t o r s [4,6]; 3) t h e three-way microwave Doppler c a n c e l l a t i o n system o u t l i n e d h e r e i n r e s u l t s i n picosecond phase s t a b i l i t y between remote l i n e - o f - s i g h t c l o c k s [3]; 4) t h e u n p a r a l l e l e d frequency s t a b i l i t y o f hydrogen masers f o r sample times i n t h e v i c i n i t y o f - ¹⁰⁰ s t o several hours [I]; and 5) t h e g r e a t advantage gained by u s i n g s i g n a l s i n simultaneous common-view from two s i t e s , l e a d i n g t o l a r g e amounts o f common-mode e r r o r c a n c e l l a t i o n i n many i n - stances [7,8,9,10]. The accuracy and c h a r a c t e r i s t i c s o f these methods w i l l be reviewed; we s h a l l then discuss how t h e y reasonably can be m a r r i e d t o g e t h e r t o g i v e an u l tr a - a c c u r a t e worldwide T/F metro1 ogy system.

The proposed S h u t t l e time and frequency t r a n s f e r (STIFT) concept i s i l l u s - t r a t e d i n f i g u r e 1. STIFT can be viewed as an extension o f t h e t r a n s p o r t a b l e c l o c k , o r c l o c k f l y o v e r , method w i t h a hydrogen maser c l o c k i n a space v e h i c l e . Time and frequency t r a n s f e r between t h e space c l o c k and a c l o c k on t h e ground i s accomplished i n one o f two ways. The f i r s t method i s by two-way microwave t r a n s - m i s s i o n i n v o l v i n g t h r e e c a r r i e r frequencies. The CW microwave system w i l l p e r m i t a d i r e c t frequency comparison between t h e space c l o c k and t h e ground c l o c k w i t h an accuracy o f 10-l4 f o r sample times o f t h e o r d e r 100 s and longer. This i s a unique f e a t u r e o f t h e STIFT system. A t i m e code modulation can be a p p l i e d on t h e microwave c a r r i e r t o perform t i m e t r a n s f e r w i t h an accuracy o f 1 ns o r b e t t e r . The user o f t h e system w i l l r e q u i r e a microwave ground t e r m i n a l l o c a t e d n e x t t o t h e c l o c k t o r e c e i v e s i g n a l s from and t o t r a n s m i t back t o t h e spacecraft. Fur- t h e r , a method o f i d e n t i f y i n g unambiguously a c y c l e o f t h e microwave downlink from t h e spaceborne c l o c k from o r b i t t o o r b i t adds g r e a t leverage t o t h e micro- wave system. The few picosecond phase s t a b i l i t y o f t h e microwave system combined w i t h t h e l o n g i n t e g r a t i o n times w i l l y i e l d frequency measurements accurate t o t h e o r d e r o f a p a r t i n 1016.

Second, t h e STIFT system can accomplish t i m e t r a n s f e r w i t h subnanosecond accuracy u s i n g t h e s h o r t - p u l s e l a s e r technique i n c o n j u n c t i o n w i t h e x i s t i n g l a s e r ground s t a t i o n s . t h e l a s e r technique can a l s o be used t o c a l i b r a t e t h e microwave system. The short-pulse l a s e r method i s t h e most accurate documented technique o f t i m e t r a n s f e r a v a i l a b l e [4]. The equipment onboard t h e space v e h i c l e c o n s i s t s o f a hydrogen maser c l o c k , a microwave transponder system w i t h antenna, a corner r e f l e c t o r a r r a y w i t h photodetectors, and an event t i m e r .

A f i r s t step implementation o f t h e STIFT system would be a demonstration

f l i g h t on t h e Space S h u t t l e . The experiment would be r e t u r n e d and c o u l d be

r e f l o w n on a l a t e r S h u t t l e mission. I n i t i a l l y , S h u t t l e missions a r e l i m i t e d t o

a l t i t u d e s o f about 370 km (200 nmi), w i t h a 57' i n c l i n a t i o n o r b i t . Such an o r b i t

wi 11 p r o v i d e many c o n t a c t s w i t h e x i s t i n g ground s t a t i o n s , and s u f f i c i e n t g l o b a l

coverage t o demonstrate t h e t i m e and frequency t r a n s f e r c a p a b i l i t y o f t h e STIFT

method. The number o f p a r t i c i p a t i n g l a b o r a t o r i e s and users w i l l depend on t h e

l i m i t e d number o f ground t e r m i n a l s which can be made a v a i l a b l e f o r t h e demonstra-

t i o n experiment. R e d i s t r i b u t i o n of ground t e r m i n a l s f o r r e f l i g h t s o f t h e e x p e r i -

ment would p e r m i t w i d e r p a r t i c i p a t i o n i n t h e experiment.

SHUTTLE TlME AND FREQUENCY TRANSFER ACTIVITY SHUTTLE TELEMETRY 1 MICROWAVE aoc~ SYSTEM MICROWAVE flME AND FREQUENCY MICROWAVE REF LECTOR ARRAY ANTENNA AND PHOTO DETECTORS LASER TlME TRANSFER Figure 1. - A sketch of the STIFT concept showing the microwave Doppler cancellation system and the laser ranging system to the Shuttle.

C8-3 98 JOURNAL DE PHYSIQUE

The n e x t phase o f t h e implementation program c o u l d be t h e deployment o f STIFT on t h e Power Systems Platform, a small, unmanned space s t a t i o n b e i n g planned by t h e N a t i o n a l Aeronautic and Space A d m i n i s t r a i t o n (NASA). The o r b i t would be v e r y s i m i l a r t o t h e Space S h u t t l e o r b i t because t h e p l a t f o r m w i l l be s e r v i c e d by t h e S h u t t l e . The main advantage would be t h e extended ( i n p r i n c i p l e , u n l i m i t e d ) o p e r a t i o n t i m e which would make t h e STIFT system a v a i l a b l e i n a quasi-operational mode.

The u l t i m a t e goal i s a f r e e - f l y i n g s a t e l l i t e i n an o r b i t o p t i m i z e d f o r a g l o b a l o p e r a t i o n a l system. Since t h e b a s i c technology r e q u i r e d f o r STIFT i s a v a i l a b l e , one c o u l d d i r e c t l y implement t h e STIFT s a t e l l i t e system w i t h o u t demon- s t r a t i o n f l i g h t s . However, making use o f a v a i l a b l e S h u t t l e missions o f f e r s s e v e r a l advantages. The program c o u l d s t a r t a t a lower i n i t i a l c o s t and t h e r e f l i g h t p o s s i b i l i t y would p e r m i t o p t i m i z a t i o n o f t h e STIFT design based on p r a c t i c a l r e s u l t s from demonstation f l i g h t s .

The spaceborne p a r t o f t h e STIFT system c o n s i s t s o f t h e hydrogen maser c l o c k , a microwave transponder, microwave antenna, corner r e f l e c t o r a r r a y w i t h photodetectors, and associated e l e c t r o n i c s . For S h u t t l e missions, t h e experiment package would be mounted on a p a l l e t i n t h e S h u t t l e bay. A deployable antenna may be r e q u i r e d t o o b t a i n a c l e a n r a d i a t i o n p a t t e r n .

The ground t r a c k s o f a 57', 370 km S h u t t l e o r b i t a r e shown i n f i g u r e s 2a and 2b f o r t h e f i r s t 16 o r b i t a l r e v o l u t i o n s . Also shown a r e t h e v i s i b i l i t y c i r c l e s f o r s e l e c t e d ground t e r m i n a l l o c a t i o n s f o r l o 0 e l e v a t i o n l i m i t s . The f o l l o w i n g s t a t i o n l o c a t i o n s have been i n c l u d e d t o i 11 u s t r a t e t h e c u r r e n t study, b u t c o u l d c l e a r l y be broadened t o i n c l u d e any ground s t a t i o n w i t h i n a l a t i t u d e o f k 57':

GSFC/Washington, DC; PTB/Braunschweig, FRG; JPL/Goldstone, CA; JPL/Canberra, A u s t r a l i a ; NBS/Boulder, CO; NRC/Ottawa, Canada; BIH/Pari s , France; and NRL/Tokyo ,

Japan. The GSFC would be v e r y a c c u r a t e l y t i e d i n time t o UTC(USN0).

The techniques t o be employed have been used s u c c e s s f u l l y i n e a r l i e r e x p e r i - ments. The microwave p o r t i o n o f t h e system i s s i m i l a r t o a system used w i t h t h e G r a v i t a t i o n a l R e d s h i f t Probe (GPA) flown i n 1976 [3]. The short-pulse l a s e r tech- nique was s u c c e s s f u l l y used i n a i r b o r n e c l o c k experiments i n 1975 which measured general r e l a t i v i s i t i c e f f e c t s on t i m e [4]. Because o f t h i s experience w i t h p r e v i o u s experiments, b a s i c new technology development i s n o t r e q u i r e d f o r t h e S h u t t l e experiment. The main new c o n t r i b u t i o n o f t h i s paper i s t o show t h a t t h e o r b i t a l elements o f t h e S h u t t l e , o r o f a s a t e l l i t e , can be determined w e l l enough so t h a t t h e u n c e r t a i n t i e s o f t h e r e l a t i v i s t i c e f f e c t s on t h e spaceborne c l o c k can be k e p t s u f f i c i e n t l y small t o a l l o w an i n d i v i d u a l c y c l e o f t h e microwave s i g n a l t o be unambiguously i d e n t i f i e d . As w i 11 be shown, t h e imp1 i c a t i o n s o f accompl i s h i n g t h i s a r e v e r y far-reaching.

The c u r r e n t o p e r a t i o n a l mode f o r comparison o f p r i m a r y standards i n t h e U.S.

(NBS), Canada (NRC), and West Germany (PTB) u t i l i z e s Loran-C, which s u f f e r s from

1 im i t e d g1 obal coverage and f 1 u c t u a t i o n s o f t h e ground-wave propagation delay,

GROUND TRACK FOR SPACELAB 0.00 TO 12.00 HOURS

JPL-G NBS-B NRC USNO BW PTB RRL JPL*

00

60

30

W n

$ 0

s

-30

-60

-90

-180 -150 -120 -80 -60 -30 0 30 80 90 120 150 180 LONGITUDE

TRACKING ClRCLES - ALTITUDE 370.00 KM ELEVATION ANGLE 10.00 DEG

Figure 2a.

GROUND TRACK FOR SPACELAB 12.00 TO 24.00 HOURS

JPL-G NBS-B NRC USNO BKI PTB RRL JPL-C 00

80

30

W 0

0

5

-30

-60

-90

-180 -150 -120 -80 -60 -30 0 30 80 90 120 150 180 LONGITUDE

TRACKING CIRCLES - ALTITUDE 370.00 KM ELEVATION ANGLE 10.00 DEG Figure 2b.

Figures 2a and 2b. - Sixteen successive ground tracks of a Shuttle f l i g h t and how

they intercept various key timing centers. I t i s interesting t o not that PTB has

s i x successive passes, e . g . , a sinewave o s c i l l a t o r spends most of i t s time a t the

extremes.

INTERNATIONAL TIME AND FREQUENCY COMPARISON (<< 1 ps)

24-Hour

Cost Frequency

Method Inaccuracy Stabi 1 i t y Factor Accuracy Comments

GPS (Common-view) 10 ns 1 ns 0.25 < 8 x 10-l4 Potential f o r global coverage-test s t a r t e d May 1981

Shuttle (STIFT) 1 ns 0.001 ns 0.25 - ^{< 10-14 Coverage} * 57' 1 atitude-earl i e s t f l i g h t 1986

VLBI and GPS 0.3 ns 0 . 1 ns 0.1 3 x 10-I= Only available when VLBI systems are oper-

(common-vi ew) a t i n g and accuracte GPS o r b i t s are known

TDRSS 10 ns 1 ns 1.0 < 10-13 Limited global coverage-planned f o r

1982 LASSO

GPS

1 ns 0.1 ns

40 ns* 10 ns

1.0 - ^10-14 Limited global coverage-pl anned f o r w

1982, experimental system M

- w

* 1.0 - ^{3 x 10-l3} Global coverage-operati ona1 1985, 3

under t e s t since 1978 ^H

9 m Communication 50 ns , < . , 1 ns 5.0** ,., < 10-13 Almost global coverage except near

Sate1 1 i t e (2-way) pol es-experimental

Portable Clock 100 ns N/ A 6.0 - ^10-13 Global coverage--best accuracy w i t h i n

reasonable d r i v i n g v i c i n i t y o f a i r p o r t s 500 ns < - 40 ns 3.0

< 10-12 Coverage excludes most o f Asia and South- ern Hemi sphere-new stations planned Cost Factor = M$.ns (user cost)

"Inaccuracy may increase t o 600 ns i f C/A code i s deteriorated f o r s t r a t e g i c reasons

**Cost includes estimate f o r annual r e n t

TABLE I.

making the system practically incompatible with requirements of high-precision standards laboratories and time services. Other laboratories are interested in the accuracy capabilities of primary frequency standards, either directly or indirectly, but adequate means for international frequency comparison do not exist at the state-of-the-art acpracy of the standards themselves. Other tech- niques of accurate time transfer have been tested experimentally or are planned for implementation in the future. A performance comparison of available and planned methods, including the proposed Shuttle experiment (Shuttle Time and Frequency Transfer Experiment, STIFT) is shown in table 1. The following defini- tions apply to the table. Inaccuracy is expressed relative to a perfect portable clock. Stability is the measure of time variations over the course of the meas- urement (i.e., related to the phase stability of the measurement system with sampling intervals and length of data determined by the method). Cost- effectiveness is the product of inaccuracy and user cost dollars (in mega-dollar nanoseconds), of course, the smaller the number the better. The 24-hour frequency accuracy is derived from time stability over 24 hours, which determines the accuracy of absolute remote frequency comparison for that sample time. Though many of the numbers represent anticipated performance, it is believed that they are well within an order of magnitude of what is feasible. Where applicable, the figures in the table I are rms values. As can be seen, the STIFT experiment looks extremely attractive, when compared with other techniques.

Microwave System. - A block diagram of the microwave system is shown in figure 3.

The key feature of the system is, for time durations longer than the signal round-trip time, that we obtain significant cancellation of several effects including the f i rst-order Doppler effect in the frequency comparison loop. The ground clock signal is first transmitted to the spacecraft and transponded back to the ground terminal to obtain the two-way Doppler shift, which is divided by two to generate the one-way Doppler shift, which in turn is subtracted from the one-way space clock downlink signal. The resulting beat signal at the output of the mixer is the frequency difference between the two clocks with the first-order Doppler shift removed. This process cancels propagation variations in the iono- sphere. In addition, this process cancels tropospheric delay, assuming reciproc- ity. The S-band transmission frequencies shown are those used with the Gravita- tional Probe A. The three frequencies were selected to compensate for ionospheric dispersion. A single antenna is used at the spacecraft and at the ground station for transmission of the three microwave links.

The frequency transfer uses the phase information of the CW phase-coherent

carrier signals. Time transfer is accomplished by modulation of the carrier

signals. The time code generated by the space clock is modulated on the clock

downlink and compared with the time code of the ground clock. The one-way propa-

gation delay, needed as correction for time transfer, is obtained from the range

r --- TIME WLSES 1

I HYDROGEN MASER TlME CODE

OSCILLATOR AND

I CLOCK SYSTEM 1

SPACECRAFT

CONTROL TRANSMITTER

ST l FT

M l CROWAVE SYSTEM

TRANSPONDED 2299.7 UPLINK CLOCK DOWNLINK

DOWNLINK MHZ 21 17.7 MHZ 2203.1 MHZ

TRANSMITER RANGE

PHASE - ^{CODE +}

MODULATOR GENERATOR

f ^{- STABLE FREQUENCY} _T ^{- CROSS} CORRELATION TIME OIFFERENCE

t ^INCLUDING

TIME PROPAGATION

H MASER

OSCILLATOR , ; DELAY

GROUND TERMINAL AND CLOCK ATSE = t , + i l f p R w -

f

PROPAGATION ZATPROPAGATION DELAY

C CORRECTION

7 t

DOPPLER-CANCELLED TlME COMPARISON FREQUENCY

COMPARISON 4 - ^'e

measurement accomplished by PRN phase modulation o f t h e transponded l i n k s . The t i m e d i f f e r e n c e between t h e two c l o c k s i s d e r i v e d from t h e delay o f t h e two t i m e codes.

One i m p o r t a n t o b j e c t i v e i s t h e development o f a low-cost, simple ground t e r m i n a l t h a t can be a f f o r d e d by a l a r g e number o f users o f an o p e r a t i o n a l STIFT system.

Laser System. - The short-pulse l a s e r technique i s t h e most accurate documented l i n e - o f - s i g h t method o f t i m e t r a n s f e r [2]. E x i s t i n g l a s e r ground s t a t i o n s can use STIFT f o r subnanosecond time t r a n s f e r i f they are equipped w i t h an atomic c l o c k and an event t i m e r . Because o f t h e h i g h e r accuracy, t h e short-pulse l a s e r technique can serve as a c a l i b r a t i o n t o o l f o r t h e microwave t i m e t r a n s f e r . It should a l s o p r o v i d e i n t e r e s t i n g d a t a on microwave versus l a s e r propagation through t h e atmosphere. Using t h i s technique, n e i t h e r t h e r e l a t i v e v e l o c i t y n o r t h e d i s t a n c e between space v e h i c l e and ground s t a t i o n s e n t e r s i n t o t h e c l o c k compari- son.

The l a s e r ground s t a t i o n t r a n s m i t s s h o r t l a s e r pulses which are r e t u r n e d by t h e corner r e f l e c t o r a r r a y on t h e space v e h i c l e . The r e f l e c t o r a r r a y i s equipped w i t h photodiodes t o d e t e c t t h e a r r i v a l o f t h e l a s e r pulses. The a r r i v a l t i m e t', o f t h e pulses i s measured i n t h e t i m e frame o f t h e onboard c l o c k by t h e event timer. T h i s i n f o r m a t i o n i s telemetered t o t h e l a s e r ground s t a t i o n which measures t h e t i m e o f transmission, t,, and r e c e p t i o n , t, o f t h e l a s e r pulse. From t h i s data, t h e t i m e d i f f e r e n c e between t h e space c l o c k and t h e ground c l o c k can be determined w i t h an accuracy o f 1 ns o r b e t t e r .

Picosecond Timing from Microwave Cycle I d e n t i f i c a t i o n . - There i s no convenient

way t o d i v i d e down from t h e S-band s i g n a l and r e t a i n an unambiguous i d e n t i t y o f a

p a r t i c u l a r c y c l e o f t h e microwave s i g n a l . However, picosecond phase measurements

can be made i f t h e clocks, t h e medium, and t h e ephemeris e r r o r s a r e known w i t h

s u f f i c i e n t l y small u n c e r t a i n t i e s . I n t h i s case, i t i s p o s s i b l e t o r e s o l v e a

p a r t i c u l a r c y c l e from one o r b i t o f t h e S h u t t l e t o t h e n e x t o r from one s i t e t o

another. Once a p a r t i c u l a r c y c l e has been i d e n t i f i e d , we can use i t s phase o r

zero c r o s s i n g f o r t i m i n g on a r e p r o d u c i b l e basis. When t h i s i s accomplished, t h e

STIFT experiment becomes t h e most p r e c i s e o f any o f t h e i n t e r n a t i o n a l methods o f

T/F comparisons being considered. The basic l i m i t o f t h i s method i s t h e repro-

d u c i b i l i t y and s t a b i l i t y o f t h e microwave system, which has been p r e v i o u s l y

documented t o be a t t h e 1 t o 10 ps l e v e l f o r i n t e g r a t i o n times o f t h e o r d e r o f

t h e S h u t t l e o r b i t p e r i o d [3]. I f t h e 10 ps l e v e l o f s t a b i l i t y can be m a i n t a i n t e d

over a day o r longer--and t h e r e i s good evidence t h a t t h i s can be done-then one

can make frequency comparisons o f 1 p a r t i n 1016 o r b e t t e r a t one day o r longer

w i t h t h i s method.

C8-404 JOURNAL DE PHYSIQUE

The p e r i o d o f t h e downlink microwave s i g n a l i s 454 ps. Therefore, one would l i k e t o keep rms e r r o r s w e l l below 1 r a d i a n a t t h a t frequency, which would be 72 ps, i n o r d e r t o r e s o l v e a p a r t i c u l a r c y c l e . The c o n t r i b u t i o n s t o t h a t uncer- t a i n t y a r e represented as t h e root-sum-square ( r s s ) o f terms i n t h e f o l l o w i n g e q u a t i o n where t h e f i r s t term i s due t h e r e l a t i v i s t i c u n c e r t a i n t i e s from t h e e r r o r s i n t h e ephemeris d e t e r m i n a t i o n o f t h e o r b i t i n g clock. The second term i s due t o t h e random u n c e r t a i n t i e s o f t i m e p r e d i c t a b i l i t y o f t h e onboard c l o c k i t s e l f and t h e l a s t term r e s u l t s from u n c e r t a i n t i e s i n t h e o v e r a l l delay from t h e space c l o c k t o t h e ground clock.

We have i n v e s t i g a t e d t h e u n c e r t a i n t i e s i n t h e ephemeris determi n a t i o n g i v e n t h e i d e a l case o f a s a t e l l i t e i n f r e e f a l l and being ranged w i t h t h e l a s e r system and/or a l t e r n a t i v e l y w i t h t h e microwave-integrated Doppler technique. The uncer- t a i n t i e s i n o r b i t d e t e r m i n a t i o n f o r t h e f r e e f a l l c o n d i t i o n compared f a v o r a b l y w i t h those f o r GEOS-3 [11,12]. The e r r o r s f o r t h e S h u t t l e experiment were e s t i - mated t o be about 15 ps (see below). To account f o r S h u t t l e drag, s o l a r pressure, and space maneuvers, i t w i l l be assumed t h a t an onboard i n e r t i a l guidance system i s a v a i l a b l e t o monitor non-gravi t a t i o n a l a c c e l e r a t i o n s . Such a c c e l e r a t i o n s can be used t o compute p e r t u r b a t i o n s i n t h e f r e e - f a l l o r b i t . Peak u n c e r t a i n t i e s due t o these p e r t u r b a t i o n s are estimated t o be about 35 meters f o r t h e 1% hour S h u t t l e o r b i t s C131. C l e a r l y , a l l o f t h e terms w i l l be dependent on t h e i n t e g r a t i o n time, which may range from 1% hours t o 24 hours f o r v a r i o u s experiments. Taking t h e case o f t h e S h u t t l e p e r i o d o f 1% hours, a 35 meter peak ephemeris e r r o r would l e a d t o about 13 ps rms u n c e r t a i n t y i n t h e g r a v i t a t i o n a l r e d s h i f t e f f e c t . The v e l o c i t y d e t e r m i n a t i o n u n c e r t a i n t y i s o f t h e order o f about 2 cm/s, which would y i e l d an u n c e r t a i n t y i n t h e second-order Doppler e f f e c t o f l e s s than 1 ps over t h a t same i n t e g r a t i o n time. F i g u r e 4 shows t h e rms t i m e d i s p e r s i o n t i m e charac- t e r i s t i c s o f t h e hydrogen maser and o f t h e microwave system as transformed from t h e s t a b i l i t y d a t a shown i n f i g u r e 5; one observes about 9 ps rms e r r o r f o r a hydrogen maser c l o c k a f t e r 1% hour i n t e g r a t i o n time.

The a b s o l u t e delay from t h e l a s t term i n equation (1) cannot be known w i t h

an accuracy o f l e s s than 72 ps (except perhaps w i t h t h e l a s e r r a n g i n g system),

b u t t h e s t a b i l i t y o f t h e microwave measurement system makes r e p r o d u c i b i l i t y

p o s s i b l e a t an accuracy l e v e l o f about 10 ps over t h e 1$ hour i n t e g r a t i o n time

(see f i g u r e 4). Hence, one knows t h a t t h e t o t a l p a t h d e l a y i s an i n t e g r a l number

o f c y c l e s o f t h e microwave s i g n a l and, u s i n g modular a r i t h m e t i c , one can deduce

r a t h e r than measure t h e delay, and hence i d e n t i f y a p a r t i c u l a r c y c l e o f t h e

microwave s i g n a l . I n o t h e r words, we can p r e d i c t t h e S h u t t l e c l o c k t i m e t o an

rms l e v e l o f about 18 ps from t h e previous pass t o t h e c u r r e n t one w i t h r e s p e c t

t o t h e ground c l o c k t i m e u s i n g our estimates o f t h e S h u t t l e ephemeris. We o b t a i n

(1 979 DATA)

I 10 102 103 ¹⁰⁴ lo5 r ⁰⁶

PREDICTION TIME, Tp (seconds)

F i g u r e 4. - An estimate o f t h e rms p r e d i c t i o n e r r o r o f t h e microwave system and o f t h e hydrogen maser c a l c u l a t e d from t h e frequency s t a b i l i t y d a t a i n F i g . 5.

NASA SPACE SHUTTLE EXPERIMENT

F i g u r e 5. - ^A comparison o f t h e f r a c t i o n a l frequency s t a b i l i t y (square r o o t o f

t h e A l l a n variance) f o r a v a r i e t y o f sampling times. The dates g i v e n be each

curve i n d i c a t e when t h e s t a b i 1 i t i e s were determined o r when t h e i r d e t e r m i n a t i o n

i s a n t i c i p a t e d . The Loran-C d a t a i s f o r ground-wave transmissions. The microwave

p u l s e and l a s e r p u l s e systems a r e p r o j e c t e d s t a b i l i t i e s from p r e v i o u s l y obtained

r e s u l t s . I t i s i n t e r e s t i n g t h a t t h e maser has i t s b e s t s t a b i l i t y f o r t h e o r b i t

p e r i o d o f t h e S h u t t l e .

C8-406 JOURNAL DE PHYSIQUE

from t h e previous measurement, a t i m e d i f f e r e n c e and a delay f a c t o r . Using these measures, we c a l c u l a t e t h e c u r r e n t p r e d i c t e d t i m e d i f f e r e n c e and delay value and compare i t w i t h what i s measured. T h i s comparison d i f f e r e n c e i s an i n t e g e r m u l t i p l e o f t h e microwave p e r i o d p l u s an e r r o r i n p r e d i c t i o n p l u s t h e i n s t a b i l i - t i e s i n t h e microwave system, which t h i s paper shows can be k e p t w e l l below t h e 72 ps level-thus a l l o w i n g us t o c a l c u l a t e t h e above i n t e g e r . Knowing t h i s i n t e g e r a l l o w s us t o remeasure t h e t i m e d i f f e r e n c e o f t h e S h u t t l e c l o c k w i t h r e s p e c t t o t h e ground c l o c k l i m i t e d o n l y by t h e i n s t a b i l i t i e s i n t h e microwave system. The tremendous leverage gained by t h i s technique i s obvious and would a1 1 ow i n t e r n a t i o n a l t i m e and frequency comparisons a t super-accurate 1 eve1 s. The ground s t a t i o n would r e q u i r e b o t h a c l o c k w i t h s i m i l a r low t i m e d e v i a t i o n f o r t h e i n t e g r a t i o n time o f i n t e r e s t , as w e l l as a microwave s t a t i o n . We have plans t o develop such a s t a t i o n so t h a t i t i s economically f e a s i b l e f o r several o f these t o e x i s t a t key l o c a t i o n s around t h e globe.

F i g u r e 5 shows an o v e r a l l f r a c t i o n a l frequency s t a b i l i t y comparison o f some standards and comparison methods r e l e v a n t t o t h e STIFT a c t i v i t y . The n e t e f f e c t o f microwave c y c l e i d e n t i f i c a t i o n on t h i s p l o t i s t o continue "SAO CW System 1976 R e d s h i f t " curve going down n o m i n a l l y as t - l from where i t ends on t h e r i g h t .

F r e e f a l l O r b i t Determination. - We n e x t discuss t h e accuracy w i t h which t h e S h u t t l e ephemerides can be determined. Assuming t h a t nongravi t a t i o n a l accelera- t i o n s o f t h e S h u t t l e can be monitored, we a r e here p r i m a r i l y i n t e r e s t e d i n g r a v i - t a t i o n a l and o t h e r systematic e f f e c t s . The g r a v i t y model GEM 10 [11,12] i n c o r p o r - a t e s s u r f a c e g r a v i t y d a t a and represents one o f t h e b e s t a v a i l a b l e models f o r t h e g r a v i t y f i e l d experienced by t h e S h u t t l e , which i s i n a r e l a t i v e l y low o r b i t . Model GEM 10 i s c h a r a t e r i z e d by t h e presence o f a l a r g e number o f h i g h e r harmonics ( o f degrees 10 t o 20) i n t h e p o t e n t i a l , whose c o e f f i c i e n t s have f r a c t i o n a l uncer- t a i n t i e s o f approximately 0.1 t o 0.3.

Evaluations o f t h e GEM 10 model f o r p r e d i c t i n g t h e o r b i t o f GEOS-3, a space- c r a f t w i t h an a l t i t u d e o f about 840 km, showed t h a t t h e s p a c e c r a f t p o s i t i o n c o u l d be p r e d i c t e d t o w i t h i n about two o r t h r e e meters. However, t h i s r e q u i r e d r e f i n e d modeling which i n c l u d e d l u n a r and s o l a r t i d a l g r a v i t a t i o n a l p e r t u r b a t i o n s , s o l a r r a d i , a t i o n pressure on t h e s a t e l l i t e , p o l a r motion, UT1 data, ocean t i d e s , and s o l i d e a r t h t i d e s ; t h e p r e d i c t i o n u n c e r t a i n t y r e f l e c t s numerous e r r o r s besides ephemeris e r r o r s .

For a S h u t t l e i n an o r b i t o f 370 km a l t i t u d e , u n c e r t a i n t i e s i n h i g h e r har-

monics o f t h e g r a v i t a t i o n a l f i e l d o f t h e e a r t h c o u l d be expected t o c o n t r i b u t e

two o r t h r e e times t h e u n c e r t a i n t i e s t h e y c o n t r i b u t e t o t h e GEOS-3 o r b i t p r e d i c -

t i o n . Thus, u s i n g GEM 10, one would n o t expect p r e d i c t e d o r b i t p o s i t i o n s t o be

i n e r r o r by more t h a n about 10 meters; i f h i g h - a c c u r a c y t r a c k i n g data i s a v a i l a b l e

from many s t a t i o n s d i s t r i b u t e d about t h e e a r t h 1 s surface, t h i s f i g u r e c o u l d be

s i g n i f i c a n t l y reduced. The 10 meters t r a n s f o r m i n t o a c l o c k e r r o r o f o n l y 8 ps

f o r a S h u t t l e o r b i t . We have taken a conservative 20 l i m i t o f 16 ps f o r t h e pur- poses o f t h i s paper.

R e l a t i v i s t i c C o r r e c t i o n s t o S a t e l l i t e Clock Time. - We adopt t h e p o i n t o f view t h a t t h e c e n t e r o f mass o f t h e e a r t h , as i t f a l l s f r e e l y i n t h e g r a v i t a t i o n a l f i e l d o f t h e sun, p r o v i d e s an o r i g i n f o r a l o c a l , n o n r o t a t i n g , i n e r t i a l frame, and t h a t a worldwide network o f c o o r d i n a t e c l o c k s synchronized i n such a r e f e r - ence frame i s our o b j e c t i v e [14]. The presence o f t h e e a r t h i t s e l f and t h e l o c a t i o n o f standard t i m e and frequency l a b s on t h e s u r f a c e o f t h e r o t a t i n g e a r t h r e q u i r e t h a t c l o c k s i n motion i n t h e l o c a l frame must have r e l a t i v i s i t i c cor- r e c t i o n s a p p l i e d t o them i n order t o o b t a i n readings o f " c o o r d i n a t e time" i n t h e l o c a l i n e r t i a l frame. The c o r r e c t i o n s f o r t h e s a t e l l i t e c l o c k r e l a t i v e t o a c l o c k on t h e g e o i d have been d e r i v e d elsewhere (e.g., Ashby and A l l a n , 1979) [14], and a r e g i v e n by

Atrltv = _{p a t h} J d s [g ^-

21

where ds i s t h e increment o f proper t i m e elapsed on t h e standard c l o c k , v i s t h e v e l o c i t y o f t h e s a t e l l i ' t e w i t h r e s p e c t t o t h e l o c a l i n e r t i a l frame, V i s t h e g r a v i t a t i o n a l p o t e n t i a l due t o t h e e a r t h ' s mass, and Vo i s t h e e f f e c t i v e g r a v i - t a t i o n a l p o t e n t i a l o f a p o i n t a t r e s t on t h e geoid, i n c l u d i n g t h e e f f e c t s due t o r o t a t i o n . The expression f o r V i s

where r i s t h e d i s t a n c e o f t h e s a t e l l i t e from t h e e a r t h ' s center, al i s t h e e a r t h ' s e q u a t o r i a l r a d i u s , 8 i s t h e c o l a t i t u d e , and J, i s t h e quadrupole moment c o e f f i c i e n t o f t h e earth. Also,

where we i s t h e angular r o t a t i o n a l speed o f t h e earth. Values o f t h e constants GMe, al, J,, and w a r e g i v e n i n t a b l e 11.

e

C8-408 JOURNAL DE PHYSIQUE

Table 11. - Values o f Useful Constants

w r o t a t i o n a l angular v e l o c i t y o f t h e e a r t h e ' = 7.292115 x rad/s

J,, quadrupole moment c o e f f i c i e n t f o r e a r t h

= 1.08263 x

GMe, e a r t h ' s mass times g r a v i t a t i o n a l constant - 3.9860045 + 0.0000002 x 1014 m3/s2 [15]

al, e q u a t o r i a l r a d i u s o f t h e e a r t h

= 6.378140 x lo6 m.

The value o f Vo/c2 obtained from these constants i s

If t h e quadrupole term were neglected, an e r r o r o f about 4 x 10-l3 would be introduced.

The r e l a t i v i s t i c c o r r e c t i o n s can then, w i t h t h e n e g l e c t o f t h e quadrupole c o r r e c t i o n terms, be expressed e x a c t l y i n terms o f t h e o r b i t a l elements as follows:

where AE i s t h e change i n e c c e n t r i c anomaly, and A t i s t h e change i n t h e coordin- a t e time.

Using t h e r e l a t i o n between t h e e c c e n t r i c anomaly and coordinate time, t h e change i n e c c e n t r i c anomaly i s

where A ( s i n E) = s i n Efinal - s i n Einitial i s t h e change i n t h e s i n e o f t h e e c c e n t r i c anomaly. Then t h e r e l a t i v i s t i c c o r r e c t i o n can a1 so be expressed as

We now examine t h e s e n s i t i v i t y o f t h i s c o r r e c t i o n , t o e r r o r s i n each o f t h e

parameters on which i s depends. I f t h e elapsed c o o r d i n a t e time, At, can be

determined to f 1 ms, then the uncertainty in the last term, VoAt/c2, is less than a picosecond. We shall assume that GMe is a known quantity having the value given in table 11. The effect of an error, 6(GMe), on the calculation of the relativistic correction, Atrl tv, may be estimated by calculating the following quantity:

The uncertainty in GMe is

The orbit eccentricity is typically very small; using e = 0.003, orbit altitude = 360 km, At = 5500 s for one orbit, the error in the correction becomes approxi- mately

Such a small uncertainty may safely be neglected.

The effect of errors in the knowledge of the other parameters appearing on the right side of equation (7) may similarly be estimated by differentiating with respect to the appropriate quantity. We then find, for a Shuttle orbit of alti- tude 370 km and eccentricity 0.003, that an uncertainty of 10 m in semi-major axis contributes an uncertainty of about 8 ps per revolution; an uncertainty of in e contributes about 2.4 ps, and an uncertainty in At of 1 ms contributes 1.6 ps.

There are two additional small effects which merit some discussion. First,

the slightly non-spherical mass distribution of the earth gives rise to higher

multipole contributions to the gravitational potential. The largest of these is

the earth's quadrupole moment, which gives a potential approximately a factor of

10-3 smaller than the principal monopole term. The gravitational redshift on a

satellite clock due to this term depends on the orbit inclination, position of

perigee, and initial and final longitudes. An estimate of the quadrupole poten-

tial's effect on an equatorial orbit at an altitude of 360 km is sufficient to

show that the net effect is quite small. For one orbital revolution, the required

C8-4 1 0 JOURNAL DE PHYSIQUE

correction due to the quadrupole potential is about 2 ns. This is a systematic effect which can be modeled quite accurately. Even if only the quadrupole term is retained, the error in estimation of this effect is only about 5 parts in lo4 of the effect itself, and hence, is about 1 ps or less.

Second, the process of synchronization of the satellite clock with a ground station by means of transmission of electromagnetic signals cannot be thought of simply in terms of Einstein synchronization and, since the earth is rotating with respect to the local inertial frame, a relativistic correction must be included.

If tA is the coordinate time of emission of a synchronizing signal from the ground station at position ;A, t;\ is the time of arrival of the signal at the satellite at position ;A, ee is the angular velocity of the earth, and t is the total round trip time of the signal as measured on the ground station clock, then (Ashby and A1 lan, 1979) [I41

The correction term depends on the angles between the angular velocity vector,

+ 1 +

we, and the vector area, 3 = 7 rA x of the triangle enclosed by the radius vectors to the positions of the ground station and the satellite. For obser- vation of the satellite within an acceptance cone of lo0 or greater elevation, and for a satellite altitude of h = 360 km, the magnitude of the area, A, is at most 2 1 rA(rA + h) sin ll.ZO = 4.17 x106/km2, while 2 ue/c2 = 1.6227 x ns/km2.

Thus, if the ground station is at a latitude of 40°, the correction is of maximum magnitude, 5.2 ns. By choosing the instant of synchronization close to that during which the satellite and the ground station lie in the same north-south plane, so that the angle between 3 ^and ee is close to 90°, the correction can be made very much smaller. This correction is also systematic and can be computed to a high accuracy in a specific application. In this example, an error of 100 m in the knowledge of the altitude of the satellite would introduce an error into the computation of this correction to Einstein synchronization of 0.2 ps at most.

Other time transfer processes, such as by means of signals from the satellite to the ground and back, involve errors of comparable magnitude.

For a satellite in a high orbit, the uncertainties in predicted position arising from uncertaintites in the gravity model should be significantly reduced.

Figure 6 shows the orbit of a satellite of 12-hour period projected on the earth's surface. The orbit is nearly equatorial; the orbit parameters are: semi-major axis, a = 26,610 km; inclination, I = 0.5O. Intersection with observation cones, of lo0 elevation angle, from NBS and USNO are shown. The shaded area is the area within which the satellite may be received simultaneously from NBS and USNO. We

have carried out a worst-case systematic error analysis of the satellite orbit

determination problem for this satellite, assuming that the gravity field can be

modeled a c c u r a t e l y by a s i n g l e term i n t h e p o t e n t i a l . Assuming l a s e r r e t r o r e f l e c - t o r t r a c k i n g d a t a o f 2 cm accuracy a r e a v a i l a b l e from b o t h NBS and USNO, t h e r e s u l t i n g e r r o r s i n Atrltv a m l e s s than 1 ps. One may a l s o use i n t e g r a t e d Doppler t r a c k i n g w i t h t h e microwave system; i n t h i s case, e r r o r s i n t h e determin- a t i o n o f Atrltv are even l e s s .

NBS USNO COMMON VIEW

-180 -150 -120 -00 -80 -30 0 30 80 90 120 160 180 LONGITUDE

F i g u r e 6. - P r o j e c t i o n o f sate1 1 i t e o r b i t on t h e e a r t h ' s s u r f a c e f o r an e q u a t o r i a l o r b i t o f 12-hour p e r i o d , I = 0.5O, and i n t e r s e c t i o n w i t h o b s e r v a t i o n cones, o f

l o 0 e l e v a t i o n angle, from NBS and USNO. The shaded area i s t h e area w i t h i n which t h e s a t e l l i t e may be r e c e i v e d simultaneously from NBS and USNO. The p r o j e c t i o n o f t h e o r b i t l i e s p r a c t i c a l l y on t o p o f t h e equator.

Plans and Conclusions. - The STIFT concept w i l l a1 low worldwide t i m e and frequency comparisons and/or measurements a t o r below 1 ns and 1 x 10-14, r e s p e c t i v e l y . I n a d d i t i o n , i f unique i d e n t i f i c a t i o n o f a c y c l e o f t h e 2.2 GHz downlink frequency can be made, then i t s phase can be used f o r t i m i n g . Nominally, t h i s would y i e l d 10 ps t i m i n g p r e c i s i o n and 1 x 10-l6 frequency measurements and comparisons. As has been shown i n t h e t e x t , t h i s can be accomplished i f t h e rms e r r o r o f t h e S h u t t l e o r s a t e l l i t e c l o c k time can be k e p t below t h e l i m i t o f about 72 ps (1 radian). There are t h r e e sources c o n t r i b u t i n g t o t h i s rms e r r o r : 1) f o r t h e 1%

hour S h u t t l e o r b i t p e r i o d , t h e random u n c e r t a i n t y due t o t h e S h u t t l e c l o c k i t s e l f

i s about 9 ps; 2) t h e r e l a t i v i s t i c u n c e r t a i n t i e s a r i s i n g from u n c e r t a i n t i e s i n

t h e f r e e - f a l l S h u t t l e o r b i t d e t e r m i n a t i o n a r e w o r s t case about 16 ps rms; and 3)

t h e same u n c e r t a i n t i e s a r i s i n g from o r b i t a l p e r t u r b a t i o n s due t o s o l a r pressure,

drag, maneuvers, e t c . as would be estimated from an onboard i n e r t i a l guidance

system a r e about 13 ps. The root-sum-square o f t h e above leads t o an o v e r a l l

S h u t t l e c l o c k time u n c e r t a i n t y o f 22 ps, which i s n i c e l y below t h e 72 ps l i m i t .

C8-4 1 2 JOURNAL DE PHYSIQUE

Knowing t h e S h u t t l e c l o c k t i m e w i t h t h i s l e v e l o f u n c e r t a i n t y a l l o w s us t o c a l - c u l a t e t h e delay from pass t o pass, since i t i s modulo one c y c l e o f t h e c a r r i e r (15 cm o r 454 ps) t o a l e v e l which i s o n l y l i m i t e d by t h e i n s t a b i l i t i e s i n t h e microwave system-approximately 10 ps o r 3 mm.

With t h e a b i l i t y t o use t h e microwave system f o r t i m i n g a t t h e few p i c o - second l e v e l on a w o r l d wide b a s i s , a whole s e t o f new experimental o p p o r t u n i t i e s open up b o t h i n terms o f experiments i n v o l v i n g accurate t i m e metrology as w e l l as i n accurate frequency metrology on an i n t e r n a t i o n a l basis. I n a d d i t i o n , i t r e l i e v e s t h e need t o have a l a s e r r a n g i n g system t o do subnanosecond t i m i n g except as may i n i t i a l l y be needed a t some s i t e s , as a c a l i b r a t i o n check and f o r s p e c i a l propagation studies. I f t h e time s t a b i l i t y o f t h e STIFT microwave meas- urement system p e r s i s t s a t about t h e 10 ps l e v e l , and t h e r e i s good i n d i c a t i o n t h a t i t w i l l , then t h e STIFT approach would a l l o w one t o make worldwide frequency comparisons w i t h an u n c e r t a i n t y o f about 1 x 1 0 - l 6 f o r one day, 1 x 1 0 - l 7 f o r 10 days, etc. This opens up o p p o r t u n i t i e s f o r s t u d y i n g w i t h much g r e a t e r accuracy:

s p e c i a l and general r e l a t i v i s t i c e f f e c t s , changes i n some o f t h e fundamental constants, etc. I n a d d i t i o n , VLBI s t a t i o n s c o u l d r e f e r e n c e t h e same frequency standard and t h u s have t h e same coherent source t o w i t h i n a few picoseconds a t each s t a t i o n , which c o u l d g r e a t l y enhance r a d i o astronomy d a t a reduction.

We p l a n t o do more work on t h e a n a l y s i s o f e r r o r s i n t h e d e t e r m i n a t i o n o f r e l a v i s t i c e f f e c t s on coordinate t i m e a t t h e picosecond l e v e l . I n p a r t i c u l a r , we i n t e n d t o examine more c a r e f u l l y t h e e f f e c t s o f n o n - g r a v i t a t i o n a l accelera- t i o n s due t o atmospheric drag and space maneuvers, which p e r t u r b s t h e f r e e - f a l l s a t e l l i t e o r b i t , as w e l l as c o n t r i b u t i o n s t o u n c e r t a i n t i e s i n t h e s a t e l l i t e ephemeris due t o u n c e r t a i n t i e s i n modeling t h e g r a v i t y f i e l d . V e r s a t i l e software packages have been developed which w i l l a l l o w us t o consider any v a r i e t y o f s i t e s , o r b i t i n c l i n a t i o n s , e c c e n t r i c i t i e s , and a l t i t u d e s . We a n t i c i p a t e t h a t t h e STIFT experiments would be f l o w n i n t h e ' 8 5 o r '86 time frame and we have r e c e i v e d i n d i c a t i o n s from several p r i n c i p a l t i m i n g c e n t e r s t h a t t h e y would l i k e t o p a r t i c i - p a t e i n t h e experiments.

Acknowlegements. - The authors wish t o express a p p r e c i a t i o n t o Dr. Peter Bender and Dr. Fred L. Walls, who have p r o v i d e d v e r y meaningful suggestions and comments.

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