A DIRECT MEASUREMENT OF THE RELATIVISTIC EFFECT OF THE GRAVITATION POTENTIAL ON THE RATES OF ATOMIC CLOCKS FLOWN IN AN AIRCRAFT by Ralph Emerson Williams PP/I 76-233 Dissertation submitted to the Faculty of the Graduate School of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1976 I , _. APPROVAL SHEET Title of Thesis : A Direct Measurement of the Relativistic Effect of the Gravitational Potential on the Rats of Atomic Clocks Flown in an Aircraft Name of Candidate : Ralph Emerson Williams Doctor of Philosophy, 1976 Thesis and Abstract Approved: C . O. Alley Professor I Department of Physics and Astronomy Date Approved : / / /( ABSTRACT Title of Thesis: A Direct Measurement of the Relativistic Effect of the Gravitational Potential on the Rates of Atomic Clocks Flown in an Aircraft Ralph Emerson Williams, Doctor of Philosophy, ]976 Thesis directed by: C. 0. Alley Professor Department of Physics and Astronomy General relativity predicts that standard clocks placed at differ- ing gravitational potentials will run at different rates. Although ex- periments confirming the gravitational redshift have been done, they in- volve frequency and not time, and need not appeal to general relativity for explanation. Therefore, considerable interest exists as to the re- sult of an accurate experiment in which real macroscopic clocks are brought together for comparison before and after separation to differing potentials. This experiment consists of flying an ensemble of atomic clocks in a military aircraft and comparing them before and after flight to an- other clock ensemble remaining on the ground. The ground ensemble in- cluded several Hewlett-Packard Cesium Beam clocks, three Efratom optical- ly pumped Rubidium clocks, and two hydrogen masers. The flying ensembl e included at least three Hewlett-Packard Cesium clocks and three Efratom Rubidium clocks. Five of the Cesium clocks were new mod els deliver ed with a high beam current option r esulting in hi ghe r s t ability tha n s t a n- dard models. The clocks were ma int a ined und er s tringent environmenta l controls to protect against vibration, magnetic fields, and changes in temp e r a ture, press ure, and power supply voltage . Five main flights were made, each at approximately 30,000 feet altitude for fifteen hours. The aircraft was continuously tracked by a theodolite calibrated radar which obtained position and velocity measurements for every second of flight. This allowed an accurate calculation of a theoretical prediction to compare to experiment. The flying clocks gained approximately 45 nanoseconds (45 x 10- 9 s) with respect to the ground clocks. The normalized results (measured effect divided by predicted effect) and the experimental standard deviations of the mean for each of the five flights were as follows: .999 + .016 .977 + .026 .963 + .013 1.002 + .026 .991 + .037 The result for the entire experiment, with standard deviation of the mean, was .987 ?. .011. The statistically expected standard deviation of the mean based on knowledge of clock quality was approximately .015. Considering this result as well as systematic errors, a final result is established of Measured value 0.987 + .016 Predicted value PREFACE Aqs9lute, true, and mathematical time, of itself, and from its own nature, flows equably witho ut relation to anything external ... (Isaac Newton, Principia) A priori it is not at all necessary tha t the "times" ... in different inertial frames agree with one another . One ized this long ago if, in the practical would have real experience of everyday life, light did n ot appear (because of of its high speed) as a means for the d etermination absolute simultaneity. (Albert Einstein, "Autobiographical Note s") And time, that takes survey of all the w orld (Shakespeare, Henry IV, Part]) Time Discovers Truth. (Lucius Seneca, Moral Essays, first cent ury A.D.) ii ACKNOWLEDGEMENTS It should be noted that the entire experiment of which this thesis is~ ptirt was of extensive complexity with relatively few people to carry the load. Many of us consistently worked well over fifteen hours a day and were away from home with few respites for months on end . I would therefore be remiss if I neglected to list those people with whom I shared those months: Dr. C. O. Alley - my thesis advisor, who conceived the experiment, obtained continuing funding, and was principal investigator. Robert Reisse - my fellow graduate student who is obtaining a thesis on another aspect of the experiment. Stephen Davis John Mullendore - other staff members of the Quantum Electronics Group of the Department of Physics and Astronomy John Rayner of the University of Maryland. Charles Steggerda Robert Merritts - our liaison man at the Patuxent Naval Air Test Center who was stuck with us night and day for over nine months costing him much of his spare time. Dr. Leonard Cutler - Director of the Physics Laboratory of Hewlett- Packard. He was the original designer of the HP Cesium clocks and worked long and hard in those periods he spent with us. I would like to list a few of the other persons who, although not as continually involved as those above, nevertheless aided the development and success of the experiment: iii iv ernot Winkler - Director of the Time Service Division of the Dr. G U.S. Naval Observatory. He lent us most of our clocks an d provided moral and political support. Don Kaufman and Joe Soucy - of NASA Goddard Space Flight Center. They came down many times to look after the hydrogen masers le nt to us. Ron Hyatt , Joe Bourdet, Richard Lacy, Chuck Little - of Hewlett-Packard who aided in the cesium clock preparations. The many other people, too numerous to mention, at Patux ent Naval Air Test Center who gave much of their time, often at odd ho urs. Harold Lowry of the tracking facility is especially thank ed. Many members of the University of Maryland Physics and A stronomy faculty, electronics shop, and main shop. Dr. Jean-Paul Richard a ided with several suggestions early in the program. Ernst Jechart - of Efratom, who lent us some of our Rubid ium clocks. My wife and the wives of those above, who probably suffer ed as much as we. TABLE OF CONTENTS Chapter Page PREFACE ??.... ? ? . ... ? ? ? ?.... . . . ..?? ?.. .... . .. ? .?..??..?. ? .?.?.??...?? ii ACKNOWLEDGEMENTS ...?. . .?.... . ..?.. ? . ? ..?.?.?..?.??..?..?.???...?.?? iii I. INTRODUCTION.......... . . . .. . ...... . ...................... . 1 II. CLOCKS, PACKAGING, AND ENVIRONMENTAL CONTROLS .?..?.??.?... 11 A. The Clocks. ? ? . . ? ? ? ? ? ? ? . ? ? . ? . ? ? ? ? ? ? ? ? ? ? . . . ? ? ? ? . ? ? . . ? 11 B. The Cesium Clock Box...... . ... . ......... . .......... 16 C. The Rubidium Clock Box ??.?.????.?..???..?.??.?????? 22 D. Other Clock Box Features .?.?.?...???.?.???? ? ??.?..? 23 III. DATA ACQUISITION. ? . ? . . . ? ? ? ? ? ? ? . ? . . ? ? . ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? . ? . ? ? ? 26 A. General. ? . . . . ? . ? . ? ? . ? ? ? . . ? ? ? ? . ? . . ? ? ? . ? . ? ? ? ? ? . . . . . . ? 26 B. The Event Timer ..???.???????.??????????..?????.???? 26 C. The Digital Phase Measurement...................... 28 D. The Analog Data................... . .... . ........... 29 IV. SOFTWARE CAPABILITY AND DATA MANIPULATION ???......???.??.. 32 A. The Raw Data Files............... ? ? ? ? . . ? ? ? ? ? ? . ? ? ? ? . 32 B. The Translated Data Files ?...????????.?????? ? ..?.?. 33 C. Data Plots and the Graphics Terminal ?...?...?????.. 35 D. Manipulation and Analysis Programs ???.?.??.?????.?. 37 V. THEORY AND THE PREDICTION OF THE EFFECT ?..?...?.??.?..?... 42 A. The General Relativis tic Effect.................... 42 B. Prediction of the Eff e ct ?...??..?..?.?.???????.?..? 43 C. Range Dat a Ac c uracy . . . . . . . . . . ? . . . . . . . ? ? ? ? . ? . . . . ? ? . ? 46 I 1- Chapter Page VI. STATISTICS................................................ 50 A. Preliminary Concept s ?.........? ? ?... ? ...???.?...... 50 B. Computation of Variances .....?.?..?....???.??????.? 51 C. Projection of Phase ...?????.???.?.??..???..?...???? 54 D. Combinations of Measurements..... . ................. 57 VII. RESULTS AND INTERPRETATIONS............ . .................. 62 A. Introduction............... . . . . . ................... 62 B. The Principal Results ? ? ???.????????? ? ???.?.??.????? 63 C. The Other Clocks ...???????.?.?????? ? ????????..????? 66 APPENDIX A. CIRCUIT DIAGRAMS..................................... 83 APPENDIX B. ENVIRONMENTAL COEFFICIENTS OF THE CLOCKS ?????.????... 94 APPENDIX C. A THEOREM FOR CALCULATING VARIANCES ?..?..?...?????.?? 98 APPENDIX D. DATA PLOTS FOR THE FIVE FLIGHTS ????????..?????????.?? 100 APPENDIX E. LISTING OF VARIOUS PROGRAMS ???????????.?????????????? 156 BIBLIOGRAPHY ?.?.???.??? ? .??..??????.?????.???????.???????.???????? 172 LIST OF FIGURES Figure Page 1. P3-C aircraft in flight....................................... 6 2. Pre and post flight configuration with the aircraft near the equipment trailer. ................................ 6 3. Clock box with lid removed. ... ......... ...... .... . .. . ......... 7 4. The clock box lid. . . . . . . . . . . . . . . . . . . . . . . . . . . . ? . ? . . . . . . . . . . . . . . 7 5. The Rubidium clock box. . . . . . . . . . . . . . . ? . . . . . . ? . . . . . . . . . . . . . . . . . 8 6 . . The clock box in position in the aircraft..................... 8 7. Floor plan of the P3-C aircraft showing the equipment location. 9 8. Map showing the flight path of the aircraft .... . .............. 10 9. Schematic diagram of the clock box............ . .. . .. ... ...... . 24 10. Block diagram of the clock box ................ ?.. ..... .. ..... . 25 11. Signal switching diagram................... . .................. 31 12. An example of the program PHASEPLOT ............... ...... .. . .. . 38 13. An example of the program SRESIDUALS ..............?........... 39 14. An example of the program RESIDUALS ........................... 40 15. An example of the program SIGMATAU ............................ 41 16. The relation of range coordinates to inertial system coordinates49 17. Sigma-tau plot for the principal Cesium clocks ........... .. ... 59 18. Sigma-tau plot for the Rubidium clocks and H-maser ............ 60 19. Typical form of phase data ..................... ..... ? ? .. ? ? ? ? ? ? 61 20. Typical form of phase data over a flight ...... . ............... 61 21. Typical form of phase data with slope removed ................. 61 Fi gure Page 22. Graph of the theoretical predic tion for flight 1 (9/29) ....... 69 23. Graph of the theoretical pr edi c tion f or flight 2 (11/11) ...... 70 24. Graph of t he theore t ica l pr edi c tion for fli ght J (11/14) ..... . 71 25 . Graph of the theore tical predic tion for flight 4 (11/22) ...... 72 26. Graph of the theoretical prediction for flight 5 (1/10) .???... 73 27. Summary shee t for flight 1........... . ....... . ................ 74 28 . Summary sheet for flight 2. . . . . . . . . ? . . . . . . . . ? . . . . . . . . . . . . . . . . . 7 5 29 . Summary sheet for flight 3........... . .. . ..... . .... . .......... 76 JO, Summary sheet for flight 4......... . .... . .. . ... .. ... . ........ . 77 31 . Summary sheet for flight 5 ..??.....?...?...?... . ..?.. ? ..?...? . 78 32. The fifteen principal measurements ...............?. . ???...... . 79 33. A histogram of flying clock and ground clock shifts .......... . 80 34. Results using the Rubidium clocks and the travelling Cesium clocks ?...............?.............?............... . ... ... .. 81 35. Phase Plot of "synthetic clocks" generated by a computer program .........?..?......?...........?.......... . 82 CHAPTER I INTRODUCTION One prediction of the general theory of relativity as fonnulated by A. Einstein is that clocks placed at different gravitational potentials will run at different rates. 1 A clock placed at a high altitude in a gravitational potential is predicted to run faster than a clock at a lesser altitude. Experimental efforts to confirm this prediction have principally involved red-shifted photons (the "gravi- tational red s 2h -1if 3t "). Such results are to some extent unsatisfying as they may be explained by energy conservation without appealing to general relativity (although the existence of a gravitational red shift d oes i.m p 1 y spaceti.m e i. s curve d) ? 14 Hence an experiment using real roacroscopic clocks which are compared "side-by- side" before and after separation to differing potentials is of some interest. Considerations of such effects on real clocks in earth orbit have been considered for some ti.m e. 15-18 However, it is only recently that the quality of atomic clocks has made accurate aircraft experiments feasible. In fact, confirmation of this effect is now of more than theoretical interest as the increasing need for precision in navigational and time-transfer applications requires inclusion of such relativistic effects. To this date the only previous effort at such an experiment ( using macroscopic clocks) is the "around the world" experiment of Hafele and Keating19 in which a set of four Cesium beam atomic clocks was flown around the world in both directions using r egula rly scheduled commercial 1 2 airliners. A qualitative confirmation of the gravitational effect was obtained. The experiment described here aspires to high accuracy and credibility through improved clocks, multiple flights, stringent environ- mental controls, and accurate tracking of the military aircraft involved. The experiment consisted of flying an ensemble of atomic clocks in an aircraft. Before and after flight the clocks in this ensemble were compared to clocks in a ground ensemble. (Time transfer between plane and ground was made during flight using a short pulse laser. Since this aspect of the experiment is not part of this thesis it will not 20 be pursued here. The reader is referred to the thesis of Bob Reisse). The remainder of this chapter consists of a very general overview of the experiment. Details will be considered later in the appropriate chapter. The experiment was performed at the Naval Air Test Center (NATC) at Lexington Park, Maryland which is about seventy-five miles south of Washington, D.C. The aircraft made available for the experiment was a U.S. Navy P3-C Orion (figure 1). This type of aircraft is normally used in anti-submarine warfare. This specliic aircraft (number 158912) is one of two P3's used for final evaluation of equipment before dis- persal to the fleet. Before and after flight the P3 was parked a djacent to a large trailer on loan from the Goddard Space Flight Center, Green- bel t , Maryland. Figure 2 shows the plane, the ground trailer, and the hanger in which some lab and desk space was made available to us. The ground trailer contained much of the ground instrumentation. Two environmental chambers, or "clock boxes", were constructed to each hold six atomic clocks. Three of these six were Hewlett-Packard Cesium Beam atomic clocks located in the main body of each clock box. The other three were optically pumped Rubidium atomic clocks contained .. 3 in a much smaller chamber attached to the lid of the main clock box. The two clock boxes were mounted on a vibration isolating system and protect e d the clocks from ma gnetic f i elds and changes in t emperature, pr essure, and powe r s upply voltage . For each fli ght one box was placed i n the a ircraft and th e other in the ground trailer. Between some fli ghts the boxes were i nterchanged to aid in suppres sing systematic errors. Other clocks were also associated with the experiment. Two hydrogen masers on loan from the Goddard Space Flight Center were also housed in the ground trailer. One more Hewlett-Packard Cesium clock of high quality was in the ground ensemble. Other HP Cesium clocks were usually included on the aircraft for a flight . However these units were not in environmental chambers and were not of the high quality of those Cesium clocks mentioned above. The principal Cesium clocks were obtained with a high beam current option and further modified for this experiment. This resulted in performance superior to standard Cesium clocks. Data gathering and storage were controlled by two Data General Nova 2 minicomputers, one of which was placed in the aircraft (with associated electronics) and the other was placed in the ground trailer. Data was taken by each computer every 204 seconds before, during, and after flight. Part of this data consisted of environmental paramete rs (temperatures and pressures). The other part consisted of phase measurements of all clocks with respect to one clock chosen as referen ce . The reference clock for the ground comput er was one of the ground se t and the reference clock for the a ir computer was one of the air set. Phase me asurements were made with a r esolution of+ 0.1 nanosecond. As each clock box weigh ed approxima t el y 1200 pounds a part of the aircraf t f l oor was modi fie d t o t ake the weight of th e clock box 4 and two racks of equipment. The total w~ight was about 2000 pounds. The equipment was located on the right side of the aircraft, aft of the wing, and near the door (figure 7). Be fore and after flight numerous cables extended from the ground trailer into the aircraft to allow each computer system to measure all clocks available. Of course, during the actual flight these wi~es were removed and the ground (air) computer system measured phases of only the ground (air) clocks. This inter- comparison of clocks during flight enables a determination of which clocks, if any, changed rates during flight. Both the Cesium and Rubidium clocks are known to make small random changes in rate from time to time. Doubly shielded coaxial cable was used to carry the 5 Mhz signals whose phases were measured. Initially there were numerous short duration test flights. Five major flights followed from September, 1975 through January, 1976. Each flight was approximately fifteen hours long with speed and altitude averaging about 250 knots and 30,000 feet respectively. The pilots were instructed to fly and make turns slowly and smoothly. The flight parameters were such that the gravitational effect was expected to be about 50 ns and the velocity effect (of opposite sign) was expected to be about -5 ns. Hence the flying clocks were expected to show a net gain of about 45 ns with respect to the ground clocks. The aircraft was purposely flown slowly to minimize the velocity effect contribution. The aircraft was flown in a racetrack pattern inside an area restricted to military aircraft. Figure 8 shows this pattern as well as the location of the radar and theodolite stations used to track the aircraft. These were the facilities of the Chesapeake Test Range of the Naval Air Test Center. The thedolite calibrated radar data contained 5 position and velocity measurements for each second of flight. This data allowed the calculation of a predicted value to be compared to experiment. Tl1e aircraft was restricted to gentle turns to keep Coriolis forces on the cesium beams in the cesium clocks to an acceptable level. 6 Fig. 1. P3-C aircraft in flight. Fig . 2. Pre and post flight configuration with the aircraft near the equipment trailer . .. . . - ?a .. C '>C ")~ )( 'lC: "< \c ( 'h 1 ( 1f l " .. t ~ Fig. 3. Clock box with lid removed. A Fig. 4. The clock box lid. The smaller Cesium clock is in place in the first Rubidium clock box is placed at the slot. The magnetic shield can lids left end of the lid. have been removed. -..J I' 8 Fig. 5 . The Rubidium clock box (some e quipment r emoved for clar i ty). Fig. 6. Th e clock b ox i n position i n the aircraft . The computer rack which is normally to the righ t of the box has been removed. Clock Package Link Tape, Misc. clock fllClff ?o,;;,s..u- ,:;t~J -7 ,. L~P~'' ~0 ==r==;~bL t~I- =rt=!= ='Ib LiJ'f_il.1j c.o, 1101~ .rV_p I - -.- Lt . I I CI--dIb?l cJ , _;i M " ---~~~ . " -~ , 1tOT /~...! Figure 7. Floor plan of the P3-C aircraft showing the equipment loca tion \.0 10 Patuxent Naval Air Test Center ~10 miles~ SCALE ? = Theololite station Figure 8. Map showing the flight path of the aircraft. The radar and theololite locations are also indicated. The aircraft flight path was in the clockwise direction generally inside the indicated oval area. CHAPTER II CLOCKS, PACK.AGING, AND ENVIRONMENTAL CONTROLS A. The Clocks The "clocks" used in this experiment are actually atomic frequency standards which may be used as clocks by counting cycles in the output frequency or by making phase measurements of one standard with respect to another. Following general usage in such a context we will use the terms "clock" and "frequency standard" almost interchangably. A review of the early work leading to the development and improvement of atomic frequency standards is contained in reference 21. This work dates from the studies of Stern and Gerlach in 1921 which demonstrated the possibility of isolating atoms of selected energy states in molecular and atomic beams . It was later demonstrated by Rabi22 and his co-workers that radio frequency fields could be used to excite resonances in such beams. Although many types of frequency standards were developed or studied, three principal types emerged: Cesium beam standards 23- 28 Rubidium gas cell standards 29-30 and hydrogen masers 31-34 ' ' ? Modern versions of each of these types was involved in this experiment. Each type will be considered separately. 1. The Cesium Clocks The Cesium clocks used in the experiment were Hewlett-Packard Cesium Beam Frequency Standards, model 5061A . . These standards are approximately 9 x 19 x 18 inches and weigh 65 pounds. Earlier mod el~, comprise many if not most of the clocks in th e ensemble used by many 11 12 national time service organizations, including that of the United States. The current international definition of the second is related to the (F=4, m=0) to (F=3, m=0) hyperfine transition of Cesium 133. This transition frequency is 9,192,631,770 Hz. This is the atomic tran- sition used in Cesium clocks to discipline a 5Mhz crystal oscillator. The heart of the unit is a cesium beam tube in which Cesium atoms effuse from an oven, are collimated into a beam, and pass through an inhomo- geneous magnetic field which directs atoms of the chosen state down the length of the tube. These atoms pass through a Ramsey type microwave cavity (using separated oscillatory fields) where they interact with a microwave signal. Resonance microwave energy will cause atomic transitions to the other state. A second inhomogeneous magnetic field then directs such atoms to a hot wire ionizer and mass spectrometer. The result of this process is a current whose magnitude depends on how closely the impressed microwave frequency matches the atomic transition frequency. This applied microwave signal is frequency modulated at 137 Hz. If the center frequency exactly matches the transition frequency the output current will vary at twice the modulation ?frequency. If the center fre- quency is off to one side of the resonance the beaM current will contain a component modulated at the fundamental frequency (137 Hz) with a phase determined by which side of the resonance the center frequency lies on. Since the impressed microwave frequency is synthesized from a 5 Mhz crystal oscillator the instrument may use the information contained in the beam current to discipline this oscillator. The result is a highly stable 5 Mhz signal. Such standards have fractional frequency stabilities over periods of days that approach parts in 10 13 or 1014 ? Since the width of 13 the Cesium resonance (about 360 Hz) would imply a stability of only fou 8r parts in 10 , it is seen that the electronic circuitry is out- standing in its ability to remain close to the center of the resonance. Some of the Cesium clocks used in the experiment were standard models normally used by the U. S. Naval Observatory for time transfer applications. These clocks are sometimes called "travelling clocks". Seven of the Cesium clocks, however, were specifically selected and modified for this experiment. These Cesium standards were serial numbers 1025, 1028, 1033, 1035, 1026, 752, and 761. The first three were in clock box 1, the second three in clock box 2. Number 761 was part of the ground ensemble. The first five of these seven units were new instruments from Hewlett-Packard delivered with a high beam current option (option #004) to obtain improved stability. All seven standards were also personally modified and checked by Dr. Leonard Cutler, Director of the Physics Research Laboratory of Hewlett-Packard. One of these changes was proprietary. A second change was the modification of the feed-back servo loop to a two pole circuit which eliminated drift or steps in the crystal frequency (see Appendix A for details). This modification was principally to reduce rate ? changes occuring during and after vibration. One other modification should be mentioned although it was not internal to the standard itself . One component of the Cesium standard is a "buffer amplifier" which accepts one 5 Mhz signal and delivers two buffered 5 Mhz signals. As several buffered 5 Mhz signals were desired from each standard, additional buffer amplifiers were used. Two such units were strapped to the front of the standard and powered from with i n the clock. The 5 Mhz output was brought to each of these unit s . This resulted in four buffered 5 Mhz signals being available from each c lock. 14 These modificat ions were made after the first flight. It should be mentioned tha t a ll Cesium clocks used in the experiment were the pro perty of the Time Servi ce Divis ion of the U. S. Naval Obser vatory , dire ct ed by Dr. Gernot Winkl er. They approved the above modif ications. 2. The Rubidium Clocks The six Rubidium c locks us ed in the ex?eriment were Efratom Rubidium Frequency Standards, model FRK-H . These standards are approx- imately 3.9 x 3.9 x 4.4 inches and weigh 2.2 pounds. They are smaller and lighter than the Cesium standards. However their stability is worse by about a factor of ten unless great care is taken to maintain constant pressure and temperature, in which case they are worse by a factor of three or four. The units operate on a hyperfine transition of Rubidium 87 analagous to that of Cesium 133. However, these standards are not beam standards. Rather, they use an optically pumped gas cell placed in a microwave cavity. Resonance light from a Rubidium lamp enters this absorption cell containing Rubidium 87, passes through the cell, and impinges on a silicon photo detector . A microwave sign a l of the resonant frequency of Rubidium 87 (about 6834.68 Mhz) present in the cavity will stimulate transitions of atoms, some of which have already been "pumped" into the higher hyperfine state by the resonance light from the lamp. These transitions affect the absorption of the resonance light as it traverses the cell. This in turn affects the magnitude of the current l eaving the photo detector. Thus, although the mechanism has changed, the situa tion is like tha t in the Ces ium s t anda rd: The output current depends on the i nput microwave f r equency . Th is frequency is frequency modul a t ed a t 12 7 Hz pr odu c ing the same si tua t ion as tha t des cribed f or the Cesium s t andard. 15 The output frequency of the Rubidium standards is 10 Mhz. Since the rest of the experimental apparatus uses 5 Mhz signals, a divide-by- two circuit immediately fol l ows each unit. A buffer amplifier is also placed on the circuit board. Hence, two buffered 5 Mhz signals are ob tained from each Rubidium standard . These units were on loan from both the U.S. Naval Observatory and the Efratom company . 1, The Hydrogen Maser There were two hydrogen masers as part of the ground ensemble of clocks . These were massive units, over six feet tall and weighing several hundred pounds. They were units #NP-2 and NP-3 on loan from the Goddard Space Flight Center, Greenbelt, Maryland. These were units that had been constructed under the direction of Harry Peters. Their f requency stability over periods of a few days was approximately the same as the better Cesium clocks, or perhaps a little better. The hydrogen maser operates on an atomic hyperfine transition of the hydrogen atom analagous to that of cesium and rubidium. This frequency is 1420,405,794.319 Hz. Hydrogen atoms in the excited hyperfine state are injected into a microwave cavity of sufficient Q to allow masing to occur . A fraction of the energy in the cavity is extracted by a coupling loop. This signal is used with a phase comparator and frequency synthesizer to lock a crystal oscillator to the transition frequency. It has been our experience that, although the hydro gen masers are excellent standards, their reliability is less than the Cesium or Rubidium standards. This may well be because these are not commercially produced units. In any event, both masers nee ded occasional repair. A series of problems caused NP-2 to miss several flight s . These were 16 usually electronics problems. B. The Cesium Clock Box Pictures of the clock box appear in figures 3-6 of chapter I. Schematic and block diagrams showing the essential features of the clock box appear in figures 9 and 10. The box is constructed of alum- i num plate and ribbing. It is separated from a base plate by pneumatic isolation mounts for vibration protection. This base plate is mounted on wheels so that the box may be moved about. The entire structure weighs approximately 1200 pounds. Power supplies and other electronics are located on the box lid, the front of the box, and inside of the box. The clock box is attached to the? aircraft by bolting the base plate to two channels on the aircraft floor. The height of these channels is such that the box may be rolled over them with minimum clearance. The wheels then only need be lowered slightly to rest the box on the channels. I n practice, the front wheels were completely removed after the box was seated. The interior of the main box contains three Cesium standards. Other features of the clock box will be considered in the following sections which consider the environmental influences and the measures taken to protect against them. 1. Magnetic Fields The Cesium clocks are already rather well protected from magnetic fields by a triple layer magnetic shield that is part of the beam tube. We have provided further isolation by placing each clock in a ma gne tic shield can constructed of mo-permalloy . Openi ngs in these cans al low 17 air circulation (see the next section). Measurements have shown that even with the lid of the shield can removed exterior magnetic fields are reduced by a f a ctor o f 100 near the middle of the can . Further tests were done by rot a ting one clock box 90 and 180 degree s in the earth's magnetic fiel d. No effect was detected to a level of several parts in 1014 , this being about the intrinsic quality of the clocks themselves. Measurements were made in the aircraft during flight using a Hewlett- Packard model 428B Clip-on D.C. milliammeter with a model 3529A Magnetometer probe (1 Gauss/amp). These measurements were made near the clock box in three orthogonal directions. Nothing was noted except the earth's magnetic field. 2. Temperature Control Temperature control of the Cesium clock box was attempted through t wo stages. The first stage involved two variable speed fans which were mounted on the lower base plate to isolate their vibration from the box proper (see figure 10). A nylon skirt closes off the area between the base plate and the box proper. Lucite panels are attached to the ribbing on the rear and side of the box. The skirt and lucite panels cause the air sucked in by the two fans to be directed over the bottom, rear, and sides of the clock box. A thermistor is attached to the outside wall of the clock box. This thermister is connected to a thermistor bridge/power controller combination (see Appendix A for circuits). This power controller delivers Oto 29 volts de to the two fans. Hence the rate of air flow over the bottom, rear, and sides of the box is regulated by the outside box skin temperature. The second stage of temp e rature control is inside the box. The temperature of each of the three clocks is indiv idually sen sed a nd controlled. A constant speed de fan (Aximax 2, model 464YS) and a h eate r 18 are associated with each clock. These units are mounted at the inside front of the clock box ( see fi gure 10). The fans a re on small spring mountings to reduce vibration. These fans are capable of moving ai r at 28 cfm against a pr essure differ entia l. Air is sucked in by a fan, moves over the heater, is delivered through a two inch diameter hos e to the magneti c shield can of the clock in question. The air enters the can through a two inch hole in the middle of the lid and exits the can at the bottom through 40 1/4 inch holes along the bottom edge of the shield. Removal of the mechanical clock movement normally found on the front panel of the Cesium standard creates a two inch hole in the front panel allowing easy passage of air through the clock interior. An average temperature measurement of the clock was obtained by three thermistors connected in parallel. One was directly in the input air stream, one was midway down the side of th.e shield near (but not touching) the shield wall, and the third was at the bottom of the can near an exit hole. These thermistors were attached to a thermistor bridge/power controller combination which supplied Oto 29 volts to the heater winding. These windings were bifilar to reduce magnetic field generation. The heater resistance was thirty oh.ms resulting in a maximum power out- put of thirty watts to each clock. To achieve good control the temperature of the clocks were maintained somewhat above room temperature. The actual temperatures were in the range of 95 to 103?F. To aid in temperature control of the clocks, polystryrene insula- tion was installed around each can. This change was made after the first flight. The result of several meas urement s on the Cesium s t andards showed tempera ture coefficients between two and ten parts in 1014 per degree Fahre nheit (see Appendix B). Hence we a ttempted t o maintain the Cesium 19 this proved to be ith i n 0.1?F. Ge nerally s to w cl ock t empe ratu re en to fifteen d egree t tayed within a os s ible i f r oom t empera ture s p uctuations s malle r ex t ent could cause fl anges of a range , al t hough rapid ch he e ff ort was ma d e to control t r a tures . He nce an in the c l ock t e mp e s achieved quit e This wa he clock boxes. pera t ure of t he area around t tem ea containing t he clocks le r in which th e ar Well in t he gro und tra i The plane was m uch more ees F. ta i ned within o ne or two degr Was mai n temperature con trol automatic . The aircra f t does have an difficult c mode until th e r worked well in the automati st t nev e sy em. Howev er, i ed toward e amount of eff ort was direct h a larg last flights ev en thoug t ailed during th e second fligh the entire syste m f th is problem. In fact aircraft cabin (the ar f~eezing in the resulting in te mperatures ne l re contro rang e ) . n their tempera tu i ned i Ces i?u m clocks bare ly rema ts of the plane 's temperature ng elemen The sensing and controlli cation near the front of heir normal lo trol s ys tem we r e moved from t con n the system wo rked well aced near the c lock box, Whe the plane and p l times variat1?on s ccur re d other grees o ? At Vari? a few de a t?io ns of only he system respo nded. This es could occur before t egre of five or more d in descent when th e changing cab ring ascent and true du Was especially he box vective cooling rate about t ure caused chan ges in the con Press spite of all th e above the e box temperatu re. In thereby affecti ng th oal of 0.1?F eral were maint ained to the g in gen Cesium tempera tures D). (see plots i n A ppendix 20 3. Pr essure Control Although pr essure control was effected mainly for the Rubidium clocks , i t was desi r ed t o keep a ll c l ocks at constant pressure, especially dur i n g f ligh t when t he cabin pres s ure would drop to 2/3 atmos ph e r e . The main Ces ium c l ock box and the s ma ller Rubidium clock box on its lid we re conne ct ed by tubin g and pressure controlled by the same system. A Granville-Phillips automatic pressure controller, series 216, and matching variable leak va lve were used to control pressure by admitting dr y nitrogen a t a r a te sufficient to counteract leakage. A National Semi- conductor type LX3701A pressure transducer was the measuring element. These units operate using a diaphragm and piezoresistive strain sensor. Pressure was held constant to within 1 mm Hg. Tests were performed to measure the pressure coefficients of the Cesium clocks and no effect was detected. The limit of this measurement 2 was approxima tely two or three parts in 10 14/lb-in- . 4 . Vibration Isolation Several aspects of this problem have been a lluded to: the variable speed fans be i ng mounted on the base plate, and the constant speed f ans being on spring mountings. Thus vibration ? from these two sources is greatly attenuated. This section will describe the shock mount system i s olating the box proper from the lower base plate. Barry Stabl-levl SLM-6 pneumatic mounts are placed at each corner of the box. Each mount is connected by pressure hose to an adjus tabl e va lve and r es e rvoir and a lso to a filling stem and press ure gauge near the front of the box. The valve/reservoir units are on th e back of the box . Ea ch mount/rese rvoir system was normally inf lat ed to 55 psi and t he valve "tune d" to ap proa ch as close as poss ible to cr i tical dampin g . 21 Th i s r es ult e d in a resonant frequ ency of three Hz with a falloff of about 12 db/oc tive . Altho ugh critical dampin g was not quite achieve d, th e second peak following an impuls e was 1/3 to 1/4 the amplitude of the primary pe a k . The pri? nci? pa 1 resonance of the aircraft inf 1 igh ti?s 9 o Hz f r om the e n gines . The most critical frequencies for the clocks are th e 1 3 7 Hz and 127 Hz modulation frequencies of the Cesium and Rubidium c locks. Although vibration on the P3 aircraft was quite noticable in flight it did not seem to be transmitted to the box which only showed gentle swaying motions during flight. No higher frequency vibrations could be detected by touching the box. A retaining pin was located at the very top of the box structure. A ring firmly attached to the aircraft surrounded this pin, normally not touching it, to prevent excessive movement of the box on its shock mounts. On take-off and on landing the box would jerk to the side and be abruptly stopped by the ring. This was the most violent motion transmitted to the box . 5. Power Supply Variations The clocks were electrically isolated from each other by placing each on a separate voltage regulator. A standby battery on the front of the clock box protected against brief (5 min) power failures. Longer power failures were guarded against by use of a "battery cart" between the clock box and the local AC line. Essential power could be maintained to the boxes for periods up to fifteen hours in the event of longer power failures, several of which occurred. Although the Cesium clocks were normally supplied with DC power they are capable of accepting AC power. Provision was ma de for doing this for repair or eme r gen cy use . ... 22 C. The Rubidium Clo ck Box The Rubidium clock box is mounted on the rear portion of the lid of the Cesium clock box (see figur e s 4,5,6, and 10) . Inside the box are mount ed the three rubidium clocks, each in a ma gnetic shield c an, and the divide-by-two and buffer amplifier circuits. Th e entire box is temperature controlled as a unit by a bifi lar heater winding in the lid of the box . A thermistor/thermistor-bridge/power-controller sequence regulates the temperature. The box is insulated. An exterior fan mounted on top of the box on s pring mountings flows air over the top plate. In the later flights this arrangement was modified by attaching a tube causing this ai.r to return and flow over the surface again ( closed sys tern) ? The speed of the air flow was re.gulated by the temperature of the heat transfer plate on top of the Rubidium box. This did improve performance. Following this modification the Rubidium box temperature could be maintained to better than 0.05?F. Previous to this modification large excursions were caused by rather small plane temperature excursions and were a distinct problem. The temperature and pressure coefficients of the Rubidium standards were measured and found to be approximately Temperature: -3 x l0-12 / degree F Pressure: -1 X 10-l3 / mm Hg (see Appendix B). The Rubidium clock box shared in the pressure control and vibration isolation of the Cesium box. :::J D. Other Clock Box Features Some features of the clock box not considered in a previous section wi ll be discussed here. Since the c lock boxes h ad to be relatively pressure tig h ta ru bb er gasket was placed between the box proper and the lid. Bolts were spaced around the perimeter about 2 1/2 inches apa~t. These bolts were t ightened with a torque wrench to 18 ft-lbs. Electrical access to the i nside of the boxes was obtained by vacuum tight multi-pin or coaxial f eedthrough connectors. Environmental parameters were monitored by sensors different from t he sensors used for control. These included a pressure transducer in the main Cesium clock box (National Semiconductor LM3701A) as well as one external to the box. Temperature measuring thermistors were placed in each Cesium clock shield can, the Rubidium clock box, and outside of the hox. This data was accumulated by the computers. It was also available f or monitoring with a voltmeter at the box itself as were other voltages not recorded by the measuring system. Three lights of different colors exist on the front panel of the Cesium clocks indicating the condition of the clock. Photodiodes were attached to each of these lights on each clock and connected to circuitry on the outside of the box where a panel of light emitting diodes repeated the information. Hence the condition of the Cesium clocks could be discerned without opening the box. There also exists a button on the Cesium clocks for resetting. A small relay was attached to the clocks and wires brought out to buttons on the outside of the clock box to allow t:his. function to fie performed without opening the box. NOT SHOWN: Box lid, lucite panels on bo a xn d s idlo ew s,e r ne yd log ne o skf ib ro t x b. etween base ?late Magnetic sh ( ic eo ldn ta cain ni sn g the Cesium clocks) - Fan and hea (H teo rs e u "~ s nf ir to m o tf h es sh ei to "\ eld tc oa pn s not shown) Slide in boa e rl de c ht oro ldn ii nc gs - ------......___ ? Cover wit e hl ectronics beneath "---?- ~ \1hee @ls ' ? ; Sho \ :---- ck mo tu sn --... -. -. -. -.". '-----=_=/ =..__:..:, ;,-~ -~q,,:-----,,, Figure 9. Schematic i ds ia gn ro at m s h oo fw tn h. e c 32 D lo x i m ck box. 26 e nx si o4 n3 s The i an sc h s ho liw d es. n are N ~ 25 17 . ?-? -- - ---?- -- - -- .. -~ 15 16 18 18 13 G 2 I J 2 2 "J G 9 12 0 1 1 1 10 G G ~ 20 19 19 -? 024 240 1. Cesium clock 13. Pres 2 s. u rB eu cff oe nr t ra om llp el ri fiers 14 . Pressu 3 r. e M va ag lvn ee tic shield cans 15. Rub 4 id. iuH me a ct le or c k box 16. Retainin S g. p4 i0 n0 sH uz p pf oa rn ts 17. Retain 6 i. ngP r pe is ns ure transducer 18. Power su 7 p. pA lin ea sl og phase boards 19. Control 8 le. d F fe ae nd s- through area 20. Nylon s 9 k. i rF tsi ve minute battery 21. Shock mo 1 u0 n. t sP ower controllers and 22 . Pressure chambers f t oh re rmistor bridges shock 1 m1 o. u nP to s wer supplies 23. Pressure ~ 1 a2 u. g eR s .F fo. r switches shock mounts 24. Wheels 25. Base mounting plate Figure 10. Block diagram of the clock box. CHAPTER III DATA ACQUISITION A. General The phases of the clocks are measured in two ways. The primary method is the use of an "event timer" to be described below. The second method is an analog comparison using circuit boards designed and built by Charles Steggerda of the Quantum Electronics Group, Department of Physics and Astronomy, University of Maryland. Application of two 5 Mhz signals to an analog phase board results in a de output voltage which varies between -5 and +5 volts as the phase difference between the two signals varies between O and 200 nanoseconds. This method is not as ac- curate as the event timer measurement and existed as a back-up in case of failure of the primary system. No such failure occurred. Recall that each of the Cesium clocks has four 5 Mhz outputs (as modified for this experiment). One output from each clock goes to an analog phase board located inside the clock box. A second output of one of the three standards, the one designated as analog board reference, goes to the "reference" input of all three analog phase boards. The other outputs go to feedthrough BNC connectors on the front of the box. One of these outputs goes to the reference input of all three analog phase boards inside the Rubidium clock box. B. The Event Time r The heart of the primary phas e measuring sys t em is an "event timer" 26 - 27 built by Charles Steggerda originally for the lunar laser ranging pro- gram . This device is described completely in ref e rence 35. It is basic- a lly a dual slope integrator in which a capacitor is charged at one rate a nd discharged a t a second slower r a te. The event timer requires a 5 Mhz t ime base as reference and also uses this time base to maintain an internal calendar and clock. It can measure the epoch of an event, such as the arrival of a NIM t pulse, to a precision of 0 . 1 nanosecond. Such a measurement wil l give the phase difference, meas ured in nanoseconds, o f one 5 Mhz signal (after having passed through a discrimina tor to gene- rate a NIM puls e) with respect to the reference 5 Mhz signal. The event timer is intimately connected with the Nova 2 mini-compu- ter which commands when a measurement is to be made and receives the re- s ult for storage or analysis. The computer console may be used to set the event time r date and time to the nearest second. If further preci- sion is desired, the event timer may be set to the nearest tenth micro- second by supplying a one seconds tick and inserting the desired offset in microseconds from that tick. As used in this experiment, the phase data as sent to the computer is modulo 100 nanoseconds. This is related to the fact tha t the 5 Mhz time base is first doubled to 10 Mhz. The event timer may be calibrated so that this "fold over" is exactly 100 ns. Experience has s hown that this calibration is then stable over periods of days . The event timers were calibra t ed previous to each ma jor flight. Further tests have shown that the instrument is linear to within? 0.2 ns. The event timer metho d of measuring phase differences is called the t A NIM pulse i s a ~ucl eo. r _lnstrument a tion ~odul e signal. This is an electrical pulse with n ominal voltage of -.7 t o -1 volt a nd nominal rise time , fall time , and middle time of 3 n o.n oseconds each . 28 "digital phase meas urement" to differentiate it from the second me thod using the a nalog phase boards which is called th e "analog pha se measure- ment" . C . The Digital Phase Me asurement Figure 11 is a b lock diagram of the digital phase measuring system. There a re two computers ("ground" and "air"), each with its associated event time r and e l e ctronics. There are also the two clock boxes, one on t he g round and one in the plane. The system is designed so tha t each of t he computers may access each clock box for phase measurements. Con- s ider one of the clock boxes. The six 5 Mhz signals from the clock box (three Cesium clocks , three Rubidium clocks) are brought to the first six inputs of a electronically controlled ten-to-one R.F. switch (Trum- peter mercury wetted relay switch type CSFZ). The remaining four posi- tions are used fo r any other clocks in the ensemble in question. Henc e e ach of as many as ten signals from each clock box may be sampled in se- quence . Following the ten-to-one switch is a similar one-to-one switch which determines to which computer the signals will go . Both of these R.F. switches are mounted on the front of the clock box. At the computer location is a two-to-one switch which determines which clock box the computer is receiving signals from. A second two-to- one switch follows this one and is related to the laser time transfer technique that is not being considered in this thesis. After l eaving t his switch, the 5 Mhz signal in question goes to a discriminator (Ort ec 436) which provides a NIM pulse to the even t timer. The event timer ob- tains its ref erence signal from one of the clocks in the en semb le associ- ated with i t. Each compu ter samples c l ock phases every 204 seco nds. The compute r controls the v a rious RF switches so tha t it may seque nc e through all the 29 5 Mhz signals at a rate of approxima t ely five per second. During this time, i t actually makes f not one but six teen consecutive meas urements o each phase. Th e mean of these sixteen meas urem ents is t ake n to be the measurement and i?s stor ed . Thi s technique helps t oe1 i?m ?i nate sys t em phase noise from the measurements. In the air comp ut e r system , t he phase informa tion is stored in the computer's memory core . It is also stored on magne tic tape (LINC Tap e I I) as a safety precaution. The computer can sample at the above rat e for about twenty-four hours before its memory is full. The contents of th e memory may be transferred by cable to the ground computer for stor- age. In the ground computer system, the data, whether resulting from its own measurements or from a transfer of data from the other computer, is s t ored on a magnetic disk. The disk can hold all data from an entire flight as well as the programs and operating system it normally muS t maintain. Data may be transferred from the disk to magnetic tape for permanent storage. This was normally done every few days . D. The Analog Data The analog data consists of de signals between -5 and +5 volts de that come from the analog phase boards and also from the environmental measuring circuits (the pressures aud temperatures ). Thes e signals l eave the clock box along a cable that goes both to the computer for storage and also to a "translation box". At the computer, the signals go through an analog-to-digi t a l converter and are sampled ever y 204 s econds immediately following the digi t al phase samplin g . The "transla- tion box" sends the signa ls to chart r ecord e r s and contains circuitry to isola te th e compu t e r from the recorders and also to cal i br a t e the r e - corder scale for eac h channel. The c ha rt r eco rd e r s used are six c ha nnel JO Honeywell recorders on loan from the U.S. Naval Observatory. These r e - corders sequence through the six input signals over a 90 second period, plotting a point every 15 seconds. The chart speed used was 6 inches per day. Two such recorders were in the gournd trailer and one in the air- .c~aft. It was therefore possible to visually monitor phases, tempera- tures, and pressures in real time. 31 '.? l (_ ] :-; [,t,J ,-. , _, *-~?~ ._, :- ! f-' C!": ,::~ ? rl / _: ~~ ) ,<. . r-1 I o ~:- .. -l--i u o : - -- ? C? 1 C! .. b-' er:r ; i:..., H ?]'- ,. __, (?-~ ?-1-.. f'.-i ~'-< ~.. ... I .. ' I ~ .. I) _~ I l ,....,, I , .~ I ~ ?~ : i'"' 7 <=" r? ~ ...... -- . . ?r -. ~ ,. .. I ?1 ~ ::f... ' J_c.> ~ . . 1 ?- ,_; : .._~ , ~"~ I D:!" SCTT I ~i 1)1 :".'I'0 . '. -t I ! ~ [-< .\ i 1-1 (-' c-i I C') : ,r $ n:: 0 i c:: - 8 ,<.?.. rL E--< !::': '.::] r.:'. C : :J 0 > 0 ( c~ (-< 0 :.:1 8 1~ R E-t ;,.: ) ~ ,..~ ;~.::-i /2 to 1I "..) ;-::J ?J (-.J ;r-: C-r i:-? Cl ' -"': G ~ 0 0 c t--1 0 u .f ~ 0 0 ~ ? --i 0 8 ~ ?p?-. . H 7I 2 1 ;::) ::,: ]2 to 0 < ..... y-- ;:r:; o0 : (.'.) H ~ 0 Pc. ~ I \:I.. -r-- J_ n --'-I I _I _ 7 1 to 2 1 to 2 0 0 H 0 r::J c::: 0 CLOCK c:'.OX ._ ____ j CHAPTER IV SOFTWARE CAPABILITY AND DATA MANIPULATION A. The Raw Data Files The data as originally taken exists as a series of "records" in a data "file". Th ese are ca 11 ed " raw" data files because most of the other programs do not work on these raw files, but on "translated" files generated from them. The records which comprise the raw data file each consist of a five word (computer word) header followed by a number of words of actual data. Each record is assigned a "record type" which is a number depending on the type of data stored in the record. Type 1 is analog data and types 6 and 7 are digital phase data from clock boxes one and two respectively. Other record types are related to the laser time-transfer operation which is not being considered in this thesis. The record header consists of the following five words: 1. The record number 2. The record type 3. The second of the half-Julian day+ 22336 4. The half-Julian day 5. The number of words of data that follow the header The format of the header is dictated by the format of the Nova 2 minicomputer and the Event Timer intimately associated with it. For example the additional constant added to the second of the half-Julian day in the third word causes that computer location to overflow at the last second of the half-Julian day. Many other features were dictated by the original use of the Event Timer for lunar laser ranging, for 32 - 33 example the us e of Julian days for time keeping. The programs used to obtain this raw data are written in the machine language of the Nova 2 and are closely related to the characteristics of the Event Timer. This programming was the work of John Rayner of the Quantum Electronics Group of . the Department of Physics and Astronomy, . University of Maryland. B. The Translated Data Files The "translated" data files are created from the original "raw" files and it is these new files that most of the analysis and manipu- lation programs work on. These new files contain only one kind of data. One such kind is the digital phase data. The program that creates this translated file consisting of digital phase data is named TRANSD. TRANSD accomplishes the following tasks: 1. Removes "cross overs" in the phase data. Recall that the phase data existing in the raw files is modulo 100 ns. TRANSD adds or subtracts quantities of 100 so that the phase record extends continuously. For example the sequence ?.. 98,99,0,1,2, .?. in a raw file would become ??. 98,99,100,101,102, .?. in the trans- lated file. 2. Puts the time in a convenient form. The time of a reading as it exists in the raw file consists of the half-Julian day and the second of that half-Julian day (plus a constant). TRANSD converts this into a fractional Julian day (FJD) such as 4539.765482 and immediately subtracts an arbitrary but fixed constant to produce a number smaller than 100, eg. 39.765482. This proceedures assures better readability and adequate 34 accuracy upon storage in the single precision computer word. For data extending over several days, having the time in fractional days is of obvious convenience. 3. Creates "paper " clocks . The mean of the three phase readings vf the Cesium clocks in clock box 1 is stored as a separate reading, and similarly for clock box 2. These created mean clocks are often called "paper clocks". The format of the translated data file consists of one header for t he entire file followed by a number of "records" of data. Each record contains a list of phase measurements for every clock, including the two paper clocks. It also contains the time at which these readings were made. This time is modified slightly for accurate storage by the following proceedure. The integer portion of the very first time in the file is s ubtracted from that and each succeeding time. For example, if the t ime of the first record is 39.765482, then .765482 is stored in the first word of the record. This same offset (39) is subtracted from each s ubsequent time before storage in the first word of the appropriate record. The offset (39 in this example) is stored -in the file header. This proceedure helps to assure adequate accuracy considering the size of the computer word. The format of the translated file header is as f ollows: 1. NC (the number of clocks in the original "raw" record) 2 . NC+2 (the total number of clocks in the translated record) 3. N (the number of records in the entire file) 4. S (the offset of the f ractional Julian day ; 39 in the abov e ex ample) 5 . BFJD (the time of the first record: leginning Fractional Julian Qay) .. 35 6 . EFJD (the time of the end record) (Here follow NC+2 pairs of numbers, each pair consisting of the first and last phase reading of that clock) As mentioned above, the first word of each record contains the time of the measurement. Then follow the phase readings in a specific order. This order is independent of what the order was in the raw files. This ordering in the translated file is as follows: l2.. } The Cesium clocks 10?[ The Rubidium clocks 3 ? .., in box 1 11. 12. in box 2 4.} 13. Mean of clocks 1, 5 . 2 , and 3 The Rubidium clocks (paper clock) 6. - in box 1 14. Mean of clocks 7, 8, and 9 87.. } (paper clock) 15. The Cesium clocks 16. 9. in box 2 Other clocks, 1 w7 i. t h ground clocks before flyi 1 n8 g. clocks 19. 20. Bob Reisse has written a program (TPTRANS) that translates the environmental data (temperatures and pressures) contained in the raw files into a translated file of the same general format as that above2 0 . C. Data Plots and the Graphics Terminal A Tektronics 4013 graphics terminal and hard-copy unit were avail- able for data plots. The usefulness of this facility can not be over- stated. All plotting programs access the translated files. Several of the main plotting programs are described below. L PHASEPLOT PHASEPLOT is a program that plots the phase of one clock with respect to another (reference) clock. Any clock may be plotted against 36 any r e f e r en ce , i ncluding of course the two paper clocks. The scales of the p l ot may be specifically selected or the program wil s lc ale self-to rende r the entire plot on the screen. Figure 12 is of such an exampla e p lot. This and other plots are progrannned so that the numbers c ompr i sing the scales are "clean" (34. 2 rather than 34.1897). 2. SRESIDUALS The relatively large rate of one clock versus another will often mask features of interest in the phase data. Hence PHASEPL0T itself is rarely used in this experiment. Rather, the slope of the data is removed resulting in a plot of the difference of each data point from this slope. There are two types of slopes that may be plotted against. One is a least squares regression line fit to the data. The second is a slope line defined by the first and last point in the data file. In the latter case the option exists for using a small number of points at each end. SRESIDUALS is the program that produces the plot, called a "residual" plot. In order to run SRESIDUALS another type of file must be created containing information about the slope to be removed. The program SLOPES creates such a file for the least squares case while the program PSLOPES does this task for the "first point, last point" slope. In either case any clock or group of clocks may be specified as the reference. An example of a residuals plot appears in figure 13. The scales may be selected by the user or the program will self-scale. 3. RESIDUALS RESIDUALS is a program that creates a page consisting of residual plots of every clock in the file. Such a plot is of enormous value i n reviewing quickly several hours, days, or weeks of data from many clocks . 37 An example of such a plot appears as figure 14. 4. SIGMATAU SIGMATAU is a program that computes and displays cr(2;T) for any clock of a translated file with respect to any other clock or group of ?clocks. (Those unfamiliar with the ?m eaning of a "sigma-tau" plot are refered to chapter VI.) An example appears as figure 15. Copies of the FORTRAN listing of each of these programs appear in Appendix E. D. Manipulation and Analysis Programs Numerous other programs have been written to truncate translated files, append them, edit them, display their contents, etc. Other programs relating directly to the data analysis will be considered in chapter VII. 0. ,, -20. " ,,. "?~ -..; 3 . '?,"' ... ..,_____ -60. --------~ -80. . ' '"' -100. ~ Figure 12. An example of the program PHASEPLOT -120. ~-,- , ......... -140. 37.8 38.0 38.2 38.4 38.6 VERT SCALE?NANOSEC FRACTIO~~AL DA'IS PHASE PLOT, FILES DF~B1122 CLOCK 2 vs PAPER REF 0, w '.X) 4.0 3. e, 2.0 ... .... .. ......., . ... ' '?, /.. ," -..~ . ??, , 1. 0 ?? # .._ ,,...,,_: ?.: ,?. .. , . ?/?. . ... .-: ?. ? ? ?? ? ? ..? .-? --:?_. ._?~ -??.-:-..? _,,-., ___ ? '?, ,.w .............. , .......... -... , .............................................. ?--????-??? ~ .. 0??~?????,-~?-?"""???????-??????-?? 0.0 . :.?. ....._ ;?-? ?, . . . .......... ::?. __, . . ?.... . .. . ...? . ' ..... :-.; :-? .-..I'.-..,"-" ?. .. . .. ." ? "" ,. ? ,"1 ? ?,.,,._ ?,; .. -1.0 -2.0 Figure 13 . An example of the program SRESIDUALS -3.0 ----------------------- -- -4.0--------- 37.8 38.0 38.2 38.44 38.6 ALE?NANOSEC FRACTIO NAL DAYS VERT SC RESIDUALS, FitEi DFGB1122 SLOP E FILE: DSGB1122 CLOCK t a US PAPER REF 0, w ?..o -T --,- I I I I I I I .. 00~ U) 0 ~'J (.() ...J l'J 0 I I (1) lJ... cow I 0:: I I I I I l. . l : _ t __l l.J...). l - 00 - ?? I _ _ __d ,._ 1 ? I I w I ...J ~ W...J .-t 0:: U) G ~ure - ?14. ,.An . examp~-the program RESIDUALS . ] 1i11 J s:;M~(2;T>. F I l~E: ~FGLONG 1 I I I -4 TA_ f ; EC) ~' S!GMA LOG s?rr; SD 2( D14 E(" t.- . 437 e.1~E-12 -12. 8? 0.SSE- -1:) ~ 4(:20 1 . 4 215 5 e.S9E-13 -13. ~~ 0.4 SE-14 3 4 :.6:?i. 106 0.6~E-13 -!3.1 6 0.37E- 1 1 E 43 2 C 3') . S1 0.S1E-1? - 4 -12.29 0.410 3 22 ~6 - ? 1- 48 4. 2 33 0.27E-13 - !3.S7 0.4 6~ SE22 -10 4. 1 32 0.2~E-1? -:3. G3 0 .4 1 1 7 E J; -)S 14G :-: 0 1 ? 5 ~. 27E- l 3 - : 3. r:_: , 7 0. t:: 7i::-1 2 ~ ?1 1:.20 . 2 0 0.19E-13 -12. -~ 0 .2~E-14 0 ~ I 1013 .. . . . . .. . ?. . .. .. .. __ -.. . .. .... 10 : 4 ...... . . . .. . . ? -1/::. > .. . T -.. . . . .. ... .. . ? .?- An example of the.. ... . program SIGMATAU 1015 .. . E _._. ...- ..... ...~ ,.-,. ,. .. . , ,,.-.... . .. . I 20J-4 I sis 1 1 ?? -1 3Je4 130~s I s T 2 ~2C 4S ECONDS) CLOCK 8 VS REF: 0~ .p. r--' CHAPTER V THEORY AND THE PREDICTION OF THE EFFECT A. The General Relativistic Effect We will not repeat here what is covered in virtually every text book on general relativity. Suffice it to say that for the metric (with the "zero" index being the time index) and for nearly Newtonian systems in Newtonian coordinates -the metric may be approximated by (1) where~ is the Newtonian potential(~~ -GM/r) and c is the speed of light. Hence the metric coefficients are approximately g = -(1 + 2~/c2) 00 and Since the proper time dT is given by c 2d T 2 = we have 2 2 c dT = (1 + 2 2 2 2 2 2~/c - V /c )c dt 2 Noting that ~.'c for this experiment is~ -7 x 10-lO an 2d so ~/c << 1, the above equation may be approximated as cdT 2 = (1 + 2 ~/c 2 - V /2c )cdt (2) Consider an inertial frame of reference in which time intervals, dt, are measured by clocks synchronized to a master clock at infinity, or by clocks whose rates have been adjusted to compensate for gravitational 42 43 pot ential s. That is, time int e rvals me asured in this frame and using i t s clocks a r e o per a tionally ind e pendent of the distribution of matt e r, Th i s time i s some time s call e d "world time ". Conside r two observe rs wi th s t a ndard cloc ks a nd i n motion in this frame. I f each measures th e time i? n t erval b? e t ween t h e same two events, they measure t:he proper time intervals d T1 and dT r esp e c t ively. Each of these times is related to the world 2 t ime by equat i on 2 . Hence if the two observers initially synchronize t heir clocks and then move apart, the accumulated time difference betwe en t heir clocks will be v2 - v2) 2 1 dt (3) 2 2c Considering the accuracy of this experiment it does not matter which time is used for the variable of integration. B. Prediction of the Effect To compute the accumulated time difference between a clock that remains on the surface of the earth and one which flies in an aircraft we will use equation 3, The inertial frame selected is a cartesian frame with origin at the center of the earth and non-rotating with respect to distant matter, The z axis will be coincident with the axi s of rotation of the earth. The coordinates of interest in this system will be the distance of a point from the origin (r) and the latitude , 8 , of such a point , See figure 16, Since the earth i s not exactly a homogene ous sph e re its g r avitat iona l potential is not exactly -GM/r, Data obtaine d f rom me a s urement s of the orbits of art i ficial satellit e s has allowe d a more e xac t de t e rmi n a tion 44 of the earth's potential. An expansion given by Allen36 is: (4) a= equatorial radius of the earth e = latitude P = Legendre polynomial of degree n .n J = constants n Allen gives values for the constants J to J ? 21 The value of J2 2 is 1 .08264 x 10-3 with the other constants being smaller by about three orders of magnitude more. It therefore seems that at the level of precision of this experiment none of these terms are important. But since the J term is large enough to make a minor diffe 2 r ence it will be included in the calculation. The V2 term in equation 3 is calculated in an inertial frame. Hence the ground clock and the plane clock will have part of their velocity due to earth rotation. It is therefore necessary to consider the reference frame in which the velocity and position of the plane are measured. This is a Cartesi~n frame with origin at the radar antenna tracking the aircraft. The z direction is the local verical with . positiv . e z being up ' ward. The x-y plane is tangent to the earths surface with positive x and y being east and north respectively. The lower case letters x,y,z and v ,v ,v will be the position and velocity X y Z components measured in this "range" frame. The origin of this frame is located at (r ,e) as measured in the earth-centered inertial frame. 0 0 Then if w is the angular rotation rate of the earth with respect to distant matter, the velocity, V, of an object in the earth-centered frame is related to measurements in the range frame by the relation 2 2 2 2 V (v,r,e) = (v + wr case) + v + v X y (S) z 45 (It might be noted as a point of interest that an alternative approach is to first transform into a reference frame corotating with the earth: which for the range coordinate system becomes 2 = 2 V v + 2v w cos8 + 2 2 2 w r cos 8 X Hence the same result is obtained. This method of first transforming to a rotating system causes the v2 quantity to explicitly appear in three parts: v 2 as measured in the rotating frame, the velocity dotted into a velocity due to earth rot~tion, and a centrifugal term.) Since the gravitational potential is expressed in rand 8 and we measure in x,y,z it remains to transform between these systems. As may be seen in figure 16 the quantity z dif f ers from the quantity r-r0 because of earth curvature. Study of figure 16 will reveal the relations tan(8 - 8) = y/(r + z) 0 0 The value used for r is calculated from an expression given by Allen 0 (ref. 34, p. 114) giving the distance from the earth's center to sea level as a function of latitude. We also allow for the height of the radar antenna above sea level. In any event, it should be noted that the result of the calculation is not sensitive to the value of r 0 ? A further point of interest is the affect of the gravitational potentials of sun and moon on our results. Since the earth is free fall with respect to these bodies the effect of such potentials across the earth diameter cancels to first order 37. In any event the effects are -- too small to af f ect the accuracy of this experiment. Using the s ubs cripts g and p for ground and plane the previous di scussion may be s urmnariz ed as f ollows: We calcul a t e v2 - v2) P g dt 2 2c where 2 r i = + ) 2 + 2 (r o zi xi tan(e .-e ) = y./(r +z . ) ,i = g or p 1 0 1 0 1 2 2 j V = (v +wr cos8) + v where v =vy =v =0 for X y X Z the ground clock. C. Range Data Accuracy It is seen that a record of x,y,z and v ,v ,v is required for X y Z calculation of a predicted effect. This data is acquired by the tracking facility of the Naval Air Test Center, the Chesapeake Test Range. Both an X and C band radar were available to track the aircraft which was equiped with transponders to facilitate tracking. Five theodolites were also ava ilable for calibration of the radar (see fi gure 8 at the end of chapter I showing the radar and theodolite positions with respect to the flight path). The range parameters were recorded each second of flight. A twenty-one point smoothing technique is appl ied to the origina l data. Thes e proceedure s are standard practice at the Test Ra nge . Their estimate of error is tha t alt i tude , z, will be + 100 fee t and that v e locity, v, will be+ 2 knots. As a n independent check on this estimate ... 47 we comp a r ed calibrated radar data with theodolit e data for a seven hour period using approximately one hundred points of comparison, The mean and s t andard d e viation of these di ffe r e nc e s we r e as follows: c (alti tud e) -1 5 . 5 feet IJ 40.6 feet o (velocity) -.087 knots a = 1. 6 knots We therefore accept 100 feet and 2 knots as being realistic tolerances on these parameters. For nominal values of the flight parameters ( z = 30,000 ft and v = 250 knots) the following errors are obtained: dz/z = 100/30000 = 1/3 % 2 2 d(v )/v = 2dv/v = 2?2/250 = 1.6% For a flight in which the velocity contribution is ten percent of the potential contribution an error (simple sum) is expected of: .9(1/3) + .1(1.6) = .46% The range data was obtained from the tracking center on magnetic t ape. Several mistakes in this data required correction . For example, t here were five to ten cases each flight of repeated data which had to b e eliminated. Experience using the range data has reveale d a few instances in the record where the radar apparently strayed. For instance, over a twenty second period the record may show the plane suddenly climb a thousand feet at rates of over 100 ft/sec and innnediately drop bac k down. These are p e riods in which the aircraft should have been in level flight. No such changes were remembered by the people on the aircraft who surely would have felt air pockets of such a nature. In any event, r e moval of s uch spurious records from the integration results in c hanges of only hundr e dths of n a no seconds out of a total of approximat ely 45 ns. Con- sidering all these fac tors we place an uncertainty of? 0.5% on the prediction ca l c ulate d using t he ran ge data. This corresponds to about ..,_ 48 will be seen later, does not seriously . 2 to .25 nanos e conds and, as ment. affect the overall accuracy obtained f rom the entire expe ri 49 I I ~ ! ' I 2. 2 2- 2. I 1- ::. ( ~ + z.) + X + Y d~ )/ I I y ' I Figure 16. The relation of rang e coordina t e s to inertial system coordina t e s CHAPTER VI STATISTICS A. Prelimenary Concepts and Definitions The subject of the statistics of atomic frequency standards has received much attenti.o n 38-41 . The general trend of notation used in these and other such articles is adopted for use here. The remainder of this section is a brief sunnnary of concepts and definitions. For a frequency standard with voltage the nominal ampl i tude and angular frequency are V and w. 0 0 It will always be assumed that E(t) and ;(t) are sufficiently small that t he definitions to follow are meaningful. The instantaneous fractional frequency deviation is y(t) = .L ?(t) w 0 and the fractional phase deviation is x(t) = L ?Ct) w 0 Note that y(t) = x(t) and that x has dimensions of time (xis the phase measured in the time domain). The average frequency deviation for a t,.. ti = ! ~ y(t) dt = ?[x(tk+T) - x(tk)j t,,_ One measure of frequency stability is the "Allan Variance1137 defined by (1) 50 51 wh ere <> denot es an infinite time average and tk+l = tk + T. Lacking da ta r ecords of infinite length, the expression used in actual practice for t he Alla n varia nc e i s /,I 2 0 (T) = .!.L le 2 Yk+l- yk) N ( = I 2 - 1 1 2 N ~ -2(~+2-2~+1+ ~) (2) I<- 2T Reference 39 discusses the accuracy expected in using (2) instead of (1). We will also make use of S (f), the one-sided (power) spectral y density of y(t) . For white frequency noise S is a constant, y S (f) = h y 0 There is the relation S (w) = = 1 2 S (w) X w y I f R (T) is the autocorrelation function X T R (T)= L111J x(t) ?x(t+T)dt = (x(t) ?x(t+T)) X T+~- -T then Rx(T) and Sx(w) are Fourier transforms of each other: ~ R (T) = -l 1? S (w) e -iwT dw (S (w) two-sided here) X 2n X X -a:> B. Computation of Variances Since x(t) is the phase in the time domain we are often interested in the variance o f quantities that are essentially phase differences; quantities of the form or , where x . = x(t.) l . 1 - 52 A u seful the or em for calcula ting such variances is the following: I f Dis a l i near combination of phases , where a . are coefficients ]. and :[a.= 0 and ( ] D. ) = 0 the n for pure white frequency noise (h d e fined on previous page ) 0 N "L""_a . a .(t. - t.J ) , where i >j => t >t l. l. i j l ;:, J J This result is proved in Appendix C. The condition that the sum of the coefficients be zero assures that only phase differences are being considered. As an example of this result consider the difference between the phase v a lues of two standards at time t 1 and t 2 and assume a mean slope has been removed so that the condition that (x -x ) = 0 is 2 sa1 tisfied. Application of the above theorem reveals that the variance of the quantity x -x 2 is 1 h 0 = 2-'.-~.-l-: ..- ; I ! . I :. .. I ? ,_ _ ~-:? :. L-f-~~ -:?: i -:- 1- :?-: i-:-:-t:-::-t---'--t-..i....,....+---+--~~--,---+--- , 1 ??: _l __ __j__~-- l_ _l +- 2 . I _l I . j -:-r : ~-...:..;-_;____,~.:....1--~~....!.-.2"-..L_;___.L_ _ .; i_...:...1.j. _ :.. ..:: .__-_+ -.. -I . ' I I I LL ?--'---''--+--'--'---+?-:---t-'--+-:-~- : ! i - ?-:---, ?I i" : .. i ? , ?; ~+- . I ' ' I I -? -- i--?r- "--'-~-=-'r-'--'-'--,--.!-c,-....:._...?.?:.1.:?.:?..':....:'. _L-..L;c.L_.:....--1__:;_.'! ...:?? ?J-..:~-1...., +?-1-?? j-?j??--- ! 080 J2640 65280 Seconds Figure 18. Sigma-tau plot for the Rubidium clocks and H-maser. The broad lines are the same as in figure 17 to facilitate comparison. The H-maser plot is largely covered by the lower broad line. The numb e r of samples is the same as the previous graph. 61 ..., >< ! I~ i '( y. ? - "l:: I ""'- I x, - Figure 19 . Typical form of phase data . ....... ~ X: t: t: .,.. 3 '- ,f- Figure 20. Typical form of phase data over a flight. -- - -;i;. - - 1 ~x UJ --? - - " I" - - \/} ,t .. .: 46 .08 Total effect 40 20 CfJ ~ 0 f._) ?.:: U:. ~ <:z.: 0 -[~~s~.~8~9~-===;:;:==:::::=::===================-\~,7-;- ~e:f( e c t -20 I 1 , , 1 t I t I , l , l , I 1 1 1 J 16 18 20 22 24 26 28 30 32 34 HOllQ.S Figure 23. Graph of the theoretical prediction for flight 2 (11/11). -._1 0 FT3 601- ..., I PoL c nLial ~ f fec t I ! 1-:- Total pf f e c t 407 I I I ~ I I I e,..r.... 201 z C c..; ~ cr. 8z < ;;;::: 0 I _ 6 . 65 \I /. e f ir.: ec ~L -20 I I I I i 1 i t I I I I 1 --r?7 16 1 l8 20 22 24 26 28 30 32 llOURS Figure 24. Graph of the theoretical prediction for flight 3 (11/14). ---.J i-' FT4 6C I .~- 52 . 85 Po Len Li a l effect ,._ 4 7. 13 Totc1l e f f e c l I i I 40~ I I I -i I I 20 Ul c:. ;;:: C u l'.i.' V: C, z: < z: 0 I 5 . 72 2 v effe~t -20 r , , , , , , 1 1 1 1 16 18 20 22 24 26 28 30 32 HOTJq_S Figure 25. Graph of the theoretical prediction for fl ight 4 (11/ 22). ' ) N FTS 601 - 54. 99 1\1 tc?nL i :11 ef f ect \(- 48 . 94 I Tot:11 effect 40_J I I 20 VJ C: 0 u t.:-l VJ ~ ~ / ~< X ~ <::> t N 0 ~ --.a -s?- (\>J --- M- J. E- 2- 9 - 55- - ? r--r-- -- ;:::- :;::- ::::, ;=- ::=- :;.;- :--,--------.-- ?,---y---....-'-( 47,.,r.I. 1N5299 1NJ880 2N2907 2N5JJJ 1N751 ~O:J)JJf l00pf JK FROM THERMISTOR .BRIDGE 1N753A POWER CONTROLLER -- - - -- -- -- --- . ---? ?? I - .: I ' - i ! I I . I co ' --.J ! .I ... -I - CLOCK "(/>) \+&-~H{<) k represen 1 t s the gain from the cesium tube comparison to the sy nchrouous d eLec t or output in volts per unit of f ractional error . k represents 2 t he co ntrol gain of the oscilla to r in fraction a l frequ en cy c h a n ge per volt. ll(s) is the tra nsfe r function of th e filter following synchro nous detect i n. '\:ef(s) ls the cesi um r eference Erequency v ( s ) ls the o os sc c illa tor free rur.ning fr eq uenc y . v (s) is o thu et output freq ue ncy . In the clocks we have k 3 . 2 x 1 10 8 volts k 5 x 2 1 0 - 9 / volt ll( s ) ~ f~ +s: (to a good 6 a pprox Lmatlon for our second order l oo p) the c ] oscd loop o utput frequency is \) ( s ) osc vre/s) k 1 k 211( 8 ) v ( s ) o ut 1 + k]_k}l( s ) 89 Putting _i_n U ie act ua l values we have 2 s v (s) v (s) == o sc ( 2 s+1 ) v re/ s ) out 2 (s- H) (s + 1) 2 The t l me / domain respo n se o f v t ? in is out o a unit st e p vref \) ( t ) out (unit step in v ) ref This is plotted in the figure following the nex t page. The response of vout t o a unit step in v is osc (1-t) -te (unit step in v ) osc Thi s is plo tt e d in the figure following the f i g ur e me ntio n e d above . The r espo n se of v to a unit ramp in v is out osc \) ( t) -t o ut t e (unit ramp in v ) osc This l s plott e d in the fig u r e following thos e above . Note tli:-it t h e r es ponse to the unit ramp vanishes as t 00 This means t h at linear drift in the oscillator causes no fre qu ency e rror o r acc umulat e d tim e error . The same thing i s true for the r espo n se to a u n it step . Therefore, if the oscilla tor moves around i n an arbitrary way diring some time interval, ther e will be no tim e e rror co ntributed provided 1 . Th e oscilla tor has at worst linear drift befor a nd after the interval, and 2 . The servo loop i s not overloade d by tile oscilJator exc ursions. This i s the i mportant b e nefi t gained by the second order loop. 90 /\ simplified sc hema ti c of the circuitcy to rc::1lize ll( s ) for the sec.oncJ order loop is shown below : our 9l I . ! ! :I -??. I -- L- -- _:_ __ j__ _ ?r-- --? ?---:- -?---i?- -- -- 1 ! . --- -- I : 'I- --- .'. -. ---Ir - ---I ??? . ! ------- ?---- -- ?---- . ' \__ ! I-0 O 1.0 ~ ' __,_ __ i---,---t---'-,---'--J-- 1---t---,-- - _;_ i:- --t--.-r- --+--.- -- ---- -- : -1---t- _ ,__ _j--+~-+_.:_-+-~?__l__~ -+---;--+-----'--+__:___j+ _____:__+_.!.._+i- -'-+ --i-t-~ --:- r-,-1 ~ l-11 1 ' -- - - - -+----,--,- -' .---r---i-':- L _'------,1--_ Ji_ _ ---t- -- '' :---, _:' _ ___ '..-~-- iI - - -i-- !I - - -~ I 1 IA.I :i: 92 I I :-------~---?--1-------r -- r-?-: , 7 - - - ,----r---, ! : ' ' ! ' : ' : I ! : I I . ! ! ; ; ' . l ? T .. ?-?-?- --- -? ??- --- ?-?-?? ' -- ... ?I ?? --??-1I ,'.. ! . i , , I ! . ---- --- - - __ ! ___ ____ ~ -- - ------ - - -- ? ---- ----- --- -- - ---,--~jt --?-------------- -? ' J _, _ _j__ ------ . ----- l'. ?----1? ~ I , . - - - - ~ ? 'I ' - ?- --,--?,--?i---- -~.-7 ,. i- - I --- 1? --~ - :_---! ?--,----! -- ?? 1 -1 -1 - --" 1 1 - ---------'------'---+1- --'---...------'-! _ _____ , _ ______ ---'------'-- _ __;_ _ ____ -' ~ ;___~r_? _?--_: _.- ~~----:_?-?__i -'-: -- ~-f-_-_- ?_--+f-_- _??_-~:_??_? _ ?~! ______~ _?~-J_?_--.1~~---L-------!'-?-?_ ___ _, ---Lrl- _ -_--.j_-l_--? _---_i _- _:-_--./---_: ---Ll-_-_-~:-_-_? --"-~_--_-_-_:-_-- -_-_-+---_-_-1L: _ --~.-..~. ..; )_____-~\;:i- -_--_- IC--- -,----;------?- " .0.. . ! .--;----: -+---l- ---f------ ---+--~- ~-:--j -?? 1---~- :----- ! IO ? I i ' -:, -,; ; ~ - '--+--'---l--+----1---+- , ! . --+-- ;:: -- ~r -?-t-?- ' --- ,-- . i i -i- -- r--:- ,>,) '----L-"---11--.:._---ll---'-~-+---'--f---'----l---+--'- ~- -,--_jlC--_? ~i -,:-8I_ ___,!_ --1- __ j_~ - ~- __ ) _ :_ i. ! j : ! : I ::,- "1 <' , .:; : ? I I : \J\ -------I, - ??- ----- /- -? j --- ? I i --- t IAJ ! r-') \J ? . . ' . ? ! ! -'I--' ! -! "' -------:- --? --- _,, 0 f: 7 ~' .:; 93 ---i --?--- -?--?--- - -- -------- . I 0_ , in l,O v i -~' . ;_"?:'.. ..._ _j...--:.- ;;--t-1---'--?? __ ,_ _ _; __ _ 1----,'---:--+----+---+---'--+----'-+--'---+_:_--1_;__.;....._+_;_i "'~"",r -:- ?i i . I i l J 1 , 7 ?-----+1--1 . : 7 -?? i I I , , I I ---'l---f----1- -+---"---+----+i- - i _::__.;---'---+-,--?.--- I !- ---:- ? --'- - ?t ?r - - ?--- LxAJ l ' APPE"t-ID IX B . ENVIRONMENTAL COEFFICIENTS OF THE CLOCKS Summarized in theis Appendix are the results of various environmental tests on the Cesium and Rubidium clocks. MAGNETIC TESTS: A rotation of one clock box 90? and 180? in the earth's magnetic field showed no effect on clock rates. Of course, this was with the c locks inside their magnetic shield cans and so is not a measurement on the clocks themselves. The limit of this measurement was approximately three or four parts in 1014 for a variation of about 1/3 gauss. PRESSURE TESTS: These tests were performed by changing the pressure in the clock box by several lbs/in2 ? No effect was detected on the Cesium clocks to the level of several parts in 101 4 . Tests on the Rubidium cloc k s showed pressure coeff 1i 3c ients between -1-0 3. 8 x 10- and -1.0 x 10 /mm Hg. This is a rather large coefficient and the effects on the clock rates are dramatic--see the graph on the next pages. TEMPERATURE TESTS: Temperature tests were performed by changing the set points of the clock temperature controllers. This allowed changes in temperature of five or more degrees. The temperature coeffecients of the Rubidium clocks varied between -1 - 22 .7 x 10 and -1 2- 3.0 o x 10 / F. 94 95 The temperature coefficients of the Cesium clocks are known to v ary depending on clock position and other factors. The coefficients that we have measured with the clocks in their normal positions in th e clock boxes are as follows: Clock Coefficient ( /?F) 10-14 1 (#1033) -3.8 X 14 2 (#1028) - 4.0 X 10- 3 (//1025) -3.3 X 10- 14 7 (ff 752) -2. 0 X 10-l3 7 10-14 8 (#1026) -1. X 14 9 (#1035) -7.1 X 10- The coefficients of #752 and #1035 were also measured by Hewlett - Packard under other conditions. Those results were as follows: Upright, panels on On side, panels off 14 #752 -5 x 10-l 4 /?F -4.1 X 10- /?F 14 #1035 -1.9 X 10-l 4 /?F - 0.8 x 10- /?F 96 .. i 6 ei. ~\\ 4". // ,,..... ~~ (/) 20. ,::: '-' See. 2g.5 FRACTIONAL DAYS RESIDUALS, FILEs DFGB111? SLOPE Flt.Es GPSGB111? CLOCK* ? US PAPER REF 1, 2, 3,15,16, !0? - 102. 103. gs_ ,.....,. r:.. 0. ._, S16- (l) H 9,,4. ?- I- .:.:., ti) H (l) ~- 0. s (l) E-< ~- sa. 86. __,-- i?S.S 2Sl.5 3(L0 FRACTI C"IAL DAYS FILE: TPTOTG111 ? A typical Rubidium clock rate change due to t emper a tur e . APPENDIX C A THEOREM FOR CALCULATING VARIANCES l n tliis appendix we prove the theorem mentioned in chapter VI. bination of phases measured in the time 'rnat is, if Dis a linear com d omain ._.-- ]) = 2 a.x. X = x(t.) = l. - 11 i w 0 a:.= a constant 1. j_ > j t. > t 1. j ~ and L a. = 0 and (n) = 0, 1. t hen h 0 2 2_ aiaj (ti- tj) i>j d in chapter where h is the spectral distribution function as define 0 VI" The condition that the sum of the constants be zero assures that dered is essentially a phase difference . the quantity consi PROOF: ::;z <+-af x? + 2 ':-,- (li(Xj j) 1 xix].. >J. - (> ~ -a? R (0) + 2 a.a . Rx(ti - tj)> (1 '-;- 1. X i >j 1. J ' where R ( T) is the autocorrelation fun c tion X 98 99 T R (T) = Lim ) x(t)x(t+T)dt = ( x(t)x(t+T)} X r~ -T Since La . = 0, we have ]._ 0 -- = > a 2 i + 2 '> (l ? a . L_ ,e__ - ]._ J i i>j Therefore equation 1 may be written (2 Recall from the summary in chapter VI that there are the relations 1 loo R (T) = S (w)e-iwTdw X 21T X - 00 and S (w) = S.(w) = w2 s (w) y X X Hence we have )oo S (w) 1 y_ -iWT R (T) = e dw X 21T w2 - 00 which for pure white frequency noise, S (w) h, becomes y 0 h R (T) = 0 loo -iwT e dw X 41r 2 - 00 the extra factor of 2 appearing because S (w) is the one-sided spectral y distribution function. Thus h h -iwT h -0T 0 1 - e 0 (n) = [Rx(O) - Rx(T)] = - dw = 4 41r ) w2 41T - 00 where the principal value of the integral has been evaluated. Insert- ing this result in equation 2 gives the required expression: h 0 2 APPENDIX D DATA PLOTS FOR THE FIVE FLIGHTS This appen4ix contains data plots and environmental plots concerning all clocks for all major flights. The clocks are referred to by number n these plots, the general sequence of this numbering system being i discussed in chapter rr. We list here a summary of the numbering scheme, !_or all flights: 13 = Mean of 7 =Cesium# 752 clocks 1,2,3 1 = Cesium #1033 8 = cesium /11026 2 = Cesium /11028 14 = Mean of 9 = cesium f/1035 clocks 7,8,9 3 = Cesium #1025 10 === Rubidium 4 = Rubidium 11 === Rubidium S = Rubidium 12 === Rubidium 6 = Rubidium Clocks l through 6 were in box Pl which flew on flights 1,4, ands. Clocks 7 through were in box #2 which flew on flights 2 and 3. 12 r Other clocks: from flight to flight. The of other clocks varied The identity identification is summarized here: 4 Flight 5 ?1-ight ]_ Flight ~ NP2 Clock ti ~ NP2 NP2 NP2 NP2 Cs 761 NP3 NP3 15 cs 761 NP3 Cs 444 Cs 761 Cs 761 16 cs 444 Cs 052 Cs 871 Cs 761 Cs 862 17 cs 862 Extra Cs 871 Cs 871 Cs 862 18 Cs 871 Cs 862 19 20 101 The units NP2 and NPJ are the two hydrogen masers. The plots in this appendix are arranged in the following order: PLOT PAGE One g raph from each flight of the flying ensemble (the three Cesium clocks) versus the ground ensemble ....... 102-106 One environmental stmllilary sheet from each flight ............. 107-111 One surmnary sheet from each flight showing the phase record of the ground Cesium and H-maser clocks versus the ground ensemble ................?................ 112-116 Three pages per flight, each page showing the phase record of one flying Cesium clock as measured by the ground ensemble and as measured by the air ensemble .... 117-131 Similar plots to the above, but for the flying "travelling" Cesium clocks ...?............................. 132-140 Similar plots to the above, but for the flying Rubidium clocks ..?....?...?.?.........?.?.................? 141-155 Depending on the type of phase plot (air or ground), there may or may not be phase data for the inflight period. If there is data, the inflight period is indicated by a vertical line at the beginning and end of the inflight period. If there is not data, a solid bar appears on , . the axis for the inflight period. In both cases this "inflight period" is really the period between the times that the cables carrying signals from the plane to the ground are removed or reconnected. Hence the "inflight period" appearing on the plots includes engine warmup, taxi, etc. The arrows appearing on the Cesium clock plots indicate the end points used by various runs of the program SHIFT (see chapter VII). Since the program works on all clocks from a given flight at the same time, arrows dictated by a :1,) ssible rate change in one clock appear on all clocks. r 0 0 0 60. 40. I 2(L J 0 ? I L:"..~: ??- ---:?? ? -? -??: ? ? ?~ ? ~ -~.-- ? ? ? ? -.~ -??- --:. .-~3 -? ?- ~ -? ? ?- ?? - ?? - -? --?- ll e ? - ? - ? " ? ? ? - - - ? " ? ? - ? ? ? - ? ? - ? - ? ? ? - ? - ? ? ? ? - - - ? - ? ? r r -20. _... Flight ensemble vs Ground ensemble, flight 1 -40 .. - -60. ~--------------.----_._--.---------"T""--..-i 85.0 85.5 86.0 86.S VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG929 SLO C PEL O FC IK LE# : 13 G DV SS G BP 9A 2P 9ER REF 7, 8, 9,15,16,17, t-' 0 ~ N = 1 (~ /+Z"~+ # 3) .., l 0 0 a 80 .. 60. 40. ------------------- 20. 0. I ? ?? --- ....t t l... - - - - . ?J~ --------+------------------------?-- ------i------------------- -20.,II I -40. Flight ensemble vs Ground ensemble, flight 2 -60. -ae. ----r------.-----.-----~---....-------,--?- --.-------- 27.e 27.S 28.0 28.S 29.0 29.S 30.0 30 V .5ER T SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG1111 CL SO LC OK PE# F1 I4 L EU :S GPA DP SE GR B 1R 11E 1F 1, 2, 3,16, ~_, ~ C l.,.J '::: 1 (#7+-,-,. 8 +* '1 ) ~ l 0 0 D 60. 40~ -- - 20. 0. ~ .. I ....... .,:-:, .. ~?---~-, - It ftf ? ? ? [;-~? ?- -? -? -? -~ -41 -- -3 ? ? ? ., ~ ? t ? r ? ? ? +? ? -? .. ? ? ? ?" ? ? ? ?? ? ? ? ,.., ? .. ? ,. -20. Flight ensemble vs Ground ensemble, fli ght 3 -40. -60. I I 28.5 29.0 i 29.5 30.0 30.5 31.0 V ERT 3 1S .C 5A LE?N 3~ 2N .0O SEC 32.S FRACTIONAL DAYS RESIDUALS, FIL~: DFTO C TL GO 1C 1K 14~ S1 L4 V O S P EP A FP IE LR E :R E GF DSG1, B 12 11, 4 3,15,16, I-' 0 .r,- = ~ (* 7-t- ~8 t-71" 9) ~ 0 ul '" ?, , 60 .. 40 .. ------------------- 20. 0. .r----------c---? --~-?-???????????? ? ??????????~-? - ????????? -20. Flight ensemble vs Ground ensemble, flight 4 -40. -60. -------,..--------r--------------------------- 38.0 38.S 39.0 39.S 40.0 VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE; DFTOTG1122 SLOPE C FL ILO EC :K # G D1 S3 G BU 1S 1 2P 2A PER REF 7, 8, 9,17, 1--- ~ 0 V, = 1 ( i -t-~t-3) l ... u 0 0 60~ ..._ ,.____....-,, 40 .. 20 . '"l;,,'I ? _,~.. ....,....._ .-------?- -?~t---------,1-I- ---, .:.., M .... _-lr..,"-.i":, ;~;~~ ? 4 ' _d .._,,.i,t? ??~???#l>-????l r-???? .. ? ......... _.,.,,.~??-?" -20. Flight ensemble vs Ground ensemble, flight 5 -40 .. -60. --.------------------,---------- 8 -6. -0 . ---8 -6 -.5 - --8 -7. -0 87.5 88.0 88.S 8 V 9E .0RT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG C 11L 0O CK# S L1 O3 P EU S F IP LA EP :E R G DR SE GF B11? 0, 8, 9,15, ~ 17, f--' ~'!- (1 0 -t-.l-t-~) 0\ I.. ... 107 GROUND (Box 2) FLIGHT 1 (9/29) AIR (Box 1) II ION I p_ t.::;,.r I ! t e J . e .,? 1'4-? .., . ,oz .a 1'~. n .s 1?2 . 7 IA le.! . & : ~ -~:- \- ;_..;;_??:??_?~_:;.:.",A'". - ?;_-i,\\c~:;~/;/:-) '"' i II] ?? 18'! - 5 I -- i .. ~?;i?~,F?; c,,,~,~~'~t":~,~-,-'-~ '"?,~i\ 1- I ? ~:; :~?T ??: .C}f ~7~-c,~~-,~'; T ( ., ,. ... ,, >,o( . 87- . ~.. - --.,..-~ _ ........, .._,,...,. ..... ____ " ? ?-? r.; . . . .. .. .... . I .I ...I ~ - .,.. i_.:, :t1 az. , 'f '." .1 -. . - f I I I N , I r; . ~ H lr ,!i I . 5 !hi .e ? ir ??M C T l c,,,,t,ll [)Ill'-, - -? ,NACT I O,,.L [UIIV i .. GROUND ( Box 1) 108 TU"', ,_. , p FLIGHT 2 (1( T 1 _ /_ 1 __ 1_.,. )... .__ t-? y--L t . l. l / " _ J_ (_ _ ?-y--- - - ?---- IS. t AIR . (Box 2 ) 9 . S ?-? P. 12 . ? I::. X. T ti .s 11 ?? 19 . 9t ' ' . 111 . ? ~.~.. .... . ,I-?.'.s" ,~~' ::-,~., .:.- ,-2, .l~. ~ ?. ~..t.-~..~..--=.. . .. ~~ 1g . 7 : I ,. ... le.? , 5 l.e..I, .. r " ? n ., N . .... Illa . r ,:,0 . ... ... ., I : -I A . S ca ., S? .s " G? .? - -5 .".'.?.? 1)5 , L 1. .a .? 3 I 5 0 ? ?C Je . 5 ffl SI 21 ?11 Pt Fi 1 I 109 FLIGHT 3 (11/14) AIR (Box 2) 15.('I l J ,O 11-0 ~ 10. 0 ~ "T--- I? .a ?! 0 1 .. . ., - ~ =---,., 1 c' ~?----==-~ ,~=, - ' ~-5 -I iN r . - . . . - .. .:. . .:. .?. .- .:..- . ... .- . . ---- -- -=.'""-;-cc-- ..- --1? . . . : ? ? ?? --, ?: - - -- t7 .7 i I I 10 0. 6 ?1 ! ; .. ... . __ .: ?. _ _f ? ?-?'-? ? . J_.-::; __._ IM.5] .-c.: ?. : ::..c , [ _.._ /'.'.) ,~::- .- -:c.- :.."-:. ... - 97.G ;.. _._.? : _-?-:_:_~ ~?-::- ?-_.:.:_~ :0:::-.a;--. ? , ? , -- 1 ? 7 -.,I ? ? ? . ? ? ? . ? 1 c.??_, :_,-:,. ..c.-..? ? t _ ,P .:. .0 '. "?.. . ":;' ?I f "i " . 97. S ~. I 100 . J ?tt<:? ,._ I I ,ca., l lt'2 . I8 ~ t : :-.: ,:- ---'? ?; j ."-?-:-:.'",~:"_: :-~'-:, ?: ::::: l/,/\:<":?-,-~ - ___ I .,.. ? I 9 J . 1, J . ,Z.0 - \ ~,'-'I,,-,???:: I. 91, 0 -1 ? ... / 1 9M ~ ? 8 9. \) ~ :::j ---- ??-i I rs ; (,3.0 1 -i :: l G7 .S ? ~- . '.'?. j 7 0 . ~ I "'?1 ~ X -1 T ::: rl 06., : :_.,,,.. _.,. : ._-: : ' I : ,~./ ' Ca . O l G7 . < , . G 7 ... L- ,-- -- - r -- - ,- - ? ??--- ??? ? 1 ..: i , .-, .': 'l . ,l ;:, :; . r> ).) . ?' r .. , ? ? 1 ? ,"'' 1, (1 ~~ . 5 J \l . ,' ) .? . '. '.'I r . ,. , J I . $ ,. : .. l. !. .. . _ 0, t ?. ,? .. , 1. . . .. 110 GROUND (Bo ?:, x;, r 2 ) FLIGHT 4 (11/22) ---, - ',- c' ,v AIR (Box 1) - -~- ---- -, ? __ ___.,,,?..____,_ I ! I FL1C. 11r H,S ;. . -, -l .- C -I I I (.. S -r . J?1 .'. 7? 15. 10 . - s . . I C<. s ~ '?-. :cu ., 1" ' . ) l ' .i ', ":, .'" ~:',"-':'. ." .1-.~-?_,- -?-:,:-'- ,. _.~-.-:='- I .~-< . 2 ? ? - - ,? ?., -l '?'J. 7 1.:?J.'.\-1 100. --: l7? S9, J ? 99 . z _J ... "'J . ~~- ? . ,-~---. i ''--_: 7 ?.- .l ?-) -. -=:-J ? J G -- . ___ 7- -~ - lO J .S LO~ .a I : o,. 7 ?!--. 10, .s ]! l ~;l, .S l <;". ; .; . I _,I_ ;; 1 T O? ? I OJ I oz . 4 I ?-??? -1 cc . 4 " ":"4, - ? ?'..:r 7~ . . ";' -, , . 1 1. -' J1 . S ru ; ,' T' l ',' ??? L t .._ , c; 111 GROUND (Box 2) FLIGHT 5 (1/10) AIR (Box 1) F!t.1 ::, f\T 'SU N I FL1c.11 r ! (----"-----, -- - ''--~----~'----y- :,.c?j - 1 1 1 I~.~, -1 7 r---- 1:; ??' .! I I lJ.0 i 1 ._ ." . .'.? i :: :J 12.0 -1 I - :'?:, I :e.o -J !_ ___ ,.. _______. ,. .. --......- -----rI. . - ---...,,.,.__ I ... __... i i i :6 .s -j .... ..... -- ""-?-??-.. ,..-.._ -~'' - ~ . .-_-:.,,? ', \ ",- ?, . ;- ?. ?. :T/, ? ,- ;- .._~r~ ., ::-,,;,.,} I ,r..,.! h"C JI ;~ ) .2 -j I I . i J ,? ~ . :,.: . ~ ":..:_." ".;._. --- ? ? ?. ' ?' +- _:?-,--, ;.?. :? I ,.-?,??-cz:'"'-"~ c _f.r_-:.--c,:;,,~ 1:::: J .e .J I[- _ --- ? j - .-?? . . / - 11..' 1.:. -. : :::2. ;1 - ..-.??. ?.. . ,-????.1 I '-?'\?-,. .?.? ., . ...?? 7I 00.s I I !CJ .O 7 I I ) 10, .? . I ~. . : .. 1?- .? c- ?,:_-., I OJ.? I I I I I I l 07.C\ j l .- I I J ?-_ -:? - -:_._: . .. - . !CS .J I I H~. ? ?1 105.G -I _1_os.a ~ I i "' . 1 I "?'? -1 co. ~ I I G9 . b'l. -? I I . 6 S. - -L' <;7 . 7 , .? I , ,6. _j I I I ss. l I G ? . -J ?i--,? ?- , - - ---- ? - - --?-? r - -- 11?-I -- -- r--- - 1 - ?1 -- - I - ...,_ 1.'-?? -0 1?.;.,:, Uf.<' -- ~-?'"'.' .? , f ':' .!i ~,J.0 11 ? ? -.I l,' '; : ...... .. , ....... t' - ',. ', f) . ?, ? ?'-:. 112 FLIGHT 1. Ground data: Ground clocks vs clocks 7,8,9,15,16,17 - 5. #8 -10. ?. j--????????;?;????????????????? ........ :??? ........ ????????????? ??????????????????????? ..?? ??? ?I _- ss. .+- -- -- - --- - -? --------. -:tt;s - 0 ? ???? ????????????????????????? ___, ,.,._.~., . ,,hr:?'"?, . r,1.,rc:. -.,--r.,?r :.-...,_ __,. ..,.,.-:,,.w_,.,. -,...-:,.,?:'?: ~ .. ~ . . ~ . .: :.'.: : .'.~ -~ ---~ . .- l - - ---- - --- - ------- s. -- ..... ??????????????????????????????????????I -s. 85.0 85.5 86.0 86.5 VERT SCALE?NANOSEC FRACTIONAL DAYS _ RESIDUALS, FILEI DFTOTG929 SLOPE FILE? GDSGB929 - -- PAPER REF 7, 8, 9,15,16,17, - 113 FLIGHT 2. 9round data: ground clocks vs clocks 1,2,3,16. 5. -ti: I i I ,,...,..,..,.,,..,..__. ...... ..' . ... .... . +?? ??????? ???? ???? ?????? ?? ?? ??? ?????? ? ??? ???? ?? ?? ????? ~~~~ I s. ~ 1I 1P 0. -3 -,.?+i =~ ?;;,-'-~=~ -s. ~ I s .. ' .. ~ -? +?+ ????? ......... I # I 5' . -3. ~ ! -10 . ~ _I -is. I -,: ;) . J ? I s. 7 #It LX.'~- -- ~ . . .. . --1. .. ? ~~~ ? ~ ? ? ?? ?? ?? ? ? ? ?? . ;~' 0 ? -~~/'? ? ~ '{?~ ?~ ? ? ? ?K ~---.. .,.._.. I I I I I -5. -i C:~-l .:.? .?. : 1s ? .... "-. ' . - I I b E' HPll?IS vn?? r,t? TQI@ "~ j rd 114 FLIGHT 3. Ground data: Ground clocks vs clocks 1,2,3,15,16 # I ?--- -- --???? ---- ?- ' ??- -??? --?-' ..J.J.... ?tt- ;;J._ tl ,:.:. .: .:. .: ~-:.. .+ ----<".?~.-:-:-::~:: .. <~:-..... ~?-r:-.~~'~.:.:..~~~.:~~<~-~--~: :.:,: t;.:..:__.:: ?~~:__::.:.:~ I I .. . ~ r, '-' ? ! ?7 I ~ /7 I I I ??j I ,,.?.. -1:-; . 7 I ,,. -1s. 'I ?-- ---- , - - - - - ? -? - ?--- - ?? ' 115 FLIGHT 4. ,G round d__ a ta: Ground clocks vs clocks 7,8,9,17 10. I s . ~ .,.,,.,.,..,_..,..,. . --- I __/ ""' , ..,. ,..~? -/ c. -10. -l s . _..., - LC . _J I I -:s. --, I I ; -:it- I 7 I: __,/~I , ,-.,..._...,,, .. ., _._':.,~~--? ,....,,,: .. ~~,--~ ... ~~~. .. :.. .........~ ~ ---? ? ?:., ... . .... ...- :'-..J_,~ ........ -- ....._ ? , --. .. . \ I lS. - 20 . - ---.---- - ? -r---- ---r- ------i--- J~ . ) JJ . S J O.a ::-, ! : ...- i:: 1: :1 C ; i..~D~'"-'"J l 122 r., . ? - 116 FLIGHT 5. Ground data: Ground clocks vs clocks 7,8,9,15,17. s . ~ -il=1 I i I . . ? . ~ :.:~(:'.:":'.::'.'.'>. --=-=:?:+=;;;.=:.-:;;;;::::.~ . ?? 5- =1 _ s. _, I , ~i # / S' ? ?? ?? ?? ? ?? ?? ------::-: ::r-. ~. ' .....- ...-...-..-...- t ?- ? ? ?- ? ? ?-?? -? ? ?- ?? ?- ? ? -? ? ?- ? ? 0, [ ---- ? 1 I _-s. d ? I I 8.:3.C SS.5 87.C 87 .S SS . 5 RES! r U9L5, F I LE: CFTOTG! 10 SLOFE FI LE: CCSG~llO PAPER R~F 7 , 3, 9 , 15 ,1 7 , 117 - 20 . -60. --------.-------r--------,--------,---- 85.0 85.5 86.0 86.5 VERT SCALE?NANOSEC F"RACTIONAL DAYS RESIDUALS, F"ILE1 DF"TOTG929 SLOPE F"ILE1 GPSG8929 CLOCK$ 1 US PAPER REF 7, 8, 9,15,16,17, Cesium clock 1 Flight 1 20 . 10 . s. -s . -1s. -20. -------,--------.------~------.---- 85.0 as.s 86 . 0 86.5 VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE: 0~70 - ~929 SLOPE FILEt PSAB929 CLOCK a 1 US PAPER REF l, 2, 3, 118 20. i ~. -,--C -2~7:.:":".:"-~;"-j-???????? ...... ?? ????? ................... ?. ..? ??-????????I ???? ????II I -20.1 -?0. 85.0 es.s 86.0 86.5 ~ SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE: C~TOTG929 SLOPE FILE: GPSGB929 CLOCKS 2 VS PA~ER REF 7, 8, 9,15,16,17, Cesium clock 2 Flight 1 20. 15. ...... 10. s. e. -s. -10. 85.0 85.S 86.0 86.S UERT SCALE? NANOSEC FRACTIOr--AL DA'-'S RESIDUALS, FILE? : ? T ~7~,2J SLC 0 E FI L? 1 PSAB929 CI.GCK S 2 VS pocER REF l , 2 , 3 , 119 (:i\), ] ,:c,. I 20. 0. -+---r??~;.::.:.._:~:;__ ?_:.., -:-: .:.::l??????????????? ???????????????????????????????????????????????????II - 20 . 85.0 85,5 86.0 86,5 '-?RT SCALE?NANOSEC FRACTIONAi. DAYS RESIDUALS, FIi.Et DFTOTG929 SI.OPE FILE : GPSGB929 CLOC~ S 3 US PAPER REF 7. a. 9.15,16.17. Cesium clock 3 Flight 1 ..... . 10. s. J ...., .-?.;--..;.;_????? ?????????'?????????????????????????????? ?????????????????????????????????? I ~ -s . -10. -20 . J...-----~------.-------,-----~.--- 85.0 ss.s 86.0 86.5 UERT S~l.??NANOSEC FRACTIONAL DAYS R?SIDUALS, Flt.Er ~F7; T~929 SLOPE FIL? ! PSAB929 Cl.OC~ ? 3 VS PAPER ~EF l, 2. 3, 120 80 . 60 . 20 . 0 . -t+-----::---c::::::::::::::m???????? ?+?????????????????????????????????l??????????????????? -20 . 27.e 27 - 5 28.0 28.5 29.0 29.5 30 . 0 30.5 UERT ~l.E?NANOSEC FRACTIONAL DAYS RESIDUALS, Flt.Er DFTOTG1111 SLOPE FIL.Er GPSGB1111 CLOCKS 7 VS PAPER REF 1, 2, 3,16, Cesium clock 7 Flight 2 ,- 1 20. 1~ - 10. I s. I I i : /4 ~ e. ~-.,,,..~---------1------------------------------------- i, .,_ "" ~- -1s. -ee . ......- ~----.----------..----..---- ..--- ,--- 27.0 27.5 28.0 28-5 2SI.S l.?RT SCALE?NANOSEC FRACTIONAL OA..,,S RESIDUALS, Flt.Er DFTOTA111 1 SLOPE FILEr CPSAB1111 CLOCK 8 7 VS PAPER REF 7, 8, SI, 1 21 ?0 . 0. +-...._..,__,.-1:r:--'--c::::::::::::a ????????t???????????- ? ???. ???????????????I??????????????????? :,....- -?e . r -60 ? .J----..----...----.---...----.---...----,-- ~--r-- i?'?.0 27.5 28.0 28.5 29 . 0 29.5 30.0 A 30.S '-?RT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, Fil.El DFTOTG1111 SLOPE Fit.Ei GPSGB1111 CLOCIC a 8 VS PAPER REF l, 2, 3,16, ..'? .. Cesi um clock 8 Flight 2 2e. 15, 10. s. . e. I I I ~..~:-~-' - ~?=iI???????????~; ,I:: -a;. .- -1e. -1s. "' -z.. ---r----,------.---~---.------.----....---~- i?'?.e 28.0 29.5 30. S \O'T SCALE?NANOSEC RESIDUALS, FilE1 DFTOTA1111 St.OPE FIi.Er GPSAB 1 111 CLOCIC a 8 VS PAPER REF 7 , 8, g , 122 ----- 20 . e. +_,??=??~?~--1;f-??~-?~ =:::?????????+?????????????????????????????????f? ???-??????-????? -20. -60. ----~----r---..,.....----,~---.----+----.---.......-- 27-0 27.S 28.0 29.0 29.5 30.0 30.5 UERT SCAL??NAl'IOSEC FRACTIONAL DAYS RESIDUALS, Fit.Ei DFTOTG1111 SLOPE FILEi GPSGB1111 CLOCKS 9 VS PAPER REF 1. 2. 3,16, Cesium clock 9 i Flight 2 ae. 15. 10. 27.e 27.5 28.0 29,5 30.0 30,5 Ul'RT SCAL??~NOSEC AES~t.s. FILE? OCTOTA1111 SLOPE FILE? GPSA81111 Ct.OCK a g VS p.:,pe:q REF 7. 8, g, 123 60. 20 . -20. -60. ~-.-----,,-----,-..__-~---.---~---....----r----,- 28.S 29.0 29.S 30.0 30.S 31.5 \?RT SCAt??NANOSEC FRACTIONAL DAVS RESIDUALS, FILE1 DFTOTG111? SLOPE FILEt GPSGB111? CLOCK? 7 VS PAPER REF 1, 2, 3,15,16, Cesium clock 7 i? r l Fiight. 3 ' ....... - 10. . iI ,,.. ? s. ~~ ?? -+----~?????--?--~-~_-,.:.-.# ... .. _. __________ I,-~ ~____ _____I- t -n-----?------??-?--------I l J I I -5. I' I ~1e. J : -1s. 28.S ~.e 30.0 30.S 31.0 31.S 32.0 32.S ~ SCALE?NFW"IOSEC FRACTIONAL OAVS RESitoALS, FILE1 Df'"TOTA111 ? SLOPE FILEI PSAB111? Ct.OCK ? 7 VS PAPER ~EF 7, 8, g, 124 60 . ?0 . ---------"' -20. -68. ~-.------,---...---'---,--...--r---~----,--- r---, 28 . 5 29.0 29.5 30.0 30.5 31.0 31.S 32.0 32.5 UERT ~LE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG111 ? SLOPE FILEt GPSGB111? CLOCKS 8 VS PAPER REF 1, 2, 3,15,16, Cesium clock 8 Flight 3 1s. ...... - 10. s. e. -ts. -ae. --r---r----.-------...---.....-----.--- ~-- -r- 28.S 2S1.S 31.5 32.5 \.OT 5CALE?NAl'?)SEC RESIDUALS, FILE1 DFTOTA111~ SLOPE FILEI PSAB111 ? CLOOC S 8 US PAPER REF 7, 8, g, 125 -~"".,,'..-. ---- ' 20 . r? -60. ---.---.---r-'----r---"""'T"----,.---.----~---r 29.0 29.5 30.0 30.5 31.0 31.5 32.5 I.ERT SCALE?l'W<>SEC FRACTIONAL DAYS RESIDUALS, FILE1 DFTOTG111 ? SLOPE FILE1 GPSGB111? CLOCKS 9 VS PAPER REF 1, 2, 3,15,16, t Cesium clocl< 9 . ' Flight 3 a,. 10. s. -ee.-------.---.....-------...----.----,----r-----r 28.5 29.8 30 . 5 31.0 31.5 WJln' ~?NANOSEC FRACTIONAL DAYS IIESIDUAt.S, FILE1 OF"TOTA111 ? SLOPE FILEt PSAB111? CU)(X ? ~ VS PA~ i:; i::F 7, S , ;, , - - - --?- - -- --?? - - - - - - ------ . --???- ?-- ----?-? - - 126 6{) ?? 20 . l 0. t??"",.,...,,.,.. .... ___ _. .,f_. __,_ _ --{ ::; ;::.- ;,_ ' 3? i????????????????????????t??????????? -20 . -?0. -60 ? .J-----r------.-----T------r-.......- ---r--- 38.0 38.5 39.5 ?0.0 UERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS. FILE1 DFTOTG1122 SLOPE FILE: GPSGB1122 CLOCK* 1 US PAPER REF 7. 8, 9,17. Cesium clock 1 Flight 4 20. 15. 1e. s. e. -s. . -10 . -15. -20. J-----.-----~------,------,------.--- 38.0 38.S 39.0 39.5 ?0.0 UERT SCAU:?HANOSEC F"RACTI QNAL DAYS RESIDUALS, FitE1 DF"TOTA1122 SLOPE FILE1 PSAB11 22 CLOCK: 1 US FHPER ~EF 1, 2 , 3, 12 7 ------------- 0. +--........?.;? .?;.:??~? ?=??..?.:?.;?;..?:..?a~???;.?.;?. ' -i' --c==--===?::,::J:l ?t ?????? ???????????? ????? t ??????????- - 20 . 38.0 38.5 ~ SCAI.E?NANOSEC 39.S FRACTIONAL DAYS RESIDUALS, FILE1 OFTOTG1 C 1L 22O CKS S LOPE2 FV ILS EP 1A P GE PR S GR BE 1F 1 22 7, 8, 9,17, Cesium clock 2 Flight 4 20 . - 15 . ..... . - s . -10. -15 . 38.0 38.S 39.0 1..IERT SCAL 3E 9?N . SA NOS?C FRACT:::ONAL DAYS RESitUALS. F ILEt CFTOTA1122 C LO SC LK OS P E FI2 L EV 1 S PP SA AP BE 1R 1 2R 2? F 1, 2 , 3 . 1 28 0. : 1 -~-- --- ----- ? ? -??? - --- ----?-- -- ----- --- -20 . 4 -40. J 38.0 38.5 39.0 39.5 ?0 . 0 ~ SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE! DFTOTG 1122 SLOPE FILE: GPSGB1122 C LOCK* 3 VS PAPER REF ?, 8, 9,17, Cesium clock 3 Flight 4 20. ts . 10. s. e . ..!.-~~~~~~-L~~----- ---~ I i -s. -10. -1s. -a,;, ? .,.j..---~-----~-----,--- - - -r------,--- 38 . 0 38.S 39 . 0 39.S VERT SCALE?NANOSEC F'RACTICNAL DAYS R?5 ICUAL5 , FILE t CFTOTAt1 23 SLOPE ? ILE1 PSAB11 22 CLOCK a 3 VS PAPER REF 1 , 2, 3 , 129 60 . e ? ------..,:."' ?.~-.T.~.-:~--~-1,".''. ?~?th-'""'""'? --+"'f.l.._ - ----->-----????-??-I?????????????????????- 86.0 86 . 5 87.0 87.5 88.0 88 . 5 89.0 \ERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEs DFTOTG110 SLOPE FILEs GPSGB110 CLOCKS 1 US PAPER REF ?, 8, 9,15,17, ;- I? Cesium clock 1 29. Flight 5 r 15. 10. s . ?? \, -a;. -10. -1s. ; ~ -.!9. ' a&.e 86 . 5 87.0 87.5 88 . 0 88.5 89 . 0 \OT ~lE?MANOSEC FRACTIOf'!At. DA'l'S RESIDUALS. FIU::1 DFT~ A110 SLOPE FILE? GPSAB1 10 CLOCK s 1 US PAPER F--~~---~--~---~---~---,----..,.-- --1- 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 VERT SCALE?NANOSEC FRACTI ONAL DAYS RESIDUALS , FILE1 CFTOTAll!l SLCPE C FL ILO EC tK S P SABllllA1 9 U~ PHPER REF 8 , 9 , 135 so. 7 :::~~ '-~ 1 :: Y???t ???????? ?????????? ????? ~ .~IH????????? ??? ???? ? -10. - -20. 28.S 29.0 29 . S 30.0 VERT SCALE?NAN 3O 0S .SEC 31.0 31.5 32.0 32.5 FRACTIONAL DAYS RESIDUALS, FILEt DFT C OL TO GC 1K 11* 4 S1 L8 O PU ES FP IA LP EE tR GR PE SF G B11 1, 1 42 , 3,15,16, "Travelling"Cesium clock Clock #18 Flight 3 40. 30. 20. 10. 0. -10. -20. -30, -40 . -"---r---,-----,r-----,- --,--- 2 -8. ,5 - --- ,---2 -9 -. r0 - -- , 29.5 30.0 VERT SCALE?NAN 3O .!S ..E 0C 31.5 32.0 32.S FRACTIONAL DAYS RESIDUA~ 5 . F!LEr DFTOTA 1114 CLOC~ ~ 18 US PAPER Rc F SLO8 P, E FILE t PSAB1114A 136 S0.] ?..). 3 1(.,. I 20.j ~ . l:~!? ???? ??-t-??????? ????????????????~ =--=-?===JI '1f-? ?? ? ? ??? ?? ?????? ?? ???? ft- -10. -20. -30. -?0. 28.S 29.0 2 9 .S 30 . 0 30.S 31.0 31.S 32 . 0 32.S VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE! DFTOTG1114 SLOPE FILE: GPSGB1114 CLOCK* 19 VS PAPER REF l, 2, 3,15,16, "Travelling" Ces ium clock Clock Pl9 Flight 3 30. 20. 10. 0. -10. -20 . 28.S 29.0 30.0 30.S 3 1.0 3 1. S 32.0 32.S UERT SCALE?NANOSEC FRACT l ONAL DA' t S RESI CUALS , F ILE ? DFTOTA:11 ? S~OPE FILE ? PSABlll ?~ CLOC~ : 19 VS P~P~R REF 8 , 137 80. 6 0 . ? - ~ 20. -60. -80. J.-.--------,-- ----~----~-----~----~-- 38 . 0 38.S 39.0 39.5 ?0.0 VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG1122 SLOPE FILEt GPSGS1122A CLOCK: 19 VS FAPER REF 7, 8, 9,17, "Travelling" Cesiur:i clock Clock Hl9 Flight 4 ?0. 30. . .., .. ? r- --.. . t :~-jt/f:'.:!t;{/;~:.~ .. ::. ._:, :- 20. 10. 0. -10. -20. -30. 38.0 38.5 3SJ.0 39.5 ?0.0 VERT SCALE?NANOSEC F"RACTIONAL D,=ws RESIDUALS, FILE t ~FTOTA11 22 ~LOPE FILEt GPS~B1! 22A CLOCK: 19 US F~r~R ~EF 1, 2, 3 , ~r-------~ 10. 0. -10. -20. -30. -..0. ->-- ---r----'------,,------~---- -~-----,--- 38.0 38.S 39.0 39.S ?0.0 VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG1122 SLOPE FILE: GPS C GL BO 11C 22K A~ 20 VS PAPER REF 7, 8, 9,17, "Travelling" Cesium clock Clock #20 Flight 4 30. 20 . 10. e. -10. -20. -30. ->-----r------,---- --,------,--- - - -,--- 38.O 38.5 39.0 39.S VERT SCALE ?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE: DF TOTA1122 SLOPE FI LE: GPSAB112 C 2L HO CKS 2C VS PAPER ~EF 1, 2, J , 139 HlO. so . 0. ?? ???--t--{~ Z3?????????????t?????????????????????? -s0. -100. ->-r- ---r- --- .--- ---,-----,r---------.-- - 86.0 86 . 5 87.0 87.5 88 . 0 88.S 89.0 VERT SCALE?NANOSEC F"RACTIONAL DAYS RESIDUALS, FILE1 DFTOTG110 SLOPE F"ILE: GPSGB 110A CLOCK# 18 VS PAPER REF 7, 8, 9,15 , 17, "Travelling" Cesium clock Cl ock #18 Flight 5 .. 60. --- . 40. 20. 0. -------"!-?????????????????? ? ' ?I ?????????????????????????????????? I -20. -60. ->-.-- -- -...----~---~------.- - ---,-- ----.-- 86.0 86.5 87. 0 87 . 5 88 . 0 88.5 89 . 0 VERT SCAL?? NANOSEC FRACTI ONAL DAYS RES IDUALS , F"ILE ? DFTOTA 11 0 SLOPE FI LE1 GP5~Bl l e A CLOCK? 18 VS P~FER REF 2 , 3 , 140 6 0 . - - 20 . -60, .J...r-- - ----,-----...-------.------,r----,-------r--- 86.0 86.5 87.0 87.5 88.0 88.5 89.0 UERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE1 DFTOTG110 SLOPE FILE C IL O GPC SK G? B 11 19 0A US PAPER REF 7, 8, 9,15,17, "Travelling" Cesium clock Clock #19 Flight 5 20. 15. ,. -10. -15. -20. -,------.-----~ 86.0 86.5 87.0 87.5 88.0 88.5 89.0 VERT SCALE?NANOSEC FRACTIONAL DAYS RES ICUALS, FILEt ['FTOT"l l10 SLOPE FILE1 G C PL 5O AC BK 1 !1~ :' ,_,. 19 US PAPER ~EF 2, 3 , 141 200 . Hl0, 50 . . .. . ???????????????? ????????????? ????????????????????????????????II -50 . -100 . -150 . -200. _,__-- ---,------.------,--------,r--- 85.0 85.S 86.0 VERT SCALE?NANOSEC 86.S FRACTIONAL DAYS RESIDUALS, FILE1 DFTOTG9c9 SLOPE FILE1 GDSGB929 CLOCKS ? VS PAPER REF _ 7, 8, 9,15,16,17, Rubidium clock 4 Flight 1 50 . 40. / I ,I 30 . ,i / 10. : / , ..... , I / . 0. .. > / ...... \ ... .. .. ..,, .; . ..' . .?, . .... ,? ?????; ?- ??, ? ?????I ???????????????????????????????????????????????? . , i -10 ' . j I \ / . \ I :::~ ~ \ ' /ii \ I -40. j ; / -50. --L- ----,~----\~?1~~,- -----Ti-----71- -- 85.0 85 . S 8 6 .0 86.5 ~RT SCAt.E?NANOSEC FRACTIONA L DAYS RESID~PLS , F I L~1 ~FTOT~~29 SLOPE FILE 1 J!PSABS29 CLOCKS 4 VS PAPER REF 1, 3 , 142 S 0 . .- 1. .... ...... .................... ..................................., , -- ....:1 -50. - 1:se. ~0. J..------,--------,---------i------,---86.5 85.0 85.5 86.0 FRflCTIONAL DAYS RESIDUALS, FILEt DrTOTG929 St.OPE FILE: GDSG3929 CLOCK I 5 VS PAPER REF 7, 8, 9,15,16,17, Rubidium clock 5 Flight 1 ,./ 30. ? I _..,.. ~ ! // X0. I ? I ~ 0. ~. ..... ~???????????????????????1????? I ???????????????????????????????????????????????????? . ~ ' ., I ,, I ?" i ?? .........__ ;/' 'v I - -30. ! ,--- -50. ~-----,-------.------,- -- - --- 85.0 SS.5 86.0 86.5 VERY SCAU:?NANOSEC FRACTIOr,A t. DAv S RESIDUALS, FILE I Dr T0~~92 ~ St.OPE FILE: 3lPSAB929 CLOCK I 5 Vj PAP ER REF 1, J, . 143 100. 0 ? -+----i.~ ;:.,. :..-=:=:-:.:-:::--::.:.-.:a-.............. ?+ ...................... ???????????????????????? ?I I -50. -100. _L_ ___- T-------.-------.------,-- 85.0 85.5 86.0 86.5 VERT SCALE?NANOSEC FRAC:rIONAL DAYS RESIDUALS, FILEt DFTOTG929 SLOPE FILE: GDSGB929 CLOCKS 6 US p~0 ER REF 7, 8, 9,15,16,17, Rubidium clock 6 Flight 1 50. 30. 20. 10. I ?., ~ I . ~ 0. _..;. :???????????????????????????????????????????~ ?????????????????????????????????? i ' / -10. / ? ..... "'-... ,.,.-.~._,,,-,/ -20. -30. -50. -.------.----?---~-------,,-------.---- 85.0 85.5 86.0 86.5 I.ERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUGLS , FI LEs rFT OTA~29 SLC?E FILE : 31PSA8929 CLOCKS 6 US PHF ~~ PE? 1, 3, 144 ?? ?????????????????????????????l ????? ??????? ??????? -50. 27 . 0 27.S 28.0 2.8.5 29.0 29.S 30.0 30.S IJERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTGllll SLOPE FILE, GDSGB11l1 CLOCK$ 10 VS PAPER REF 1, 2, 3,16, Rubidium clock 10 Flight 2 ao0. 600 . 400 . 200. 7 0. -,..~---- -?00. -?00. -800. --- --.----.----.----~----.---r----.-- --.-- 27.0 2 7 .S 28.0 2 8 -5 29. 0 2 9 .5 3,.'l.0 30.S l,.?RT SCAL? ? ~~NOSEC FRACTI ONAL OAVS RES!OUALS, FILE : tcTOTA l ll l SLC?E Fl~Er PSAB ll l l CLOCK ~ 10 VS ?A?ER PEF 8 , 9 , 145 5 0. ? 0. ??? c::::???:-;-:-:.,1 ,- ........ +?~? -??????????????????????????l??_:???????????????? 27.0 27.5 28.0 28.S 29.0 29.S 30.0 30.S IJERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE1 DFTOTG1111 SLOPE FILE: GDSGB1111 CLOCK* 11 US PAPER REF 1, 2, 3,16, Rubidiu~ clock 11 Flight 2 300. 200 . 100. 'I ' ????????????????~?????????????????????????????????????????????????????????????? I - 300. ---.----...----.---~----,-----,-- ---,----~- 27.0 27.5 28.0 2e.s 29.0 29.S 30.0 20.s VERT SCALE? NANOJ~C RESIDUA~S. FILEt DFTOTA1111 ~LOPE Fl LE ? PS~B1111 CLOCK a 11 VS 0 HPER REF S, 9, 146 100. 0. i \ -50. I \ \ -100. 27.0 27.5 28.0 ?2s.s 29.0 29.5 30.0 30.5 VERT ~LE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE1 DFTOTG1111 SLOPE FILEI GDSGB1111 CLOCKS 12 US PAPER REF 1, 2, 3,16, Rubidium clock 12 Flight 2 100. 0. . ...... . . ....... l.. - ?-- ?--?- .... -- --- --?--- -- -- - .. -- . . . . -- - -- -- .. --- -- -- ? . . - . . - -100. 27.0 27.5 28.0 28.5 29. 5 30.0 30 . 5 VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FI!.!:: t DFTOTA 1111 SLOPE FILE:1 Ps.:131111 CLOCK a 12 us PAPER REF a. 9, 147 s0. e. --.-J?-~ :::::.-:;:--::- .. . ... . ....... .?. .J?? t1!++!1TU? ?? ???????????????????????????????????????????????II?? -s0. -100. ..--- 30.8 31.0 31 .2 31. ? 31.6 31 .8 32.0 32.2 32. ? VERT SCALE?NANOSEC FRACTIONAL. DAYS RESIDUAL.5, FIL.Et RBTOTG1114 SLOPE FILEt RBDSGB111 ? CLOCKS 10 VS PAPER REF 1, 2, 3,15,16, Rubidium clock 10 Flight 3 200. 150. -...: 100. 50. 0. ????????????????????????? ??-fl?????+????????????????????????????????????????????????????????? -50. -100. -150. -200. -----.----r--~---,,----.,---,----,-----,---,--- 30 . 8 31.0 31.2 31. ? 31.6 31.8 32.0 32.2 32. ? \..IERT SCAL??NANOSEC FRACTIONAL DAYS RESIDUALS, FILE1 ~BTOT~1114 SLOPE FILEt RBPSA8111 ? Ct.OCK a 10 VS P~?~R R[F 8, 148 200. 100. ? ?100 . ?? 15 0. 30.8 31.0 31.2 31."4 31.6 31.8 32.0 32.2 32. ? VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE: RBTOTG111 ? SLOPE FILEI RBDSGB111 ? CLOCK a 11 VS PAPER REF 1, 2, 3,15,16, Rubidium clock 11 Flight 3 200 . 1.50. 100. ~ 0 . e. I --.- -- -.- -------- .. -- ------f- -tl----ft-?-? .. --- . -- -----?--?--????-? --?-?????-?-?-?---? ??------- ~s0 . -- 100. 30..2 31.0 ~l.~.- 31."4 31.Gil. _ 31.8 32.0 32.2 32. ? l?RT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FI LE I RBTOTA 1 11 4 SLOPE FILE1 R3PSAB111 ? CLOCK a 11 VS PAPER REF 8, 149 150. S 0 . - ...:.:=r:::::-.:::-....:.; .::? ';;I- ? tH ?-?Hit 11---?--? ?? ?????????t---?? ??-?-- ?-??-??????? ?-?????I l?? --s0 . -1 00. - 150 . 30.8 31.0 31.2 31."4 31.6 31.8 32.0 32.2 32, ? VERT SCALE?NANOS?C FRACTIONAL DAYS RESIDUALS, FILE1 RBTOTG1114 SLOPE FILE1 RBDSGB1114 CLOCKS 12 VS PAPER REF 1, 2, 3,15,16, Rubidium clock 12 Flight 3 200 . 100 . 50. -------- I e, . -l-.J.-...?=? -~-? ?:.:.:.-... .... .. . .. .. . .. .... j. . -tl? -???+?????-???????????????????????-????????????-????????????-? - 50 . - 100 . ??150 . ? 30 . 8 31 ? 0 3 l . 2 31 . ? 3 1 ? 6 31 ? 8 32 . 0 32 . 2 32 . ? ~~ RT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS , F I~E1 RBTOTA1 1 14 SLOPE FILE 1 RBPSA811 14 CLOCK a 12 US PA?ER REF 8 , 150 -100. 38.0 38 . 5 39.0 39.5 ?0.0 VERT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE1 RBTOTG1122 SLOPE FILE1 RBDSGB C 11L 2O 2 CKS ? VS PAPER REF 7, 8, 9,17, Rubidium clock 4 Flight 4 100. 0. II _- -- ? ?????????????????????? ?,? ?1 ?????????????????-??????????????????????? ! -50. ;-\ ; ' \ iI "' . I ' -100. ->-,- ------,-------,---------.--~--.......- -=,--- 38.0 33.5 39.0 39.5 ?0.0 UERT SCAL??NAN05EC FRACTIONAL DAYS RESIDUALS , FJLEI RBTOT~ l122 SLOPE FILES RBP C SL AO B1C 1K 2~ 2 ? VS PAFER kEF 1, 2, 3, 151 200. 50 . ?? 150. ~ 200. J...------~-----.--------.r------,-- 38.0 38.5 39.0 39.5 ?0.0 IJERT SCALE ? NANOSEC FRACTIONAL DAYS RESIDUALS, FILE! RBTOTG1122 SLOPE FILE: RBDSGB1122 . CLOCK* S VS PAPER REF 7, 8, 9,17, Rubidium clock 5 !_ Flight 4 200 . 150 . ..... . 100. 50 . - 50. - 100. -150. - 200 . -'lr------ -,-------,--------,-------,--- 38.0 38.S 39.0 39.5 40.0 ~!?RT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILE1 c,;n :::,?rA1122 SLCPE FILE! RBF'5 A!l1!22 CLOCK: 5 VS PAP~? ~EF 1, 2, 3 , 152 38.0 38.5 39.0 39.5 ?0.0 VERT SC1=1LE?NANOSEC FRACTIONAL DAYS RESI~LS, FILE1 RBTOTG1122 SLOPE FILE! RBDSGB1122 CLOCK* 6 VS PAPER REF 7, 8, 9,17, i. Rubidium clock 6 Flight 4 100. ..... - 50 . 0. -50 . -100. -'-,,-------,-- --- ---r------ ,--------.--- 38.0 38.5 33 . 0 39 . S VERT SCALE ? NANOScC FRACTI ONA L DAYS RE SIDU<\ L S , FI LE t OSTC' ... 1'>1122 su:?0 E FILE! RBPSA9 1122 CLOCK? 6 US PA?E~ FEF 1 , 2, 3 , .. - . 153 ?:: j I I "? 1~:=::::??~.+:~:=:,;-c:;~ ............ ..+ .. ........... . --~0. ~ - 100 . { '"T1----T,----""T,-----,,1- ---T)_ ___) r----- T) ___ 86 . 0 86 , 5 87.0 . 87.S 88 . 0 88,5 89.0 VERT SCALE? NANOSEC FRACTIONAL DAYS RESIDUALS, FILE: OFTOTG110 SLOPE FILE1 GOSGB110 CLOCK a ~ VS PAPER REF 7, 8, 9,15,17, Rubidium clock 4 Flight 5 60. 20. 0 . - 20 . _._.------.---- -r----?~----""T-----,------,--- 86.0 8 6 .5 87.0 8 7 .5 88. 0 88.5 89 . 0 I..JERT SCALE? NANOSEC FRACTI ONAL OAVS RES I DUALS , F ILE t CFT(',T<'\1! 0 S LOPE F I LE t PSAB 110 CLOCK~ ? US PAFER ~CF 2 , 3, .J 154 5 0 . 0 . - 50. !00 . 86.0 86.5 87.0 87 . 5 28.0 88.5 89.0 \..?RT SCAL??NANOSEC -- I FRACTIONAL DAYS RESIDUALS, FILEt DFTOiG110 SLOPE FILEt GDSGB110 CLOCK? 5 VS PAPER REF 7, 8, 9,15,17, Rubidium clock 5 Flight 5 80 . 60. 20. - 80 . -r-----...-----p---------,---------,----~----.----- 86.0 86.S 87.0 87.S 88.0 98.5 S9.0 ~IERT ~LE?NAMOSEC FRACTIONAL DAYS RESIDUALS , FILEt ~FTOTAll O SLOPE F!LEI PSAB110 CLOCK ? 5 VS ?HFER REP 2 , 3, 155 ~?50 . ~ -,. ..~ -,r----.,----..,.,-----.,------r-----,-----,---- 86? 0 86.5 87.0 87.5 88.0 88.5 89.0 UE:RT SCALE?NANOSEC FRACTIONAL DAYS RESIDUALS, FILEt DFTOTG110 SLOPE FI LEt GDSGB110 CLOCK* 6 US PAPER REF 7, 8, 9,15,17, ? Rubidium clock 6 Flight 5 80. G0. 20 . o. -60. - ?80 . ......,,-- --~- ---.-----.---- ~----, 86.0 ? 86.5 87.0 87.5 88.0 88.5 89,0 VERT SCALE?NANOSEC FRACTIONA L DAYS RESlDUALS, FILE1 OFTOTA110 SLOPE FILEI PSAB11O CLOCK a 6 US PAPER REF 2, 2, APPENDIX E LIS TING OF VARIOUS PROGRAMS Th? is a pp endix con t ains sever a l comput er programs written in ' ORTRAN f or the Data General NOVA 2 mini computer . This version of FORTRAN is s lightly dif f er ent fr om the FORTRAN of larger computers. I t s hould be noted as wel l t ha t the programs, like the experiment, ~er e of t en mo di" f?i ed i? n haste when time was s ho rt. The result is that a be t ter s et of programs doing t he same jobs could be written if one were s t arting from scr a tch . There has not been the time nor the real need to do this. ]56 - ,, 157 TRANsn - The progr am TRANSD tra ns lates the raw digital clock phase data i .n t o the new file f orma t. l::T EG:C:R "'TY"E, I:C UF< 2 , 1033 ), r:; r,E:'.<2 , l :3 ),F1':.~' 1E<7) ~ = A!.. ~ JF(2~l , 7 J <2 Z l, SAVE<2i> , Y?<2Zl , YLC~3),05( 2 ) : ALL JFCATA C/:1.LL .C\SG c I ) ':?. I TE< I 0 , I) FG:-::;A T< ' OUT F ILE ? ',Z> 2 ?..E:AS ACCE?T ? , CLOCK BOXES = 0 , DO 5 I=!,6 n , C r:x ( I ., I ) = I It;D?X <2 , Il=I+6 DO 6 I =7, 10 (, !:lCEX < I., I >= 0 IiJ!:E~ < 2 , I ) =2 t?-iC?=7 I?c; ;:; . = ?J ,2 > '.?lC? = !4 -~Y?!: ' =I:?:J .s ::::n :::!..OCE a o x i , CH.o:::--: u.. F02 ';H E FOLLQ '.,"IN G:' J F CI, 2 ? 1 > GO ~-o l Z A::C~? T ? ~!AS~?.. N:' 2 ', J , K !!:i:EX CJ, K >= 15 t.iC?=:,0:C? + I 13 DO I l I = I , 5 ACCE?7 ' SPA?E CLO CK ',J, K l? GO : 0 1 2 p;:::::::; cJ, !D = OSCJ3 ) l +l l :;c?=~.:c~ +1 J 2 '?JR I T E c: r ;; A ::,y C2 ; . J :3 ; C?, t-! C? , _; , :-r < I >., TS < r )., 'T" ? C l >, , ::? , J = I, ~! C::J' ?.!:AC ::CI: l.~ ::Y ( ! , E'.,C=[2 ) 1J :=:, ,= ,?::=-:::,1 sEc,.; r::A'.', :,i .1,CI !::t.:F (l, J ),J=r, ~~! ) l f(C : T~?E , E: , f ) . Q~ .C R7 Y?E , E: ,7>) CJ TO 15 GO TO 13 Ifct:::: . ='.) .J) GO 7.J 16 I7C:.TY?E . ~~ - 6 ) GC TO 220 :: C I 5 J E= I, I 0 r :?;:=-c::: , E)= I :J:..1 r c 1~ x, l 50 I .:, :.? :'" C I , ; : ) = :? '30 TO 1 6 : .:c:.:u::, :: I:i.'\2Y CI, : iJ D= 6:Z ) ~l '" , :C: TY,:>E, I S.S, J CA, t?l'.J , < I I:\.1F C 2, J ), J = I, NI'; ) Jf <~TY~Z - ~~ -7) GJ TO 16 :JO 25'.J :~=1 , 1 C~ 253 ! :3c.' :- C2 , E )= :J 16 !F< !: . :; ;:: . , > SO TO IS T':'?: ' ?" ! '.":ST :ocr:;, : ? C.-",L!.. T: 1: _;. : c I:- :_::; , c. ,::;,,_y , J:'":-:.".") CAL!.. FJ~AYCI S:c, .;~~Y, FJD, FJCS ) S=?,. . 1C - 0?.3ET ~?...i:=r--J J ~ - 158 TRANsn continued --:i -e----v .~. L?L?-.-rcv ? c !?,?. ?-Ic-_?_ - -..., >. v.._ ;-,r-:,:. ;. ,.1-r- v- .-... ~-r.1 Jr?c- l ? - - - JJ -=(FJS- ::;,- ~:T - :)+:-J~ s S?? -1, E r: ;,,,?, c: i fJJ C COt?,?!J7:C: :;u::- CC 25 J=l, '. JJ CO ~5 .-:= I, 1 2 IF - IF+3UFC3 I lF )/C 3?S F.L,.-. JE6 ) 3F=-l? E6 IFC~3.E '.l ?2l GO TO 35 SUF<7)= 3 F IFCYF(7).LT?-?9E6l YF(7l= IF E< US FU CF 7C l 7). GT.-?9 E6 ) YLC7)=3UF(7) G O TO 4'.J 35 EUFC13l= EF IFCYFCIJJ.L T.-. ~S6 ) YF I CF l< 3 )S =U 5F U < F I C 3 1) 3. l GT . - ?? 9 S6 l YL CI ~ 3F l = =< BB UFU CF IC 37 l )+3L'F C8 l+ 3UFC9))/3 I ?F CBF.LT.-.JE6 l SF=-l?E6 BUFC 14)=3F IFCYFC14J.LT.-.9~6) YF I (F l4C )=3: 8J UF FC1 C4 1) 4. l JT .-.9 Z6 l YLC W 14R JI =T 3E U FS (I lN 4A l ~YC2l ,YLC20l CALL ASGC ! > .91NAEYCI) ~C,NCP,N,5,BFJD,EFJD,CYFCJ),YLCJ),J ? l, NC ~> ~EAD ACCE?T ' EVERY N? ', K I= Y.- I '.l'.'UTECle,2> 2 FOR..'1.C\T C ? TVPE 1-iEADER? ??, Z) READCll,3> NANS~ l FCP.~ATCSI> IFCNA."JS'..J.NE,'Y'> '.iO TO 10 ~RITECl0,5> ~C,~C?,~,5,3FJC,EFJD,CJ,YFCJ>,YLC J>,J=l,NCP> 5 FOP.~,ATCI X,/,' Ii CL:)C!?'.S =',13,S Y,'TOT AL CLOC Y. S=',13,S Y. , 'TOTAL POI NTS =',IS,/,' OFTSE:T=',F6.J,8;:,?FI P.5 : FJC=',F C:: - 6 ,/, 22Y, 'L.C\ST FJC=',F9-c,//,' CLOCY. FIRST POI!IJT LAS T ?:) HJT',/, 20< IY., I4, 2F I o. 2, I>, II> IFCK. EQ. 0 > STO? 10 READ 3WAP.YCl,E1JC=20> FJD,C.9UFCJ>,J=l,NCP> FJD=FJD+S .,. I? I+l IFCI.NE.Y.> GO TO 10 'JRITEC!0, 15> FJD, C3UF,J=l,NCP> 15 FORMAT( IX,' FJD= ', Fl 2. 6, 3C/, 8F9? 2 ? . 1=0 GO TO 10 20 IF GO TO 25 WRITEC10,15) FJD,CBUFCJ),J=l,NC?) 25 WRITEC!0,26> N 26 FORMATCIX,/,' TOTAL POINTS=',IS) STOP ENO R 160 ES - Prepares a slope file based on a least squares regression line. SLOP SLOPELIST - Displays the contents of a slope file. TYPC: SLO P i::S DOU GL::: '.' :':E CI S I0 ,1 SX<2 ::J), S: :x c20,,SY(21J),SY Y(20),SXYC20) DOUaL::: ;:, :1::c IS I OtJ F:J ( 2 ~ ), DF J D, Y REAL Bt:FC2 ::J ), Y rC 2::J ), YLC 2J) HJ T:::G ::: :, ~l C!.J( ( :C J ), F: J .JE C7 l CALL AS GC l) TY?:C: '::=: ?.'\P: :: CL O CE :' CALL CLoc; ; s ( NP, r,, CLJ '. ) 1:?.ITZ< 13 , 3) FOP.MAT(' SLO?E FILE NAME'? ',Z) READC!l;4) FN .llJ~E( l ) ~ FORMATCS13) CALL FOPDJ C2,FrJA! li::) tJ C,NC?,::-J, S, BFJD, EFJD, CYFCJ),Yl.CJ),J= l,N C P ) READ BINARYC I) DO 5 K= 1,NCP SXCK)=O? SXXCI0=0? SY<.!0=0? SYYCK)=0? SXYCK)=0? S RNCK)=0? ICOUNT=0 !0 READ BI~LO.RYCl,END=lS) FJD, CBUFCJ),J=l,N CP> DFJD=FJD-3FJD DO 1"0 K= I ,NCP 1FCEUF(E>.EJ.-J.E6) GO TO !Z3 CALL PAP CLO CK C. SUF, NP, t?J CLK, PEUF, S 100) Y=BUFCiO-P3UF CALL SU:1 ( SX( J{), s;.~ CK), SYCK), SYYCIO, s:~CK), RN CK), DF JD, Y) 100 CONTINUE GO TO 10 15 TYPE ? TOTAL POIN?TS= ',N 'JR! TE - BINARYC2) NC, NCP,N, S, NP, CN CLK, J= I, NP) TYPE 'CLOCK Al A0 R?R SX. Y N ? 00 20~ K=l,NCP CALL REG CS X, SXXClO, SYCK>, SYYCK), SXYCK) , RN CK>, Al, A0, R."l, SSXY) A2l=A0-Al*3FJD SRN=F.N CK) lJRlTE BINARYC2) Al, A0, P.P., SSXY, SRN WRITEC 10., 20 > K, Al., A01 p_q., SSXY., SRN 20 FORMAT( IX, I 3., Fl 3. 5., F 12? 5, F9 ? 4., Fl 0 ? 3., F6? 0 > 200 CONTINUE STOP END R SLO?ELIST INTEGER NCLKC20) REAL AIC20),A0( 2 3l, ~ ~<20>,SSXYC20l,?.NC20l CALL ASGC!) READ BINARY(!) NC, NCP,~.,S, NP,(NCLKCJ>,J~l ,N ? ), CA I ( J ) , A 2' CJ ) , P 'i ( J ) , S S XY .. '( !_ C: ~ ) ., ' .' < : ., '.: J ) , :~< 2 > I :! "'." ::: , ::: :-' , : ?: L, : < 2: l, ff .'\., c. < 7 l C.; LL AS 'j(ll A::c:::.:-ir ? ~_:::. ;:- CL-:) : ;-: <,, L I S "'."): ? iJ P,CJCL!: (Jl,J=l, '.P) ;; := IT E: < 1 ::' , J l 3 FO ? '. iA : <' SL O"!:: FIL E :J.o :; ::;? ', Z l ?C: .<\ C(l!,4) F. l'\ I JC:(ll 4 F0"":1AT< S 1Jl CALL FC ::>::::; < 2, P !Ai?i :C:l . . !'E: .I\C ar r;A?~'(I) ,; c, r-:c;:,, r; ,s, ::; fJ[,,EFJC, (Yf(Jl, YL(J),J=l, tJ C?) .t.\CCE:?7 'ii ? O I ~; T S 1: ; A'.,'C: ', :-~~ :-I ACC::"T 'S: !\FT, S T G~ FJC: ',, FJ:)l., :'JD2 FJC!=FJJ l -3-. J ~~ l 1FCFJC2.,T.J. ~3 1l FJD2=FJC 2 -S- . Z J J1 1CT=2 tJTES"."= :J- U'..:: i -1 M=i 3 co s !(=1,:--;c? SYC!O= J . SXYCY.l=J. S'fcJ;J= :J . S":'Y C1 : l = ~. SXYCi0=0 ? S RN CY.)=~? IC=3 10 ~:SAD SH:A"YC1,:S'.JD=3?, ?1; ci-:>,At, t>. J , :C:c' , 55:VYl 14 YCM, K>=At ?Xct ! l +A2' 1F<:: .2:.2J :;J T J 15 h=2 JO TO 8 1S i-l"llT.:: i3It: At>Y(2) 1?,Ul'-1,r,c?,N, s,;,;::,, ,~:c:.1?Jl,J=l,NP) XXl=XC!l+S ~ ~2::".C 2l +S ~~lTECt ~ ,17) XY !, ~Y 2 17 F C ?.."!AT C 1 X, /, I 3 X, ? T I = ' , r I J ? 5, t; X, ' '!' 2 = ' , F 1 0 ? 5 > TYPE ' Al A3 X I X2' ::c 2~c ,:2 1.,r~c? Al" CYC:?, i:l-YC 1, J: ) l/C: <2 >-:VC 1 l) .I\J=YC!, Y. l-Al? ~ Cl) ;..'l'l.lTE Sr:-IA !"': CZ l A l, ..' .\ J,YCl, J-; J,':'< 2 ,l-'. l,XCll '.;:l IT EC 1 , YLC20J 2 EAL 5 t:FC 2e J, ;;;uTE(l,3., I) F0?.!1.~i(? FILE? ', Z> ADC 11, 2 J F'N.4l?iEC I) ~ E F"O ?j1ATCSJ 3> 2 E) C.!\LL FO?~',(l,f:1Ai1 CT? : ?., T,D T .4CC:C:?T 'T, CC:?T '?~A SE TST CT 2Y 2 ~)1 ',ITST A IT5T=ITST??2 ACCEPT 'CLOCY.? ', I :' TY?E 'REF PA?ER CLO CK CALL CLOCJ~S GJt>,NC LK> C D?~4'?! . & LABEL A XIS . CALL H:ITTCO) CALL MOVA S Cll0,Il 0) L DR~A3 (54~,JJ0) CAL CALL i?iO V.43 CI 10, l I 0) CALL D~WAE C!l0,77 9) L=130 DC 3 r.= l, 9 C.IU.L T!CXCL,110,1 5) J L=L+50 I.?150 DO 4 IC= l, 5 CALL TICYCll0,L,2 a> 4 L=L+J50 L=150 DO 5 IC= I, 4 ALL TIC ':' Cll 0 ,L+45 ,1 0 ) C LL TI CY CII J ,L+l 05 ,10) CA L=L+J5 0 ~ 163 SIGMATAU continued C.ALL :;OVA3C 11 0 , 80> C.'\LL A:J :-'. OD ?; ~ ITE.C I 2, 6 > 6 rC :=-::i .HCl :'.,' 2 04 3 16 3264 13056 s2 2 24?,1 C, 1L 6L x , '7! 10 c'J sA ::2 :cmC? i, 1 o35 s> n L,'l.3Y=- 15 L=135 DO 8 K= I, 5 '.: .'\LL Ai;: :OD :.; ti IT EC I !'.'., 7 > '/ ?0:".: lATC I X, '10') CALL ~ OVA3C23 ,L+12> C.I\.L:... AtJ! 10 !) ?: :-I7ECl 2, 2Z Z> L~3Y , C :'.: ;,; T C I :?, I 3 ) !. . ;'l. SY= L,'\ :g ':' + 1 i.. =L+lSO 8 C!\ i..:... !: OV,'\J CC,L> C~ LL :-lO'JA~ C~,75~) C;..:..L f\:Ji'J OD ?_.; :='. I 7: < I 2 , 9 > := :?; ti.: '. E. < I > 9 F Gr,~:-~ 7 C3 :?X., ' S I G:-L; C2 j T)., FILE:: ', S !3,//,32X, 1 ' 7 /, 'j C SEC ) LOG SIG SD DEL'> C: cc: :?UTE l:l:!.:.R=l I !J '.fr~ = 1 1 0 TA L =T?INTER TST=uT?INTi::n F'E: .. ;D El~ .A? Y( 1) ~;C,~iC!", t~ , 5, 3FJD, EFJD, (YF(J),Yl_(J),,.j= l,r;cp) N=3 ND='J 1 5 :::: _.; [; 3 1~: .l\::'.':' ,J=l, NC:c>> C;,LL !" ,, ?:::L QC!'. <3 t.;?, ,:?, ,?J CLY., ? 3,ff, S 15) IF< 2~FCI).LT.-.7:6 ) GJ TO 15 - - 25 -~-=c J 'J 1:; :-;?i:--?1):? :- :-=?=-=---- --------- 33 "l EAC' S i t: ,'\ :'" Cl, E:-l C= 45 ) :: 1,C S'..JFCJ),J=l, :J C?) Tl=- I? Z6 C~LL ? ~~CL CCKC ~UF, M0 , UCLK,? S~ F,54 J ) IFC3~:CI).L : --. 3:6 > GO TO 4J TI= EiJ F C I ) - :0- 2TJ f DS=CSl-~ ~ >~ ~6~ ~: . DSS=CS2- S 3>? 66 4 ~ . l:C'J il: : IC':"J, 7: ,:- :)) .LT.-. :;:t: > GJ TO 40 IFC A55 CSS: - 71~ >- G7.7 ST) CJ TC ~J r,c;;2s cos -:-~c >. :T . 73 7> cc TJ cJ SIG~A =CT!-2? ? T 2 + T3 >? * ? IF C5 I::; ::.~. ? ST . I, : 7) GC TO Ll: src:: .A= SIS:: ... \. / ( : ? ? ;:;::; .:)S) A\' E= A\,' E: +3 I G: :.a. SiJ= S 'J+S I G: !.'I**: N=::l!+I GO TO 41 4('J l; C= 1l S+I 41 T3=T2 T2=TI SJ=S 2 52= S I GO TO 25 164 SI GMATAU continued L;5 Ir<"! 0 L ".? ? l ) G?J TO 99 S IG:?P.= :'\ 1::::1:: I : C?i ? G T ? l ) S 5 J = <5 C- AV C: .- * 2 F ! ) / Cl - ! ) S 5;)= 5 ,1?T 1.!\ ) 5 SD':" l ? E- I 8 * '.: 5:; / <2 . "'5 I G:?: /'.I. ) LS I G:1A < rr : c."! i ) = ? n ALI OT GE I( 3t ' <.l 5, 5 I:1 ; :-) : .~) r_; ;; , ,,J, S I G. ?l ,'l: , LS I C:-, .!\ ( I::T: ), S 5 S!0 j ,ND FO :=l!!Ai(J 2X, ,7. 3 , rs, ;;:9 . 2 , f 7, 2 , E:9 ? 2 , 1 3 ) IF< N? E: 1 ? I) GO TO 99 l!jU:t= ! ~FJ!?l + 1 wr :::"=n r:::r.?2 GO TO 10 C99 ?LOT ~5C !;; L.L 7L 5 S'.l lt ;D AI=L S IG~A (l)- 2 ? 4222 A2=LSIG ~A Cl)- 2 , 4JE2 /2? CP.!.L :1ov :::A CI?, L S I G,?1!:i < l ) ) CA!.L DAS !-:A C9 , , A 1 , 1 2 ) CALL MO VRE. > CALL D.'< 5P.A (9,, A2, 12 ) C.' CALL .-IO'JA3 C4 3J ,30 ) . C.!:I 1 L,1 L;: !T A!E :C :-:O 1 De , 12'.l > I, ( MCL K r (o J: )=.: ,-; J,; =T l( ,I N:'. , ? >' . CL '.JC}( ', 1 3,' \JS ?SF : .,--13, 7( ?,.,I ~? 120 C ?.?,L i ;!:. .?, - c I) STO? ;::;; L 165 PHASEPLOT - A grap ph i ac ss e p oro f g ar nam y ct lh oa ct k p wlo itt hs the h r espec t to any choi ce of reference clock. T YP:0. P P.AS:::.? LOT I~J ".' S::i C: ?- i;:LJ-:<2'?l , fN A:?JS C7 l REAL B'.J FC 2J J, Yf C23 ), YL C20 ) CALL ASGGCJ, HJ,;:?,Zl ACCE?T ' CLO : Y. ? ', 1 TYPE ' REF ? Aa Eq CLO: K: ? RC!E~ALDL 9CHLO:CA:Y:Y.S GO TO 10 XI= Bf JD- 2 ? * C? 0 ;J 2 3 c I I l X2=EfJD+ 2 ?* Yl"'Y!-? l* D Y2 2 Yl+i?2?D 12 CALL INITTC~) C ORA'? ACXAISL L S '.T I NDC130,67 0 , 13 2 ,649> CALL V'.JI ~JDC S+ XI, X2 - YI, YI, y2-Yl > CALL AXIS(S+?l, s +x2 , Y1, Y2) CAI.L MO'JA3CJ,7 -il l C.iTAR II.TL ECA fIJ :0?!O, D3 J > FN A:'1 E C I >, I, 1,os" AT ? , N J=AN I O , NS E PG ) ', ,s x , ' FR ? Ap C!{ TA IS OE N A? LL O OT A, Y 5 F 'I /L 27E X' , ,,;(3,/27X? 'GLOGK',!J,' VS ?APER SEf ', 1 1 C PLOT CALL V~INDC X!, X2- Xl,Yl,Y2-Yll DO RE5A0 D J=a-H1J,AN? .YCI > fJ D, ( 3'.J fCJ),J=!, NCP> CALL PAPCL OCK C3Uf , N::i, NCL K, P3Uf, $ 5 0 l IF GO TO 5 0 Y2 8UfCI)- PBU F CALL "NTA ;/C 20), S5:":Y ( 2e J, ::o:1 c 20 ), YF ( 2'.3 ),VLc ~ 2JJ , A0 ( 20 J, rr:, ( c, PEAL G'.J F( 2 JJ, A J ( CALL .l\ S:iG Cl, !"::,v :c:J ?E ' SL O?E FI L: :' T':' CALL ASG 3C 2 , S~~~ E J I ACCEC>T ' CLJCY.? ', ACCE?T ' RA'.JG i::ClS >? ', R ,C ~ CL Y. CJJ,J= J, NP J, C 2 J ~C , NC 0 , ~ , S , ~P . READ B! NAR Y CJJ, "'.1/ CJJ, J= l, rJC ? J (Al CJJ, .C.J CJ J, "'.?. C .JJ, SSY.Y , (';'F(J ), YL (J), J = I , :J CP ) c , ~; c _::i ,r; , S , EFJ D, E FJ G P.E:AD B Hii\ ?.':' ( l) r , "' FJ C?? ?, ;c;IN , XN AX CCE?':" ' S TAR T, STCA IF CALL DASHAC'01AX, o ., C ?LOT FJ D, CE'JFCJJ,J=l,N CPJ J 30 READ 9HIA P. YCl, e:D= 5 0 IFCBUFC1J,E 1 ,-1, E6 J GO TO 38 f , 1;? , ;,.;cu:, ?:Ur, 535 ) CALL PA?CL OCV. ( 5U FCIJ- ?9UF- AlCIJ ?F J D- ACC !J Y=BU CALL ?NTACFJ D,Y) GO TO 4 0 ALL TICCFJ D,20 J 38 C 40 CONTINUE GO TO Jg C i/RIT.E LEG:::N D 50 CALL MOVAB C~,1 00 > CALL .l\NMO C NAMECIJ,!,C NCL KC J>,J=l, NP) ITEC10,60J FNAME C!),S .l\YS',11, ~R C.l\L Z=N.l\."./JSEC ',J S X, 'f PA CT IO rJ AL D LO CK FORMATCIX, ' V?.C> T S ! SY, 'C ', 5 13, ' S LOPE FIL E : ', 5 13,I, JSX', 'R '.:: SIDUAL S, FIL E : VS PA:-> E~ REF ', 7CI 2 , ', ')) IJ.,' C.4LL NEA T C I> STO? E:ND R 167 SlUFTV - A ver s ion of several shift programs that generate the I.ix fi" 'TI1is version allows var i a ble endpo i nts. TY?r. SH IFSTEAV L TC4,2C J, TA VC4 , Z:) ,G TA~ C2:J l, DSL J~E <23 l, SCC R 2E 0.f ).\ L ::c:F C2:J ), Yfl C2C J, YF2 C2 :'. ), YL I C2'Z ) ~ , YL2CH 2~:T ) E:S EP. N C4 , 2 l, t.J CL!-: C1 0 l, F'.i Ai-\ EC 7 l, c; /IJE C7 l TY?E CALL AS GG CI, FIJA!1 El ?C.A?ALDL A3 SWSGACr:Y2C,GIN) Ar~; EC,l !?:C? .- :-; 1, S J, ErJCt , EFJ D P J. ,E CA Y~ f l5 CI JN )A ,'? :'Y LC iC2 l J )~ ,JC ", iN ?NC C?, PN >2 ,52,3:JD2,EFJD2,(YF2CJ>,YL2CJ),J"i?NCP> DO 3 !=1,4 DO 3 J=!,NC? TCI,J)=0? Tt>.UCI,J)=0? ACNCE'R=E0 F C!..OCh? U,Ll ST ):', t,?,CNCLJ{CJ),J=l,N?) A CCE?T 'II 0 Ol lJTS I !~ AVE?.AGE c1.;1,c;ES J0): ?,KP ACCE?T 'Tl,72; ,3,T.t.;: '? TJ,T2,T3,T4 TT2cT2 TT4=T4 IFC7l?EQ.0?) Ti=Sl+BFJCI 1F?24? r:-~= c:-J-T2 >? 24. TF=Ci4-T3)*2 ~ 4~ ? ITECl e fQ ,.t? ,;.: )' ..'\ T"'. 1?( ,J T:-' , ' J T ,Tl= I,T', 2F ,7 T? 43 ,? T4 H~ ,, T' FT 3=',f7-3,8X, ?cr 2 /, -3 TY t ),' =T ',2 F= 6', ?r 27 ?'. J H, P4 .5: '. ', , 'T4=',F7-J, eX, '(TJ-T 2 >=',f6?2?' HF.S', ;,35::,? . PIC.ZTA=CC 3 I ~ A~Y(l,E:-!C=l2) fJ[?, CoUfCJ),J=!, N CP> ICT=ICT+l !:CFJC.LT.TSTI> GO TO 5 r.: O 10 1=1, NC ? I: W ?LT??? 9E6 ) GO TO 8 "."( ! ,I )=TC!, I J+ 7 f J D TAU< I, 1 )= TA1..' C !, I )+ EUF< I) 1; (1,1)=1' (!,l) IF +C IC TT2? r;:s . :J .)? P.: rD-( r J : ., .Li-7ST2 )) 1 r G? O iT TO2 ? 1:: 0C :.. J . ~ ?>? .ti:;:;. .(I CT ?LT?ct: t+!- K!" ))) GO TO 10 If(:!(2,I>?'.;E?J, " l ::::J TO 1;, I?IN ! <5 l,J) ['~ = 52 - 5 1 :r-c=:.-'.\=D 3 ::; I :JA?YC'.: , E J J = 2 ~) FJC, ( 3C!"? L7?? ? C:::c6 ) GO-TO I S 168 SHIFTY continued J 6 -:" CJ , I) =T CJ , I J +FJC + OS ; ,".\'J CJ , I J =7." U CJ , I )+ 3U FC I> :i CJ , IJ = r; c J , r J+l T74 , '.:;: . : .J, A::: .c FJS , LT , 7ST[j JJ GO. TO 22 I 8 I : CC ,'.\ ' !c.' ,CI CT ,L T ,C l. :? +J- Y. " )J) GO 70 2:3 IF C CTT4 , c. c , 2 ? ) 0 I F C: , C4 , !) , ::i E , : :? ) GO T O c:~ IFC ~ :J? CI), L7 ,- , 9E c J GO TO 20 ( l1 ,! ) =7C 4 ,l)+ F JD + CS 19 T , I l=7.4L' C4 , I l+ S UFC I) TA!..'C 4 t,; '. , 2 ( ! 2 , ', ', r 2 , 2 ; '.)) , / ) ' N r, ;; 2 ~; J ,:,Ji. ', 4 ( 6 ( / , 14 , : I J,3 , F J J . J , 7 J .il , DO 7;, I=l, 2 70 !Y?E ' ' 2 ) 7N.4:?,E C I), G:-.:M!EC I J, KP 'JRITEC 10 , 7 T S ') 5 13 , ', ', S JJ, ', ', 1 2,' ? 72 F'O?l?!.4TCI:":, ' ? .4G.C: 2 OF SH I FT : ', TIO: JS ' TY?E' DELTA T:".\:.J C.O .LCliU, '?TH IC :i CL OCJ-; Zi:: "'.J ? ', ~! Z ACC'.::PT ' MAl'.E CNCL KCJ>,J= I,Ll ACCE?T ' S AS:C: CL CCJ; S ET U,L ISTJ : ',L, IFCL,EJ, 0 ) GO TO 100 SX= 0 ? SXX=Z, DO 75 I= I, L K=NCLl-C I) IFC K, EQ , ~ Z) GO TO 75 SX= S X+D T.4'J C: -: ) SXX=S XX +i, T.4U CK> + DTAU C Y. ) 75 co.:,.;rrnuE 169 SHIFTV continued t>JJ=L ~R.'1 =SX/ !".N q SD= S Cl " T ( ( S:::-:- 5;,* SX / F!'J ) IC 0!J- I ? ) ) RSC~= P.5 :)/ 5'::?! , < :>'.J ) '.JP. I T :!:: C I a, 7 7 ) :- :':: , :' S iJ , " 5 c:-; 77 . 11 .,. ',f6.J,1 , F 0?~~1'.\Tcsx, ?r:-_t. L'= ',F7.J,::X, ? s .r.= ',F 6.J,Jx , ?s.0 1 80 ACCE?T 'CL OCr.'.; U,LI ST); ', L,C!C L!<(J),J=l,U IfCL,E ') .Q) SC TD lt-"3 SX=0 ? SXY=~. DO 85 I= I, L K=NCLKC I> lf GO TO 85 SX=SX+DTAU ?DTAUCr.) 85 CONTIN UE ~'"L Rl'.=SX/P.U CSD=S'J::ZT CCS XY: - 5:-(? SX /f':'J) IC R:-: -1.) ) SD:?!= CS D/S:! :lT C" f.J > A=?.;,:- P.?H B=S'JJ=?T C? !S D:1?~SD:1+S D!1? SDM > ~~ITE t: c ~EAL A2 ( 2J >, s: c :J ), ~J c ::J , Y4 ( 2: >, ~! l< :c ,.~:: c::, ;;~~: ~ ;~:~~~ ::~; ~ ;; ~ t I;~:?: (-, :) .t :: ::.. ::.f\:( :: ) .t :~ c:.. ::c ( 2::, ) ":"Y?;: ' :'\I::: :: r:?~:..~ r1:...L :' CALL !\ 5 3 C I l _ ., , _ ?. " ~i:::/l.:; srr;,'.\'."'."(1) :?: i..: ,! 1,t:C'.:> !, :: 1, :: , .. ?! ,(NCL:".l(J),J-l,, .. I), (.IU c J), ::; 1 (.;), ':" I C. _r) , ' .'? <.;) , :-: : CJ), J = I, , ; C.., I ) , ':"I, T 2 _ >,J=!, M ,A > ACC'.::""T ' !\I'.". '.'. c.? (.f, Ll::7 l: ', t,PA , ( ' lCLL A YI ( ICL:-: )='.'! ( r:u : )- :''.:" ! f C.C\LL "A?CLJCl' ( ':<'., t _; -:_c., ,j cu::~ . ?i::L" F, S I e2 > Y2< ICL!:>= Y2 < I CL U- '.:>'.;,!J F DY=Y '.: < I CL! : >- Y 1 r? :.:: : 1,,T!,T':" ;: , cv : ,' ""T _;1,?:, ; T !=', f[.L; , ' ~:= ', F E,ll ,/, FO?t!.".\T (! Y, l ,I ":-:~.SE r: 1Fr= ?,r 1 . :; ,? ::S ' , / ) TY?E ''3 ~~9 '.')':'. : :" IL E:' C,'.\LL .C\SS <::) ~E.C\C ::,r::.;:,v c z > ri !.J l l l, , i C'.:> l, '. ; 1, 5 1, ' .;::i 1,C t;C L; : 1c J> ,J = !, ::-:, 1), <..; I C..; ) , :: ! CJ) , ': I CJ ) , ,_- : ( J ) , : ::,: CJ), J= I , ,: c::i 1 ) , T':" I , 7T '.: TY?E. ' :3l~C -, OST FI~!: :? CALL /\'.:'JCJ ) ~?A D 3 lt?!!\-:,_y ( J ) t::..1:-:: , tJC '.:>2 , :1~ . 52 , tl P2 , c:cL~ '.2 (J),J = 1, :, ::i2 ,. T 4 (.,; 2 CJ), :: CJ l, Y 3 T ' '.;iJO :-i::F" c .; ,Lr 3T) : ?, :: ? : ,c NC !.. 170 SHIFTM continued ::c 2:J ! = J, r:cro 1 T I CI ) = l\ I C I ) ? C- :- I + 5 - 5 J ) + 3 J C I ) Y YT2 CI)= A2 CI> ?C T2 +5 - 5 2 J +32 CI) 20 DO 25 I-=J, ;; :::::; K= N CLY.S C I ) ' :'T l CX ) +_q I Cl{ J *< T2 - Tl J ) ) / I :n . +. 5 J DEL TA= l '! J ? "'IF I ;'. C C'( T 2 Cl '. J - C . 25 YT2CY. : = ':' 7 2 c;~) +?: ::L ! ,'\ LOC K CA !, ~FS , ~ CL KS, SG l, l l 0 ? l C.'\LL PA?C ? A'.' CLOCI : CA '.? , :;~.:, , :1C L! -: '.:, SG 2, i 1 ~ ?2' ) C.l\LL SA 1, 1 1 ;:;;:, J C.l\LL Pil. ?CL OCYC~. J, ;; :-' .' \ , l: C!... i'. .l \ , ? J 2 3 ) C.!1.LL ? !\.?CLCC!<: Ll\2 , ;; ?A , 1, CL:C..'\ , 5A2, SL?I= S . '\ I- S?J t StP2= 5A'.? - 5S2 l:SL? =S L 0 2 - SL ? J DY? =CC SL 0 J +S~ 0 2 J/ 2, ) ? CT 2 -T J) C':'YT=r:?r + C'.' '.' DO 4J I= J , :::=. c; K=r?;cL: . .: ( I ) T! ) c. ??. . ' C , =: ? + cc ::: .~.1-!\ l ( l '. )+ 5.~. 2-11. 2 0 : ) ) / 2 , ) ,< ( 72 - !O+YT J CU DIFF =YT2 C ICL !'. )- YT 2 C: J- ':' T J C I CL TSFTC K)=CIF?- S':'~ CKJ 5 FT(K)/ l ee .+. 5) TSF'T( l'. )= 7S r 7 ( %) - J ei . ? IFI X (T , IFCTS?TC K),LT, -J Z .J TSF TC KJ= TS FTC K)+J 3;J CONTI NUE . OCl '. CT 5rT, N"'.: , )iCL KG, S Hif"';, $ J 0;J J CA.LL ?A?CL ~RITECJ J ,5 3 ) SL?!, CS L ? ,DYYT E OF AI R REF \.;RT GND FEF : ',fg .3, 50 FO?.NAT CJ ~,/,' SL CP .J,/,) ECTED PHASE DIFF= ',f7 ? CEF .;i i ? r?t?-1 - 2--1 co 4 :-1,:? ? T( I,. ,) cu--G~?:::u2 NG?DSQf. TcrRo-12 . ;*x2~~9;3,:,:t2+93Se.ix2J QC.? :)0 + '.:.C.T..;tl C -93='0 . / '. P ?, -12, J ) UG?J(RG,G ~l VVG?C~?~G*DC05(CGlJ*~2/C 2,XCXt2) S WRITE<6,61 6 F"JR"'lAT( , NEXT FILE ' l READC5,7J N 7 FOR"'IATC ) IFCN.EQ,0) GQ TC =0 10 RE~DCN,11,END?S,E~R?l2 1 Nl,H.~,SEC,IX,IV 11 FOR"1ATCI8,lX,2 I2 ,F6,3,318,27X,3I6) Tl?T2 T2?6~<60tH+M>+SEC RP?DSORT(CR0+IXC3)1*X2?IXCl)Xi2+IX(2l*?:2l QP?00+DATAN CI X( 2J/(~0+:XC3l)l DU?U)U2+IV(2)*X2+IUC3)Xt2)/C2, XCXl2)-VVG :Fu: ?DC.: ::ivJ1-r, 11 : :F<,...EQ.Y~) ~o _ 10 ML?r'" o.; 16 I?1,:: 16 P1:1?1r9~7 c:) t.F:TS<9,l 8) .-,'' ,IX,: lJ ,P !8 F0~~~T rlX,2 I2, 2 ~.~:7,2X,3:6,2X,3F7.31 t.FIT:'.10,l? l ... . ?-.rx.: u ,P 1? FC~A- : : x ,I2, ' :',J=,2~. ~:7,~X, 3I6,2X,3~7.3) GO T:i l~ Z0 DO 2~ I?1,3 22 ~(IJ? lu9*- c:> ~!TE <6 ,17) ,-,, /1,IX,I U,P EriD EOF' AT LIN:: 5: It 172 BIBLIOGMPHY 1. A. Eins tein, J a rb. Radioakt., !!:_, P? 411 (1908) 2. For a review of ear l y wo rk (inc luding references 3-6 below) see Theory of Rela tiv i t y by W. Pauli, p. 153 (1958) J. K. Schwarzschild, s. B. preuss . Akad. Wiss., p. 120 - (1914) 4. c. E. St. John, Astroph. l?, !?.?.' p. 249 (1917) 5. J. Evershed and Royds , Bull. Kodaidanal Obs. ,39 6. L. Grebe, Phys. 1-,11:, p. 662 (1920) 7. w. s . Adams, Proc. Natl. Acad . Sci. , 11, p. 382 (1925) 316 (1954) 8. D. M. Popper, Astro12hys. l?, 120 , p. 9, J. Brault, Bull. Am. Phys . Soc .,!, p. 28 (1963) 10. R. v< Pound and G. A. Reb ka, Phys , Rev. Lett.,!!:_, p. 337 (1960) 11. R. v. Pound and J. L. Snider, Phys . Rev. Lett., Q, p. 539 (1964) 12. R. v. Pound and J. L. Snider, Phys. Rev. ~. 140, p. 788 (1965) 13. More recen t red- shif t experiment s are: F. Roddier, Ann. 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