apollo-soyuz pamphlet no. 4 gravitational field

8/8/2019 Apollo-Soyuz Pamphlet No. 4 Gravitational Field

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Apollo-SoyuzPamphletNo.4:Gravitational Field(NASA-EP-136) APOT.Tn-snvn* n >,NASA-EP-136) APOLLO-SOYOZ PAMPHLET NO. 4:GRAVITATIONAL FIELD (National Aeronauticsand Space Adninistration) 40 p MF A01;SODHC set of 9 volumes CSCL 22A N78-27150UnclasG3/12 24992


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This is one of aseries of ninecurriculum-related pamphletsfor Teachers and Studentsof Space ScienceTitles in this series ofpamphlets include:EP-133 Apollo-Soyuz Pamphlet No. 1: The FlightEP-134 Apollo-Soyuz Pamphlet No. 2: X-Rays, Gamma-RaysEP-135 Apollo-Soyuz Pamphlet No. 3: Sun, Stars, In B etwee nEP-136 Apollo-Soyuz Pamphlet No. 4 : Gravitational FieldEP-137 Apollo-Soyuz Pamphlet No. 5: The Earth from OrbitEP-138 Apollo-Soyuz Pamphlet No. 6: Cosmic R ay DosageEP-139 Apollo-Soyuz Pamphlet No. 7: Biology in Zero-GEP-140 Apollo-Soyuz Pamphlet No. 8: Zero-G TechnologyEP-141 Apollo-Soyuz Pamphlet No. 9: General Science


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Apollo-SoyuzPamphlet No.4:Gravitational FieldPrepared by Lou W i l liams Page and Thornton Page FromInvest igators ' Reports of Exper imenta l R esul ts and Withth e Help of Adv is ing Teachers

IWNSANat ional Aeron aut ics andSpace Administ ra t ionWash ington , D.C. 20546October 1977


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Fo r sale by the Superintendent of Documents,U.S. Government Printing Office, Washington, D.C. 20402(9-Part Set; Sold in Sets Only)Stock Number 033-800-00688-8


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Preface

The Apollo-Soyuz Test Project (ASTP), which flew in J u l y 1975, arousedconsiderable public inte rest; first, because the space rivals of the late 1950'san d 1960's were work ing together in a joint endeavor, and second, becausetheir mutual efforts included developing a space rescue system. The ASTPalso included sign ificant scientif ic experiments , the results of w hich can beused in teaching biology, ph ysics, and mathematics in schools an d colleges.This series of pamphlets discussing th e Apollo-Soyuz mission and experi-men ts is a set of curriculum supp lements designed for teachers, supervisors ,curr iculum specialists, and textbook w riters as well as for the general pub lic.Nei ther textbooks nor courses of s tudy, these pamphlets are intended toprovide a rich source of ideas, examples of the scientific method, pertinentreferences to standard textbooks, and clear descriptions of space experiments.In a sense, they m ay be regarded as a pioneering form of tea chin g aid. Seldomhas there been such a forthright effort to provide, directly to teachers,cur r icu lum-re levan t reports of current scientif ic research. High schoolteachers who reviewed the texts suggested that advanced students who areinterested might be assigned to s tudy one pamphlet an d report on it to the restof the class. After class discussion, s tudents might be assigned (withoutaccess to the pamphlet) one or more of the "Questions fo r Discussion" fo rformal or informal answers, thus s tressing th e appl icat ion of w hat w aspreviously covered in the pamphlets .The auth ors of these pamphlets are Dr. Lou W illiam s Page, a geologist, andD r. Thornton Page, an astronomer. Both have taught science at severaluniv ersities and have published 14 books on science for schools, colleges, andth e general reader, including a recent one on space science.

Technical assistance to the Pages was provided by the Apollo-SoyuzProgram Scientis t, Dr. R. Thomas Gi uli , and by Richard R. Ba ldw in,W . Wilson Lauderdale, and Susan N . Montgomery, members of the group atth e N A S A L yndon B . Johnson Space Center in Houston w hich organized th escientists ' participation in the ASTP an d publishe d their reports of exper imen-ta l results.

Selected teachers from high schools and univers i t ies throughou t th e UnitedStates reviewed th e pamphlets in draft form. They suggested changes inwording, th e addition of a glossary of terms unfamil iar to s tudents , andimprovements in diagrams. A list of the teachers and of the scientific inves-t igators w ho reviewed th e t ex t s fo r accuracy follows this Preface.

This set of Apollo-Soyuz pam phlets w as initiated and coordinated by Dr.Frederick B . Tuttle, Director of Educa t iona l Programs, and was supported byth e NASA Apollo-Soyuz Program Office, by Leland J. Casey, AerospaceEngineer fo r ASTP, and by Wil l iam D . N ixon , Educa t iona l P rog ramsOfficer, all of NA SA H eadquarters in Was h ing ton , D .C .


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Appreciation is expressed to the scientific investigators and teachers whoreviewed the draft copies; to the NA SA specialis ts who provided diagramsand photographs; and to J . K. Holcomb, Headquarters Director of ASTPoperations, an d Chester M . Lee, ASTP Program Director at Headquar ters ,whose interest in this educational endeavor made this publication possible.

I V


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TeachersAnd Scientific InvestigatorsWho Reviewed the Text

Harold L. Adair, Oak Ridge National Laboratory, Oak Ridge, Tenn.Lynette Aey, Norw ich Free Acad emy , Norw ich, Conn.J. Vernon Bailey, N AS A Lyndon B. Johnson Space Center, Houston , Tex.Stuart Bowyer, University of California at Berkeley , B erkeley , Cal i f .Bill W esley Brow n, California State Un iversity at Chico, C hico, C alif .Ronald J . Bruno, Creighton Preparatory School, Omaha, Nebr.T. F. Bu dinge r, Unive rsity of California at Berkeley, Berkeley, Calif .Robert F. Collins, Western States Chiropractic College, Portland, Oreg.B . Sue Criswell, Baylor College of Medicine, Hous ton, Tex.T. M. Donahu e, Unive rs i ty of Michigan, Ann Arbor, Mich.David W . Eckert, Greater Latrobe Senior High School, Latrobe, Pa.Lyle N . Edge, Blanco High School, B lanco, Tex.Victor B. Eichler , W ichi ta S tate U nivers i ty , W ichi ta , K a n s .Farouk El-Baz, Smithsonian Institution, Washington, D.C.D . Jerome Fisher, Emeritus, University of Chicago, Phoenix, Ariz.R . T. Giuli, NASA Lyndon B. Johnson Space Center, Houston, Tex.M. D . Grossi, Sm ithsonian Astrophy sical Observatory, Cam bridge, M ass.Wendy Hindin , Nor th Shore Hebrew Academy, Great Neck, N.Y.T im C . Ingoldsby, Westside High School, Omaha, Nebr.Robert H. Johns , Academy of the New Chu rch, Bryn At hy n, Pa.D. J. Larson, Jr . , G rumm an Aerospace, Bethpage, N .Y .M . D. Lind, R ockw ell Interna tional Science Center, Thousand Oaks, Calif .R. N . Little, U nive rsity of Texas, Aust in, Tex.Sarah M anly , Wade Ham pton High School, Greenvi l le , S .C.Katherine Ma ys, Ba y City Indep enden t School Distr ict, Bay City, Tex.Jane M . O ppenhe imer , Bryn Ma wr College, Bryn M a w r , Pa.T. J . Pepin , Univers i ty of W yom ing , L aramie , Wyo .H. W . Scheld , N ASA Lyn don B. Johnson Space Center , Hous ton, Tex.Seth S hulm an, N aval Research Laboratory , W ashington, D.C.James W. Skehan, Bos ton Col lege, Wes ton, Mass .B. T. S later , J r . , Texas Educa t ion Agen cy, Aus t in , Tex.Robert S. Sny der, NA SA George C. M arshall Space Flight Center, Huntsvi l le , A la .Jacqueline D. Spears , Port Jefferson High School, Port Jefferson Stat ion, N.Y.Robert L. Stew art, Monticello High School, Mo nticello, N .Y.Aletha Stone, Fulmore Junior High School, Au s t in , Tex.G. R. Taylor , NA SA Lyndo n B. John son Space Center , H ous ton, Tex.Jacob I . Trom bka, NA SA Rober t H. Goddard Space F l ight Center , G reenbel t , Md.F . O. Vo nbu n, NA SA Rober t H. Goddard Space F l ight Center , Greenbel t, Md.Douglas Win kler , W ade Hampton High School , Greenv i l le , S .C.


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Page Intentionally Left Blank


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Contents

Section 1 Introduction .*, i : ' f c . . .>.."...':#,:., :&*&... = .' 1 ; * ' - . . \ : . ' . . . . ' ' ' " y v ' . ' ' Section 2 TheDoppler Effect *.' ....'....": .'.*. 3A. The^DisGOvery. pfMascOns'orv.


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Figures

Figure 2.12.22.32.4

Doppler Shift for Sound Wa ves From an Approaching Train 4Doppler Shift From the Component of Velocity in the Lineof Sight 6Effect of a Mascon on the Speed of a Passing Orbiter 7Beat Frequency in the Sum of Two Waves of DifferentFrequency 8A Pendulum Used To Measure g From 4ir2UT2 9A Gravimeter fo r Measuring g by the Extension of an AccurateSpring 10Measured Doppler Shifts of MA-089 Signals, Showing ApolloSeparation From the DM 13Measured Doppler Shifts of MA-089 Signals During EightOrbi ts 14Map of Revolut ion 12 7 Showing Rate of Change of ElectronDen sity at an Altitud e of 222 Kilometers 15Schematic of the ATS -6/Apollo Com municat ion Links 18Apollo Space craft Groundtracks for Experiment MA-12 8 20Changes in Apollo Veloci ty Toward ATS-6 Caused by Gravi tyAnomalies in the Indian Ocean and Himalaya Mountains 21

Figure 3.13.2

Figure 4.14.24.3

Figure 5.15.25.3

V I I


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1 Introduction

After 4 years of preparation by the U.S. National Aeronautics and SpaceAdminis t ra t ion (NASA) and the U.S.S.R. Academy of Sciences, the Apolloand Soyuz spacecraft were launched on J u ly 15 ,1975 . Two day sla ter at 16:09Greenwich mean t ime on Ju ly 17, after Apollo mane uvered into the same orbitas Soyuz , the two spacecraft were docked. The astronauts and cosmonautsthen met for the first international handshake in space, an d each crew enter-tained th e other crew (oneat a t ime) at a meal of typical American or Russianfood. These activities and the physics of reaction motors, orbits around theEa rth, and weightlessness (zero-g) are described more fully in Pamphlet I ,"The Spacecraft, Their Orbits, and Docking" (EP-133).

Thir ty-four experiments were performed while Apollo and Soyuz were inorbit: 23 by astronauts, 6 by cosmonauts, and 5 jo in t ly . These experiments inspace were selected from 16 1 proposals from scientists in nine differentcountr ies. They are l isted by numbe r in Pamphlet I , and groups of two or m orear e described in detail in Pamphlets II through IX (EP-134 th rough EP-141 ,respectively) . Each experiment was directed by a Principal Investigator ,assisted by several Co-Investigators, and the detailed scientific results havebeen published by NA SA in two reports: th e ASTP Preliminary ScienceReport (NASA TM X-58173) and the ASTP Sum mary Science Report( N A S A S P - 4 1 2 ) . T h e s impli f ied accounts given in these pamphlets have beenrev iewed by the Principal Investigators or one of the Co-Investigators.

As described in Pamphlet I, the orbit of a spacecraft is controlled by theEarth 's gravitational f ield . If the Ear th ' s gravi ty is "smooth," th e spacecraftmoves in an elliptical orbit at a predictable velocity. However, if there areirregularities in the E arth's grav ity, a spacecraft in low orbit wil l speed up andslow down as it passes over them. Such irregular motion has been observedfo r spacecraft in orbit around the Moon and has been looked for on NASAmissions passing other planets.For m a n y years, th e acceleration of gravity g was thought to be the same onal l parts of the Earth's surface. Then it was discovered that g is higher thannormal in some regions an d lower than normal in others. These regions arecalled "gravi ty anomalies," and they are caused by the high or low density ofth e Ear t h ' s crust . D etecting them is useful in locating ore deposits, coal,oil,an d gas. Two of the Apollo-Soyuz experiments were designed to detectgravi ty anomalies from the motions of spacecraft .

Ex perimen t MA-089, Doppler Tracking , was supervised by G. C. Weif-fenbach of the Smithsonian Astrophysical Observatory in Cambr idge , Mas-sachusetts. T he objective was to detect gravity anomalies by measur ing th echanges in the distance between tw o satellites ( the Apollo Command Moduleand the Docking Mo dule) as they passed o ver an anomaly and were acceler-ated by its higher gra vita tion al force. B oth satellites w ere in the same loworb i t , and th is techn ique became know n as the "low-low" method .


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The Principal Inve stigator for Ex perimen t M A-1 28, Geodynamics, was F.O. Von bun of the NA SA Robert H . Goddard Space Flight Center (GSFC) inGreenbel t , Maryland. The exper iment w as designed to detect gravityanomalies by me asuring the changes in distance be tween the Apollo space-craft and the ATS-6 satellite, which was in a much higher orbit. Thisprocedure became known as the "high-low" method, in contrast to the"low-low" method of Experiment MA-089.


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2 TheDoppler Effect

When an automobile blowing its hom or a train blowing its whistle passesyou, there is an obvious change in the pitch of the sound that you hear. Thepitch becomes higher as the vehicle approaches an d lower as it recedes. In1842, Christian D oppler, an Austrian scientist, pointed out that this chan ge isto be expected when an y source of periodic output such as sound waves movestoward or away from an observer. The pitch (the higher or lower tone) ofsound is a measure of the frequency of sound waves, which ar e periodicchanges in air pressure that we can hear. The Doppler effect is usuallyillustrated by a diagram that shows sound waves crowded together in thedirection of the m otion of the train whistle and spread o ut on the other side.Figure 2.1 gives a more precise explanation.The train whistle gives out sound waves of frequency/ , about 500 hertz(500 cycles/sec). These waves travel through the air at the velocity of soundv s, about 320 m/sec. As the train approaches at velocity v, its distance from alistener (observer) standing near th e track is decreasing. Therefore, eachsound wave has less distance to travel than th e preceding wav e (Fig. 2.1 ). The"period" T of the sound wave is T = \ / f , which is the t ime interval betweenwaves, or about 0.002 second for the train whistle. In the interva l T, the trainmoves a distance vT. The n ext sound w ave thus arrives early by vT/v s seconds,and the period of sound w aves heard by the observer is T' =T (vT/vs). Thefrequency that he hears is/' =/+ (vflv s), and the wavelength A he measuresis X' = X - (vA/Vy).

The Doppler shift isA T " = r - 7" = -vT/vs

or

or

AA = A' - A = -vA/Vy

where T, f, and A are the period, frequency, and wavelen gth , respectively , ofth e train-w histle sound as heard or measured on the train. A s Dopplerexplained the phenomenon more than a century ago, the same reasoningapplies to light waves or radio waves, except that they move with a m u c hlarger speed, 3 X 108 m/sec (the velocity of light c). Light wav es from th e


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moving tra in would thus be shifted to a higher frequency ("blue-sh i f ted" byA / = +/v /c o rAA = -Av/c)as th e train approaches. T he l ight waves would be"red-shifted" (negative A /, positive A\) as the train recedes. T he terms"blue-shifted" and "red-shifted" are used because higher frequency wavesof visible light ar e blue an d lower frequency waves ar e red, as described inPamphlet I I . The shift is very small for normal train velocities (60 km/hr or16.7 m/sec or 37 mph), which ar e less than one-m il l ionth of the velocity ofl ight . However, most satellites, planets, stars, and other astronomical objectsmove much faster than tra ins (from 7 km/sec to hundreds of kilometers per

seconds apart

Figure 2.1 Distance-time plot showing the Doppler shift for sound waves from an ap-proaching train with T of 2 milliseconds. Waves received by the observer haveT' of 1.95 milliseconds.


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\ / Observer on Earth

Figure 2.2 Doppler shift from the component of velocity in the line of sight.


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To measure the Doppler shift A/acc urately, both the broadcast frequency/an d the frequency received on Earth /' m u st beknow n accurately. This is doneby using crystal oscillators to control a radiofrequency electronic circuit at2000 megaher tz (2 x 10 9 cycles/sec) with a deviation of only a fraction of1 hertz (1 cycle/sec). These crystal oscillators made it possible to mea sure theDoppler shifts on Apollo-Soyuz very accurately. The moving object ( the

Orbiterslowed down by M

Orbiter, mass m,speeded up by M

Dense mascon undercrater on Moon

Effect of a mascon on the speed of a passing orbiter. Figure 2.3

Apollo Command Module or the Docking Module) had a crystal-controlledradio. The frequency of radio waves received was compared to the frequencyof a similar crystal. The two frequencies were almost th e same, but the sum ofth e i n co m in g wav es and the standard crystal oscil lator gave a "beatfrequency" equal to the difference between the two frequencies, as sh own inFigure 2.4.

Wave 1f = 2 gigahertz

Wave 2f = 2.25 gigahertz

Sum of waves 1 and 2has beat frequencyf = 0.25 gigahertz

Beat frequency in the sum of two waves of different frequency. Figure 2.4


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P Questions for Discussion(Doppler Shif t)

1. The ex h au s t of a racing car (wi thout a muffler) makes 10 "put-puts" pe rsecond at a speed v of 50 k m /h r (3 1 m p h ) . If the car is going away from you atthat speed, how many "put-puts" will you hear each second?

2. A police car is parked on a side street at a 45 angle to the o n co m in gtraffic on a h ig h way . W i l l th e Doppler radar on the police ca r give th e correctspeeds of cars on the h i g h w a y ?

3. The lunar orbiter had an orbita l speed of 1.7 km/sec . How did theDoppler shift of its 2000-megahertz radio tran sm itter change as it movedacross th e center of the Moon and rounded th e edge as "seen" by a radioreceiver on Earth? (Assume that there are no mascons.)


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-

If you have a stopwatch that is accurate to 0.1 second, your value of T isgood to 0.00001 second.

A n accurate pend ulum is st i l l the best in strum ent to measure g, and suchmeas ureme nts have been made at hundreds of geophysical stations all overthe world. Ho wever, a pendu lum wo n' t work on a roll ing ship or in anairplane f ly ing th rough bumpy air.Scientists therefore produced a "gra-vimeter," which has a small mass m on a spring (Fig. 3.2). The force ofgravity on m isFg = mg. Ifg is slightly larger, th e spring is stretched slightlyfarther. Gravimeters have complex ways of m a g n i f y in g this extra stretch.

Protective box at constanttemperature with removablesupports for mass m

Accuratematchingpointers

Reading (when pointersare matched)

Figure 3.2 A gravimeter for measuring g by the extension of an accurate spring.

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Some use bent quartz fibers as part of the spring, and the instrument isprotected from careless h an d l in g and temperature changes that might affectthe readings. E ach gravim eter is calibrated against a standard pe ndu lum justbefore it is used. A good gravimeter ca n measure g with an error of less than0 .1 mm/sec2 .

Gravity Anomalies and Earth StructureGeologists on foot have carried gravimeters into mountains an d across plains.They have taken them along seacoasts in automobiles and out into oceans insubmarines . In some places, they have made surveys wh ile f ly ing in airplanesat constan t a l t i tude . The acceleration of gravity g is slightly smaller athigher altitudes because the distance from the center of the Earth is greater.The force of gravity is proportional to 1/r 2 , where r is the distance from th eEarth 's center . G ravity readings are usua lly corrected to what they wo uld be atse a level.Maps of g corrected to sea level show m any max imu ms and m inim um s;that is , h u m p s and troughs in the force of grav i ty . If the Earth were per-fectly homogeneous, there would be no maxim ums and no min imum s. Themeasured values thus tell geologists about the structure of the Earth's crust .In general , g is higher over contin ents where dense rocks are near th e surfacean d lower over deep ocean basins where the dense rocks are far below. Othersmaller structures, such as iron-ore, coal, oil, and salt deposits, can bedetected. Caves and unde rgrou nd lava f lows can also be located. G ravim etersurveys are useful in prospecting fo r oil. They also indicate th e shape of buriedcraters and extinct volcanoes.

Grav imeter su rveys by foot, automobile, o r su b m ar in e are slow butrelat ively accurate. M easuremen ts from airplanes, al though faster , tend to beinaccurate . Measurem ents of g from satell i tes have the advantage of coveringvery large areas in a short t ime. A primary objective of the gravity experi-ments dur ing the Apollo-Soyuz mission was to determine how accurate themeasurements from a satell i te wou ld be. Of course, a gravim eter cannot beused in a spacecraft in orbit because ev eryth ing there is weight less and gwould be measured as zero. (The spring would pull the mass m to the top ofth e box in Figure 3.2 because Fg = 0; see Pamphle t I .) The method useddepends on the accelerationsof the spacecraft (as in the discovery of masconson the Moon). Because Apollo-Soyuz was in a low (222-k i lometer a l t i tude)circular orbit , small changes in g at the Earth 's surface could be detected.A higher sa te l l i te would be less sensi t ive to changes in g.

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c Questions for Discussion(Gravimeters, Gravity Anomalies)4. An old-fashioned pendulum clock keeps accurate t ime at sea l eve l ,

bu t th e owner moves it to a hotel on Pike 's Peak, at an alt i tude of about4 kilometers (14 000 feet). Wil l it run fast or s low?5. W h e n an airplane goes into a banked turn , wha t happens to the reading

of a gravimeter onboard th e airplane?6. If g is 9.8000 m/see2 on the surface in the Midwestern United States,w h a t is it at an altitude of 12 kilom eters (39 000 feet)? (The radius of theEarth is 6378 ki lomete rs . )7. How does th e Earth 's rota t ion reduce g near th e Equa t o r?

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4 The "Low-Low"Satellite Technique

W he n two satell ites in low orbit follow one another past a gravity anoma ly,the first is speeded up before the second one is and the distan ce between themincreases. Then the first satellite is slowed down (back to normal) before thesecond one is and the distance between them decreases (Fig. 4.1). The MA-089Doppler Tracking Experiment was designed to detect these changes indistance. A crystal-controlled radio transmitter was m ounted on the D ockingModule (DM), and a receiver with a similar crystal was placed on the ApolloCommand Module (CM). Each weighed abou t 7 k i lograms. Whi le the DMwas attached to the CM, the radios were warmed up and tested for constantfrequency. This test showed a s l ight change of about 3 parts in 1012; that is,th e broadcast frequency of 324 megahertz (324 mill ion cycles/sec) variedby only 1 mil l iher tz (0.001 cycle/sec).

O n Ju ly 23 at 19:45 Greenwich mean t ime (GMT the t ime in Gr een wich ,Eng l a nd , used as standard t ime on the Apollo-Soyuz mission) , the DM wasunlatched from the Apollo CM. Before releasing the DM , the astronauts usedth e Apollo reaction-control jets to spin Apollo and the DM at about onerotation every 72 seconds. After the DM was released, the Apollo CMgradual ly ceased spi nni ng and backed away from the DM. The purpose of theD M rotation was to stabil ize it with it s rad io an tenn a toward Apol lo . Al thou ghthis approach worked fairly wel l , the DM still had a smal l wobble tha tbrought i ts an tenna first toward an d then away from Apollo. This wobble

-6

s -10-1 2

1 6

CM propulsion

19:40 19:45 19:50 19:55 20:00 20:05 20:10 20:15 20:20 20:25GMT, hrmin

Doppler shift of the 324-megahertz frequency showing the DM drift after sep- Figure 4.1aration and the CM rocket firing.

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introduced an u n w a n t e d but small periodic Doppler shift in the DM radiotransmission.

The Doppler shift as Apollo backed away from the DM at 1.3 m/sec iss hown in Figure 4.1.A t 20:20 G M T , th e Apollo reaction jets were fired toseparate th e Apollo from the DM more quickly. When they reached 300ki lomete rs , th e astronauts fi red th e je ts in the other direct ion so that Apollostayed about th e same distance behind the DM.

Although the radio receiver could measure the difference in frequencyaccurately, there were three antic ipated com plicat ions in mea surin g theaccelerat ions caused by grav ity anom alies. First , the DM mov ed into as l ight ly different orbit from that of the CM. This change in orbi ta l shapecaused a periodic increase an d decrease of the separation every 93 m i nu t e s ,the t ime for one t r ip around th e Earth (see Fig.4.2 and Pamphle t I ). Second,atmospheric drag on the two orbiters w as sl ightly different, which caused agradual increase in separat ion. Final ly , e lectrons in the Earth ' s upper a tmos-phere between the two orbiters caused a small shift in the frequency of theradio t ransm iss ions .

The sl ight difference in orbi t was checked by ground observ at ions so thatcorrect ions could be made . The atmospheric drag was est imated in advance(i t caused a smooth , long- te rm change in separat ion). After correcting fo rthis , short-term changes du e to gravity anom alies could still be detected. Theeffect of electrons could be measured by us ing tw o f requencies , 162 and 324megahertz . The electrons changed one frequency more than the other, soboth the Doppler shift and the shift due to e lectrons could be calculated fromth e two measured f requency changes .

The f requency shif ts were measured over 10-second interv als for 13.8hours as the DM and the CM circled the Earth nin e t imes . Du ring these nineorbits, they passed over various parts of the Earth 's surface and should haverecorded man y gravi ty anomal ies . Ho wever , u n l ik e th e tes ts made whe n th e

01 02 03 04 05 06 07GMT, hr

09 10 11 12 13 14

Figure 4.2 Doppler shifts during eight orbits (corrected for ionospheric effects).

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CM and DM were still connected, variations in the DM radio-signal strengthwere so large during the actual experiment that the CM receiver could notmeasure the Doppler shift accurately. Because of these difficulties, the"low-low" techn ique detected no gravity anomalies during th e Apollo-Soyuz f l ight , but another attempt on some future mission may be successful.

Nevertheless, the MA-089 Experim ent was able to measure the ionizationof th e low-density atmosphere at a 222-kilometer alt i tude. The electrondensi ty varied from 3 X 10 9 electrons/m 3 on the nightside of the Earth to5 X 1011 electrons/m 3 on the dayside. More interesting were the manysudden changes in ionization. Most of these occurred as Apollo-Soyuzcrossed the Equa tor , w hich indicates that the ionosphere (see Pamphlet V) isirregular in that region . Figure 4.3 is a plot of the chang e of frequ ency du ring

Map of revolution 127 with plot of MA-089 frequency changes. The electrondensity between the Apollo CM and the DM can be computed from the changein frequency.Figure 4.3

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one revolut ion (number 127). This plot shows a big "wave" due to changesin electron densi ty just west of California on the even ing of J u ly 23, 1975.This wa ve had a wave length of 690 kilometers over which th e electrondensi ty changed by 35 percent . T he wave extended 7200 kilometers a longth e Apollo-Soyuz orbi t .

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5 The "High-Low"Satellite Technique

A satel l i te a t very high al t i tude is a lmost unaffected by gravity anomaliesbecause of the \/r2 in N e w t o n ' s Law of Grav ita t ion. Therefore , Dopplert rack ing of a low satellite (accelerated by gravit y ano ma lies) from a highsatellite should make measurements of those accelerations possible. T hesituation is complicated because the low satel li te (Apollo) m oves at c ha ng i ngangles to the high-lo w l ine (Fig.5.1). W hen A pollo was direct ly un der the highsatellite, there was no Doppler shift because there was no component oforbita l veloci ty a long the high-low l ine.

A The ATS-6 Geosynchronous SatelliteThe ATS-6 com mu nica t ion s sa tel l it e was in a 24-hour geosynchronous orb i t35 900 kilom eters above Lake Victoria in East Africa . At tha t he ight , 42 280kilometers from th e Earth 's center, it circles th e Earth every 24 hours an dremains over the same point on the Equator a l l the t ime (hence the namegeosynchronous "in t ime with th e E a r t h " ) . T he ATS-6 satellite w as locatedin this po si t ion to broadcast te levision programs to I n d i a an d Afr ica , and itwas a lso used for communicat ions w i th Apol lo-Soyuz (see Pamphle t I ) . I tre layed voice, radio, and t e lev is ion communica t ions on several c ircui ts toth e ATS receiver in Madrid, Spain. NASA has several other ATS satel l i tesplanned that wi l l eventu a l ly re lay "real-time" te levi sion and radio trans-missions to or from any part of the world.

The STDN receiver-transmit ter at Madrid (Fig. 5.1) is part of N A S A ' swor ldwid e Spacecraft Tracking and Data Ne twor k of 17 groun d sta t ions andseveral ships. When Apollo-Soyuz was 5 above th e local horizon, each ofthese radio stations could relay messages to or from Apollo an d S oyuz .

The Apollo spacecraft in low E arth orbi t , the ATS-6 satel l i te in high orbi t(actual ly more th an 160 t ime s high er than Apollo), and the ground receiversat Madrid, Spain, are shown schematical ly in Figure 5.1. The radio fre-quenc ies used between each pair ar e given in gigahertz (1 0^ cycles/sec). The2.25-gigahertz radio signals from Apollo to ATS-6 have a Doppler shift ofA /= 2.25 x 10"v^c, where v^ is the component of Apol lo ' s orbita l veloci ty valong the Apollo/ATS-6 l ine. The Doppler shift (and v^) was zero w h e nApollo passed direct ly under the ATS-6 and v was perpendicular to the l inefrom Apollo to ATS-6. T he shift was a m axi mu m (v^ a lmost equa l to v) whenApol lo w as near th e horizon as seen from th e ATS-6. These Dopple r-shi f tedsignals were then radioed to the ATS receiver in Madrid on a 3.8-gigahertzcircuit with a l m os t no Dopple r shift because th e position of the ATS-6 isnearly fixed in the sky.

I t would also have been possible to measure the Doppler shift in theApollo 2.3-gigahertz radio transmissions to the STDN stat ion in Madrid

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Figure 5.1 Schematic of the ATS-6/Apollo communication links.The ATS Ranging stationis designatedATSR; the NASA Spacecraft Tracking andData Network stationis designated STDN.

Apollo spacecraft >*V t-;J.y:;; r

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(A/ = 2.3 x 10 9 Vj/c), but the effect of ions in the lower atmosphere com-plicates such measurements (see Sec. 4). Ions had little effect on theApollo/ATS-6 link or on the ATS-6/Madrid link because these radio wavestravel only short distances through the ions, and a small correction could bemade for the ion effect.

P The MA-128 Geodynamic ExperimentThe objective of the Geod ynamic E xperiment was to measure gravity anoma-lies as small as 0.05 mm/sec2 over features as small as 300 ki lometers . Tw oareas were selected: the center of Africa , whic h has positive gravity anomalies,and the Indian Ocean trough, w hich has a negative gravity anoma ly. Apollopassed over central Africa on its 1 15th orbit (revo lutio n) around the E arthan d over th e Ind ian Ocean on revolutions 8, 23, and 53, as shown in Figure5.2. Mea sureme nts were made on these orbits and on revolutio ns 120 and 135.Gravi ty anomalies were measured in the three areas shown in Figure 5.2.Because the ATS-6 satellite was almost directly overhead in Afr ica, thecomponent v^ in Figure 5.1 was directed nearly up or down over eachanomaly (as over the mascon in Fig. 2.3), and the sensit ivity for measuringthe strength of the anomaly was high.

The radiofrequency crystal oscillators were stable enough that velocitychanges as small as 1 mm/sec w ere detected. Errors in the measured valuesof v^ were about 0 .5 mm/sec. Measurements were made on 108 orbits fo rthe 40 m inut es of each 93 -min ute orbital period durin g w h i c h Apollo waswith in 7500 ki lometers of the point in East Africa directly under th e ATS-6.(Dur ing th e other 53 m in u te s of each orbit , Apollo either cou ldn ' t see theATS-6 or saw it so near the horizon that many ions were in the line of sight.)W h en Apollo was rolled or turned in any way, i ts radio an tenna was movedart i f icial ly . The t im e of such maneu vers was recorded at the Mission C ontrolCenter (MCC) at the NA SA L yndon B. Johnson Space Center (JSC) inHouston. The MA-128 Doppler measurements at those t imes were no good(the scientists didn't want to misinterpret a spacecraft roll as a gravitya nom a l y ! ) . In general , two or more orbits over the same gravity anomalywere used to estimate i ts strength.

Q Results of the Geodynamic ExperimentChanges in v^ ( the compo nent of Apollo's orbital velocity toward th e ATS-6)during three orbits over the Indian Ocean and the Him alaya Mou ntain s areshown in Figure 5.3. After correction for the effects of ions an d electronsbetween Apollo and the ATS-6, th e Doppler shifts ( A v ^ ) definite ly show th e

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80

60

40

20

20

40

60

80I

40 20 20 40 60L o n g i t u d e , d e g

80 10 0

Figure 5.2 Apollo spacecraft groundtracks for Experiment MA-128.

Ind ian Ocean anomaly. The Himalayan anomaly is less certain, however,because there was a high den sity of atmospheric ions over the Him alay aseach time Apollo passed over. If the changes in v^ are converted to thestrength of the anomalies, the two largest anom alies correspond to changes ing of 0.6 and l .O mm/sec2 , about I 0 ~ 4 g . Other orbits showed 10 5-ganomal ies in Asia Minor , I0~ 6 -g anomalies in central Africa, an d less wellde te rmined anomalies in the Southern Hemisphere. Some of the anomalies inAsia Minor ar e associated w i t h cont inen ta l drift (movement of large sectionsof the Earth 's crust) in that area (see Pamphle t V).

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-2

Revolution 8July 16 , 1975 Himalayananomalousarea

Indian Oceananomaly10 mmI I i

/V

i:-\. V f 't

i

Revolution 23July 17, 1975Himalayananomalousarea

ft.- r.A.A -V"/"< "5 ' v :- Indian Ocean .anomaly

10 min1 1 i

':t"u,

t

17:02 7:12 7:22 7:32 7:42 7:52 6:37 6:47 6:57 7:07 7:17 7:27

GMT, hrmin

Revolution 53July 19 , 1975Himalayan"anomalousarea i

Indian Ocean -anomaly10 mmH ' *

5:55 6:05 6:15 6:25 6:35 6:45GMT, hrmin

Changes in Apollo velocity toward the A T S - 6 caused by gravity anomalies inthe Indian Ocean and Himalaya Mountains. Note that VA changes agree well onthree orbits.Figure 5.3

The M A-1 28 Exp er ime nt a lso p rov ided new data abou t the Ear th ' s a tmos-phere. M easu reme nts made jus t as Apollo disappeared from ATS-6 viewbelow th e horizon (or as Apollo reappeared above th e horizon) show th erefraction (bending) of radio waves in the Ear th 's atmosphere. These refrac-tions can be used to derive th e temperature T and the pressure P of theatmosphere through which th e radio waves passed. Using m easu r em en t staken at 1-second intervals for 30 seconds before Apollo disappeared below

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or after it reappeared above th e horizon, th e scientists derived T and P forseveral altitudes. In one place, the values derived agree with measurementsmade from a balloon fl ight , which means that the "high-low" satellitecombinat ion ca n collect certain meteorological (wea ther) data rapid ly. L ater,wh en satellites are positioned at several lo ngitude s around the w orld, th istechnique w ill give measurem ents of T and P wherever lo w satellites cross aring about 9000 kilometers from the point under each high satellite.

~ ~ ) Questions for Discussion(Doppler Effect, Spin, Orbits)8. W ith crystal oscillators controlling radiofrequency to 1 millihertz in334 megahertz, what is the smallest velocity along the line of sight thatcan be detected?9. If the DM had not been stabilized by a spin, what could have happenedto prevent collection of the Apollo-DM Doppler measurements?

10. If the Earth rotated once eve ry 12 hours (instead of once every 24 ho urs),ho w high would a geosynchronous satellite have to be?

11. Figure 5.1 shows an intermediate position of Apollo relative to theATS-6. Where would th e Doppler shift be at a m a x i m u m ? W h e re w o u ldApollo be for zero Doppler shift?

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Appendix A

Discussion Topics (Answers to Questions)1. (Sec. 2B) The Doppler formula isA/=fv/vs. The "put-put" frequency/is 10put-puts/sec. The speed of the carv is 50 km/h r or 13.9 m/sec. The speedof sound vs is 320m/sec. Therefore, A/= (10)(13.9/320) = 0.434 put-puts/sec,and/ ' = / - A/=9.566 put-puts/sec.2. (Sec. 2B) The Doppler radar on the police car will detect only the com-

ponent of a car's velocity in its line of sight, 45 to the highway (car'svelocity v). It will thus read v cos 45, or 0.707 v.3. (Sec. 2B) A t the center of the Moon as seen from Earth, the orbiter ismov ing across our line of sight (0 = 90 in Fig. 2.2); therefore, the Doppler

shift is zero. At the edge of the Moon, the orbiter is mov ing direct ly away fromus (9 = 180), and vc = -v = 1.7-km/sec recession. The Doppler shift isthenA/= -fvlc = -2 x 109 (1.7/3 x 105) = -1.13 x 104 hertz or -11.3kilohertz ( 1 1 . 3 kilocycles/sec re d shift).

4. (Sec. 3C) The period of a pendulum swing T = 2irjLlg. At sea level,g = 9.80 m/sec2; at a 4-kilometer (14 000 foot) altitude (4 kilometers fartherfrom the Earth's center), g is smaller (9.786 m/sec2), so T would be larger.The ratio of T on the mountain to T at sea level is /9.80/9.786 = /1.0014 =1.0007. The period is thus 0.0007 longer on the mounta in , and the clock run sslow by (0.0007)(1440 min/day) = 1.0 min/day.

5. (Sec. 3C) The airplane in a banked turn is accelerated toward thecenter ofits turn , an d this acceleration increases th e gravimeter reading.

6. (Sec. 3C) By Newton 's Law of Gravitat ion,F = G M m / r2 = mg. Thus,g is proportional to \ lr 2 , where r is the distance from th e Earth's center. A t a12-kilometer altitude, r is 6390, an dg at that altitude is (6378 km/6390 km) 2 =0.9962 t imes g at sea level, or (0.9962)(9.8000) = 9.763 m/sec2.

7. (Sec. 3C) A t the Equator, a mass is movi n g at v = 460 m/sec in a circlewith a radius r of 6378 kilometers as the Earth rotates once every 24 hours.Part of the gravitational force Fp = GmMg/r2 is used to keep m moving in thiscircle at acceleration a = v2//-. Therefore, a spring balance or gravimeterrecords /" m v 2 /r = m g ma, and g is reduced by a = v 2/r. "Centrifugalforce" is the term used to describe m v 2/r .

8. (Sec. 5D) In the Doppler formula A/ = fvlc, we need A/ larger than1 millihertz. So v must be larger than (1 millihertz//) c, or (10 V3.34 X 10")(3 X 10" m/sec) = 9 x 10 4 m/sec, or 9 X 10 ' mm/sec, or 0.9 mm/sec.

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9. (Sec. 5D) If the DM had not been stabilized, it would probably have"tumbled" so that its transmitting antenna faced away from Apollo. In thatcase, no radio signals could have been received by Apollo.

10 . (Sec. 5D) The period T of a satellite is related to its distance r from th eEarth ' s center by Kepler 's Law (see Pamphlet I): T 2 is proportional to r3.If 7 is reduced from 24 hours to 12 hours, r3 must be reduced by (24/12) 2 = 4.The altitude of the geosynchronous orbit, 35 900 k ilometers , plus the radius ofthe Earth, 6378 km = 42 278 = r. Therefore, the new r3 = (l/4)(42 278)3 =( l /4)(7.56 x 10 13) = 1.89 x 10 13 , and r = 2.66 x 10" kilometers, or26 600 kilometers from Earth's center, or 20 200 kilometers above the Equator .

11 . (Sec. 5D) The Apollo's Doppler shift would be a m a x i m u m w h e n itsorbital velocity v was along the Apollo/ATS line of sight, at the lower left inFigure 5.1. The Doppler shift would be zero when Apollo passed under ATS-6as it moved across the line of sight.

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Appendix BSI UnitsPowers of 10

International System (SI) UnitsNames, symbols , an d conversion factors of SIQuantity

Distance

Mass

Time

Temperature

AreaV ol um eFrequency

Density

Speed,velocity

Name of unit

meter

kilogram

second

kelvin

square metercubic meterhertz

kilogram percubic metermeter per second

units used in these pamphlets:Symbol Conversion factor

m 1 km = 0.621 mile1 m = 3.28 ft1 cm = 0.394 in .1 m m = 0.039 in .1 /im = 3.9ox 10~5 in. = 10 4 A1 nm = 10 A

kg 1 tonne = 1.102 tons1 kg = 2.20 Ib1 gm = 0.0022 Ib = 0.035 oz1 mg = 2.20 x 10'6 Ib = 3.5 x 10'5 oz

sec 1 yr = 3.156 x 107 se c1 day = 8.64 x 104 sec1 hr = 3600 sec

K 273 K = 0 C = 32 F373 K = 100 C = 212 Fm 2 1 m 2 = 10" cm 2 = 10.8 ft 2m 3 1 m 3 = 10 6 cm 3 = 35 ft3Hz 1 Hz = 1 cycle/sec

1 kHz = 1000 cycles/sec1 MHz = 106 cycles/sec

kg /m 3 1 kg /m 3 = 0.001 gm/cm 31 gm/cm 3 = densi ty of wate r

m/sec 1 m/sec =3.28 ft/sec1 km/sec = 2240 mi/hr

Force newton N 1 N = 105 dynes = 0.224 Ibf

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Quantity

Pressure

EnergyPhoton energyPowerAtomic mass

Customary UnitsQuantity

Wavelength oflightAcceleration

of gravity

Name of unit

newton per squaremeter

jouleelectronvol twattatomic mass unit

Used With the SI UnitsName of unit

angstrom

g

Symbol

N /m 2

JeVW

am u

Symbol0

A

g

Conversion factor

1 N/m1 = 1.45 x 10-Mb/in2

1 J = 0.239 calorie1 eV = 1.60 x 10'19 J; 1 J = 107erg1 W = 1 J/sec1 amu = 1.66 x 10"27 kg

Conversion factor

1 A = 0.1 nm = 10-' m

1 g = 9.8 m/sec2

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Unit PrefixesPrefix

fe ngig*megakilohectocentimillimicronanopico

Abbreviation Factor by w h i c h unitis multiplied

T 10"G 10M 10*k 10h 10*c 10-2m 10'3ft ID'6n lO'9p 10-12

Powers of 10Increasing Decreasing10 2 = 100103 = 1 000104 = 10 000, etc.Examples:2 x 106 = 2 000 0002 x 1030 = 2 fol lowed by 30 zeros

i o - 2 = 1 / 1 0 0 = o . o i10-3 = 1/1000 = 0.00110~* = 1/10000 = 0.000 1,etc.Example:5.67 x ID'5 = 0.000 056 7

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Appendix C

GlossaryReferences to sections, A ppendix A (answers to questions) , and f igures areincluded in the entries. Those in italic type are the most helpful.acceleration (a ) change of velocity with t ime. (Sees. 2A, 3 , 4 ; A p p . A ,

nos. 5, 7; Figs. 2.3, 5.3) The acceleration of grav i ty at the Earth 's surfaceis called g.

ATS-6 communications satellite a satellite in geosynchronous (24-hourperiod) orbit 35 900 kilometers above East Africa, used to rebroadcastradio signals to and from the control station in Madrid, Spain. (Sees. 1,5A , 5B, 5C; App. A, no. 11; Figs. 5.1,5.3)basin a depression. Basins on the Moon are large craters caused by meteorimpac t . Ocean basins on E arth are deep places in the floor of the oceans.(Sees. 2A, 3B)

beat frequency wh en two sources are em itt in g sound waves of a differentf requency ( /", , / ,) , the com bined so und swe lls and falls in int ens ity ,producing beats. T he f requency of the beats is/2 /, . (Sec. 2A ; Fig. 2.4)c the velocity of l ight, radio, and other electromagn etic wav es, 3 X 10 8m/sec. (Sec. 2)

Command Module (CM ) the part of the Apollo spacecraft in wh ich theastronauts l ived an d worked; attached to the Service Module (SM) unt i lreentry into th e Earth 's atmosphere. (Sec. 4 ; Fig. 4 .3)

component (radial) of velocity the fraction of a velocity vector that is alongth e line of sight of an observer; it is only this fraction that produces Dopplershift. (Sees. 2 / 4 , 5 to 5C; App. A , nos. 2, 3, 11; Figs. 2.2, 5 .1 , 5 .3)

crater a circu lar depression. Most of those on the Moon w ere produced bymeteor impact . (Sees. 2A , 3B; Fig. 2.3)crystal a solid composed of a to m s or ions or molecules arranged in a regu lar

repet i t ive pattern. In an electronic circuit , it oscil lates with a f ixed fre-que nc y . (Sees. 2A, 4 , 5B; Ap p . A, no. 8)

Docking Module (DM) a special compone nt added to the Apollo spacecraftso that i t could be joined w i th Soyuz. (Sees. 1, 4; App. A, no. 9; Figs. 4 .1 ,4.3) See Pamphlet I .

Doppler shift th e change of frequency and wavelength in the spectrum of asource approaching an observer (blue shift) or receding from him (redshif t) . (Sees. 2, 2 A, 4, 5 to 5C; App. A, nos. 1 to 3, 8, 11; Figs. 2. 1 ,2 .2 , 4 .1 , 4 .2)

drag, atmospheric th e fr ic t ional forces opposing spacecraft veloc ity , causedeven at high a l t i tudes by the low-densi ty Ear th a tmosphere there . Atmos-pheric drag lowers the orbit. (Sec. 4)

frequency (f) the n u m b e r of oscil lat ions or wav es leaving a sound sourceor a rad io an tenna or a l ight source per second. (Sees. 2, 2A, 4, 5A, 5B;Figs. 2.4, 4.3)

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oscillator an electronic device producing radio waves of a g iven f requency .Crystal oscillators give a highly accurate frequency. (Sees. 2A, 5B;App . A, no. 8)

pendulum a mass suspended from a fixed point so that it can swing back an dforth freely. (Sec. 3A ; App. A, no. 4 ; Fig. 3.1)

period (T) the time taken by a satellite to travel once around it s orbit , or thet ime between tw o successive swings of a p en d u lu m or between tw o suc-cessive w ave crests in radio or light waves. (Sees. 2, 3A; App. A , nos. 4 ,10;Fig. 2.1)

r the distance of a satellite from th e Earth 's center .radio waves electromagnetic waves of wavelength between 1 mill ime ter andseveral thousand kilometers and frequencies between 300 gigahertz and a

few hertz. The higher frequencies are used for spacecraft com mun ications ,the lower fo r N a v y c o m m u n i c a t i o n s . (Sees. 2, 2A, 4 , 5A to 5C;App. A, no. 9)

reaction-controljets small propulsion units on a spacecraft used to rotate it orto accelerate it in a specific direction. (Sec. 4)

refraction the bending of electromagnetic rays such as l ight or radio waveswhere th e material they ar e passing through changes in densi ty or otherproperties. (Sec. 5C )revolut ion the revo luti on or orbit num ber of a spacecraft in orbit around theEarth. (Sec. 5B ; Figs. 4.3, 5 .2)

Service Module (SM) th e large part of the Apollo spacecraft that containssupport equipment; it is attached to the Command Module (CM) unti ljust before the CM reenters the Earth's atmosphere.

sound waves pressure oscillations in the air. The speed of sound is 320 m/sec.(Sec. 2; App. A, no. 1; Fig. 2.1)

vector a directed quantity , such as velocity , force, or acceleration. Vectorsymbols (v, F, a) are given in boldface type.wavelength (X) the distance from th e crest of one wav e to the crest of thenex t , usua l ly measured in angstroms fo r x-rays and visible l igh t and incentimeters or meters for radio waves see App endix B. (Sec. 2)

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EP-136

NASANational Aeronautics andSpace Adm inistration