Explorer Satellite History

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TEMPERATURE CONTROL I N THE EXPLORER

SATELLI TES AND PI ONEER SPACE PROBES

External Publication No. 647

JET PROPULSION LABORATORYCALIFORNIA INSTITUTE OF TECHNOLOGY

PASADENA 3, CALIFORNIA


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Nat i onal Aeronaut i cs and Space Admi ni st r at i onCont r act No. NASw-6

Ext er nal Publ i cat i on No. 647

TEMPERATURE CONTROL I N THE EXPLORER

SATELLI TES AND PI ONEER SPACE PROBES

E. P. Buwal daA. R. Hi bbs

T. 0. Thos t esen

Copy No.27

JET PROPULSION LABORATORY

California Institute of Technology

Pasadena 3, CaliforniaMay 7, 1959


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Jet P ropu ls ion Labo ra t o r y Ext er nal Publ i cat i on No. 64

CONTENTS

Page

I . I nt r oduct i on . . . . . . . . . . . . . . . . . . . . . . 2

I I . Anal ys i s of the Temper at ur e of the Sat el l i t e Shel l . . . 5

A. Mat hemat i cal Devel opment . . . . . . . . . . . . . . 5

B. Ef f ect of Sur f ace Char ac ter i s t i c s . . . . . . . . . . . . . . 15

I I I . Aver age Temper at ur es of :: he Sat el l i t e Shel l . . . . . . 17

I V. Temper at ur e Pr edi ct i ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

V. Temper at ur e f or 1958 ALPHA . . . . . . . . . . . . . . . 20

VI . The PI ONEER Pr obes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

VI I . Concl usi ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Fi gur es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Re f e r e nc e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

FI GURES

1. Di mensi ons and Or i ent at i on of Payl oad . . . . . . . . . . . . . . . . . . 28

2. The Rat i o of A / Aj f or t he Coni cal Sect i on of t he

Payl oad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3. Geomet r y of Ear t h- t o- Sat el l i t e Radi at i on Process . . . . 29

4. Rel at i onshi p Bet ween r j Coordi nat e Syst em and

Di r ect i on of t he Sun . . . . . . . . . . . . . . . . . . . . . . 29

5. Aver age Temper at ure of Coni cal Sect i on of t he Payl oad

Shel l vs Angl e Ar ound Or bi t f or Launch 20 Bef or e NoonTr ansi t , h = 1000 mi l es, 9 = 0 , 10, 20, 30, 40,

50, 6 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


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7.

OU o

9 .

10.

1 1 .

12.

13.

14.

15.

FI GURES ( Cont d)

Page

Aver age Temper at ur e of Coni cal Sect i on of t he Payl oad

Shel l vs Angl e Ar ound Or bi t f or Launch 50 Af t er Noon

Tr ansi t , h = 1000 mi l es, 9 = 0, 10, 20, 30, 40,

50 , 60 . . . . . . 0 . . . . o o . o . . . o o . . . . 30

Aver age Temperat ur e of Cyl i ndr i cal Payl oad Shel l vs

Angl e Ar ound Or bi t f or Launch at Noon Transi t , h = 1000

mi l es, cp = 0 , 10, 20, 30, 40, 50, 60 . . . . . . 31

Aver age Temperat ur e of Cyl i ndr i cal Payl oad Shel l vs

Angl e Ar ound Or bi t f or Launch 90 Bef ore Noon Tr ansi t ,

h = 1000 mi l es, cp = 0, 10, 20, 30, 40, 50,

^ O 1JJ ooOOOOC'OO0'DOOOCQ*OO*

The Sat el l i t e 1958 ALPHA . . . . . . . . . . . . . . . . 32

Measur ed Cyl i nder Shel l Temper at ur e vs Ti me f or 1953

ALPHA, Febr uar y 1 t hr ough 12, 1958 . . . . . . . . . . . 33

Measur ed and Pr edi ct ed I nt ernal Cyl i nder Temperat ur e

vs Ti me f or 1958 ALPHA, Febr uar y' 1 t hr ough 12, 1958. . 34

Measur ed Cone Shel l Temper at ur e vs Ti me f or 1958

ALPHA, Febr uar y 1 t hr ough 12, 1958 . . . . . . . . . . . 34


ALPHA, Febr uar y 13 t hr ough 24, 1958 . . . . . . . . . . 35


ALPHA, Febr uar y 25 t hr ough Mar ch 8 , 1958 . . . . . . . . 36


ALPHA, Mar ch 9 t hr ough 20, 1958 . . . . . . . . . . . . . . . . 37


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Jet Propu l sion Labo ra t o r y Ext er nal Publ i cat i onNo-

FI GURES ( Cont d)

Page

16. Measur ed Cone Shel l Temper at ur e vs Ti me f or 1958

ALPHA, Mar ch 21 t hr ough Apr i l 1, 1958. . . . . . . . . . . . . . . . .

38

17. Measur ed Cone Shel l Temper at ur e vs Ti me f or 1958

ALPHA, Apr i l 2 t hr ough 13, 1958 . . . . . . . . . . . . . . . . . . . . . . . . 39

18. Measur ed St agnat i on Poi nt Temper at ur e vs Ti me f or

1958 ALPHA, Febr uar y 1 t hr ough 12, 1958 . . . . . . . . . . . . . . . 40


1958 ALPHA, Febr uar y 13 t hr ough 24, 1958 . . . . . . . . . . . . . 41


1958 ALPHA, Febr uar y 25 t hr ough Mar ch 8 , 1958 . . . . . . . . 42


1958 ALPHA, Mar ch 9 t hr ough 20, 1958 . . . . . . . . . . . . . . . 43


1958 ALPHA, March 21 t hr ough Apr i l 1, 1958 . . . . . . . . . . . 44


1958 ALPHA, Apr i l 2 t hr ough 13, 1958 . . . . . . . . . . . . . 45

24. Measur ed and Pr edi ct ed I nt er nal Cone Temper at ur e vs

Ti me f or 1958 ALPHA, Febr uar y 1 t hr ough 12, 1958 . . . 46


Ti me f or 1958 ALPHA, Febr uar y 13 t hr ough 24, 1958 . . . 47


Ti me f or 1958 ALPHA, Febr uar y 25 t hr ough Mar ch 8 ,

1958 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

27. Payl oad Conf i gurat i on, PI ONEERS I I I and I V . . . . . . . . . . . 49

I

Page


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FI GURES ( Cont d)

Page

28. PI ONEER I I I Payl oad Temper at ur e . . . . . . . . . . . . . . . . . . . . . . . . 50

29. PI ONEER I V Payl oad Temper at ur e. . . . . . . . . . . . . . . . . . . . . . . . . . 50

Page


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ABSTRACT *

The J et Pr opul si on Labor at or y par t i ci pat ed i n t he l aunchi ng of

t he EXPLORER sat el l i t es and t he J UNO I I space pr obes ( PI ONEERS I I I

and I V) . Thi s par t i ci pat i on i ncl uded payl oad desi gn and t he met hod

of achi evi ng t emper at ur e cont r ol . Thi s Publ i cat i on descr i bes the

basi c t heor y f or t he passi ve t emper at ur e cont r ol of sat el l i t es and

space pr obes and t he appl i cat i on of t hi s pr ocess t o t he EXPLORERS a

PI ONEERS I I I and I V. Some r esul t s of i n- f l i ght t emperat ur e measur e

ment s ar e al so present ed.

Thi s paper pr esent s t he r esul t s of one phase of r esear ch car r iout at t he J et Pr opul si on Labor at or y, Cal i f or ni a I nst i t ut e of

Technol ogy, under Cont r act No. NASw- 6 , sponsor ed by t he Nat i onalAer onaut i cs and Space Admi ni st r at i on.

Page


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I . I NTRODUCTI ON

The cont r ol of t he t emper at ur e of a sat el l i t e or space pr obe i

i n pr i nci pl e, a ver y si mpl e pr obl em. The t emper at ur e i s det ermi ned

onl y by t he amount of r adi at i ve heat whi ch t he body r ecei ves, t he he

gener at ed i nt er nal l y, and t he heat whi ch the body re- r adi at es or

r ef l ect s t o t he sur r oundi ng empt y space. The body i s not i n cont act

wi t h an at mospher e of any appr eci abl e densi t y.

. Thus, i n pr i nci pl e, i t woul d be possi bl e t o achi eve al most any

t emper at ur e i n a sat el l i t e or space pr obe and t o hol d i t at an al mos

exact l y const ant val ue, wi t hout r ecour se t o r ef r i ger at i ng or heat i ng

devi ces. Onl y si mpl e mechani sms woul d be r equi r ed i n order t o adj us

a syst em of r ef l ect i ng or absorbi ng scr eens on t he out er sur f ace.

However , i n a mi ni mum- wei ght vehi cl e, such as t he EXPLORERS an

PI ONEERS, even such si mpl e mechani sms as t hese are t oo cost l y - i n

t er ms of wei ght - t o permi t t hei r use. I t i s necessar y t o use a com

pl et el y passi ve t echni que t o achi eve t he necessar y t emperat ur e cont r

For t he EXPLORERS and PI ONEERS, t he t emperat ure r est r i ct i ons a

i mposed by t he el ect r oni c equi pment car r i ed i n t he i nst r ument sect i o

At t emper at ur es bel ow about - 5 C, t he bat t er i es cease to operat e

pr oper l y. However , i f t he t emper at ur e were t o f al l bel ow t hi s l i mi t

no per manent damage woul d be done. The equi pment woul d f unct i on

proper l y i f i t wer e war med up agai n.

OAt t emper at ur es above +50 C, t he el ect r oni c equi pment does no

operat e pr oper l y. However , i t does not suf f er per manent damage unt i

Ot he t emper at ur e exceeds +80 C.

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Ther ef or e, t he ai m of t he t emper at ur e- cont r ol t echni que was t o

at t empt t o hol d t he t emper at ur e of t he el ect r oni c equi pment bet ween

t he l i mi t s of - 5 C and +50 C; but , i n any event , t he t emper at ur e w

never t o exceed. +80 C.

The onl y compl et el y passi ve t echni que avai l abl e i s t hat of

cover i ng the out er sur f ace wi t h mat er i al s whi ch have t he pr oper

r adi at i ve char act er i st i cs. Even when t he sur f ace i s pr epar ed i n t he

best possi bl e way, some t emper at ur e var i at i on i s i nevi t abl e f or a

sat el l i t e.

As t he sat el l i t e moves i n i ts or bi t , i t passes al t er nat el y

bet ween sunl i ght and shadow. The per i od of t hi s cycl e i s, of cour se

t he per i od of one r evol ut i on ar ound t he ear t h, or about 1 1 / 2 t o 2

hr. Thi s wi de var i at i on coul d be avoi ded onl y i f a hi gh i ncl i nat i on

of t he or bi t t o t he equat or wer e at t ai ned, t hus keepi ng t he sat el l i t

cont i nuousl y i n sunl i ght .

For t unat el y, t he equi pment wi t hi n t he sat el l i t e need not exper

ence t he same degr ee of var i at i on as the shel l . Test s on a pr ot ot yp

model showed t hat t he el ect r oni c equi pment coul d be so wel l i nsul at e

f r om t he shel l t hat i t s t emperat ur e var i ed onl y a. f ew degr ees;

wher eas, t he f l uct uat i ons i n shel l t emper at ur e exceeded 100 C bet we

ext r emes.

I n t hi s case, t he t emperat ur e of t he el ect r oni c equi pment st ay

near t he aver age t emper at ur e of t he shel l , aver aged over one or bi t .

However , as the or bi t r egr esses ar ound t he ear t h, as the l i ne of

apsi des pr ecesses about t he or bi t , and as t he ear t h t ur ns about t he

sun, t hi s aver age t emperat ur e var i es. Fur t her mor e, t he at t i t ude of

t he sat el l i t e wi t h r espect t o t he sun i s al so i mpor t ant si nce t he

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EXPLORER i s r oughl y cyl i ndr i cal i n shape.

Thus, i t i s necessar y to:

1. Fi nd sur f ace mat er i al s whi ch wi l l mai nt ai n t he aver age

t emper at ur e of t he shel l wi t hi n t he pr escr i bed bounda

ri es, keepi ng i n mi nd t he l ong- t er m var i at i ons caused

by t he mot i on of t he pl ane of t he or bi t , t he l i ne of

apsi des, and t he ear t h.

2. Launch at t he r i ght t i me of day i n order t o achi eve t h

pr oper at t i t ude of t he sat el l i t e wi t h r espect to the

sun; or sel ect sur f ace pr oper t i es consi st ent wi t h a

pr escr i bed l aunchi ng t i me.

3. I nsul at e t he el ect r oni c equi pment f r om t he shel l ( f or

the sat el l i t e).

Thi s Publ i cat i on out l i nes t he mat hemat i cal devel opment of t he

heat - f l ux equat i on f or t he shel l . The r esul t shows how t he t emperat

of t he shel l depends on sur f ace char act er i st i cs, posi t i on of t he or b

t al pl ane, and at t i t ude of t he vehi cl e. Thi s out l i ne i s f ol l owed by

a di scussi on of t he sur f ace- char act er i st i cs pr obl em and a descr i pt i o

of t he mat er i al s used on the sur f aces of t he EXPLORERS and PI ONEERS.

/A compar i son i s gi ven of t he pr edi ct ed and obser ved t emper at ur e

of t he el ect r oni c equi pment . , and a pr esent at i on of al l of t he t emper a

t ur e dat a r ecei ved f r om EXPLORER I - - 1958 al pha, and PI ONEERS I I I an

I V, al l of whi ch wer e desi gned and f abr i cat ed at t he J et Propul si on

Laborat or y.

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I I . ANALYSI S OF THE TEMPERATURE OF THE SATELLI TE SHELL

A. Mat hemat i cal Devel opment '

The r at e of change of t he t emper at ur e of t he shel l of a

sat el l i t e i s

d rp_ ! S + I e - X _

dt me

wher e

Tp = t he t emper at ur e of t he shel l

I g = t he r adi at i ve power absorbed f r om sunl i ght

I g = t he power r ecei ved f r om t her mal r adi at i on of t he ear t

R = t he power r adi at ed f r om t he shel l

t = t i me

me = t he t ot al heat capaci t y of t he shel l

The use of t he t ot al heat capaci t y of t he shel l i mpl i es t hat t h

assumpt i on has been made t hat al l part s of t he shel l ar e i n good

t her mal cont act wi t h each ot her ; t hat i s, i t i s assumed t hat t he

r at e of heat t r ansf er by conduct i on f r om one par t of t he shel l t o

anot her i s much gr eat er t han t he r at e of heat t r ansf er by radi at i on

bet ween t he sur f ace of t he shel l and t he sur r oundi ng envi r onment .

I t al so i mpl i es a second assumpt i on; namel y, t hat t he el ect r oni

equi pment on t he i nt er i or i s so wel l i nsul at ed f r om t he shel l t hat i

can have no ef f ect on t he t emper at ure of t he shel l over t he t i me

per i ods of i mpor t ance. The f i r st assumpt i on i s val i d, but t he secon

i s somewhat quest i onabl e. Act ual l y, t he t emperat ure of t he i nt er nal

equi pment di d var y sever al degr ees i n t he per i od of one or bi t ; hence

hence i t di d have an ef f ect on t he shel l t emperat ur e. However , t he

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Je t P ropu lsion Labo ra t o r y Ext er nal Publ i cat i on No. 6

ef f ect on t he aver age shel l t emper at ur e i s not gr eat ; consequent l y,

f or t he pr esent pr obl em, i t i s pr obabl y not wor t h t he added compl exi t

to i nt r oduce t hi s ef f ect.

Sol ar r adi at i on i s r ecei ved by t he sat el l i t e i n t wo ways. Fi r st

r adi at i on i s recei ved di r ect l y f r om t he sun at t he r at e

/ 5 1 = AS a ' l 5

wher e

Ag = t he pr oj ect ed ar ea of t he sat el l i t e as seen f r om t he

di r ect i on of t he sun

ccj_ = t he coef f i c i ent of absor pt i vi t y of t he shel l f or sol a

radi at i on

S = t he sol ar const ant = 1. 94 cal / cm / mi n

The pr oj ect ed ar ea of t he sat el l i t e f or t he r ecei pt of di r ect

sol ar r adi at i on i s, nat ur al l y, a f unct i on of t he shape of t he

sat el l i t e. I n t he pr esent anal ysi s i t has been assumed t hat t he

por t i on of t he sat el l i t e body whi ch i s i mpor t ant f or t emper at ur e

cont r ol has t he f ol l owi ng char act er i st i cs: ( l ) I t has a coni cal

nose. (2) The base of t hi s cone i s at t ached t o a cyl i ndr i cal sect i on

of t he same r adi us. (3) The combi ned sur f ace of t he cone and

cyl i nder i s exposed t o r adi at i ve heat t r ansf er wi t h t he sur r oundi ng

envi r onment . (4) The base of t he cyl i nder i s t her mal l y i nsul at ed

f r om t he r emai nder of t he payl oad and act s as a r adi at i on shi el d f or

t hi s base ar ea. A sket ch of t hi s conf i gur at i on i s shown i n Fi g. 1.

The pr oj ect ed ar ea of t he sat el l i t e f or t he r ecei pt of r adi at i on i s

a f unct i on of t he angl e of or i ent at i on 77 shown i n Fi g. 1.

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Jet P ropu ls ion Labo ra t o r y Ext er nal Publ i cat i on Mo. 6

I n or der t o det er mi ne t hi s angl e f or t he r ecei pt of r adi at i on

f r om any par t i cul ar sour ce (e. g. , t he sun) , i t i s necessar y t o make

some assumpt i ons about t he mot i on of t he satel l i t e.

EXPLORER I was l aunched i nt o orbi t spi nni ng about i t s l ongi t u

di nal axi s. I f i t wer e a r i gi d body, i t woul d mai nt ai n t hi s spi n

or i ent at i on f or a consi derabl e per i od of t i me, si nce no appr eci abl e

ext ernal t or ques are act i ng per pendi cul ar t o t he angul ar moment um

vector.

However , EXPLORER I i s not a r i gi d body. Ext endi ng f r om i t s

si des ar e f our wi r e ant ennas ( ai r cr af t cont r ol cabl es) . The f l exi ng

of t hese wi r es i nt r oduces appr eci abl e i nt ernal dampi ng. Si nce no

ext er nal t or ques are appl i ed by t hi s f l exi ng, t he angul ar moment um

must st ay f i xed i n bot h di r ect i on and magni t ude.

The onl y way t hat ener gy can be di ssi pat ed i s f or t he mode of

spi nni ng t o change, event ual l y r eachi ng a mi ni mum ener gy mode f or

const ant angul ar moment um.

Thi s i s what happened. Wi t hi n a day af t er l aunch, EXPLORER I

was r ot at i ng end over end about a t r ansver se axi s, wi t h t he angul ar

moment um vect or st i l l poi nt i ng i n t he or i gi nal di r ect i on.

Si nce t he angul ar moment um vect or mai nt ai ns a f i xed di r ect i on i/

Newt oni an space, i t i s conveni ent t o def i ne t he or i ent at i on of t he

sat el l i t e wi t h r espect t o t hi s di r ect i on. Si nce t he spi n ar ound t hi s

vect or t akes pl ace wi t hi n a per i od much shor t er t han any t hermal t i m

const ant s i mpor t ant f or t hi s pr obl em, t he ar ea of t he sat el l i t e i s

aver aged over t he angl es 77 t r aversed i n one spi n cycl e.

Let 17 be t he angl e bet ween t he angul ar moment um vect or and t he

di r ect i on of a sour ce of r adi at i on. Let be t he angl e bet ween t he

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Jet P ropu ls ion Labo ra t o r y Ext er nal Publ i cat i on No.

l ongi t udi nal axi s of t he sat el l i t e and t he pl ane def i ned by t he

angul ar moment um vect or and a l i ne f r om t he sat el l i t e to the

r adi at i on sour ce. Then f or a mot i on consi st i ng of spi n about a

t r ansver se axi s, t he average ar ea i s

wher e 17 i s def i ned by cos rj = cos s i n 77 , and t he f unct i on A(77) f o

t he coni cal sect i on conf i gur at i on of t he EXPLORER i s shown i n Fi g.

wher e i t s r at i o wi t h t he t ot al sur f ace ar ea A^ i s pl ot t ed as a

f unct i on of 77. For the cyl i ndr i cal sect i on, t hi s f unct i on i s s i mpl y

2r l ^ s i n 77.

I f t he sour ce of r adi at i on i s t he sun, t hen 77 =

The sat el l i t e wi l l al so r ecei ve sol ar r adi at i on whi ch i s

r ef l ect ed f r om t he ear t h. The r adi at i ve power r ecei ved by t he

sat el l i t e t hr ough r ef l ect i on f r om an el ement dS of t he ear t h s

sur f ace ar ea i s

rr

die = (P.A .) a-i i(a) cos a cos/3 - -2 1 ^

wher e

P. A. = pr oj ect ed ar ea of t he sat el l i t e seen f r om t he

sur f ace ar ea dS

i ( a) = t he r adi at i ve power r ef l ect ed at an angl e a t o t he

nor mal of t he sur f ace el ement wi t h pr i mar y radi at i o

normal t o t he el ement


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Jet Propu l sion Labo ra t o r yxt er nal Publ i cat i on No.

(3 = t he angl e bet ween the di r ect i on of t he sun and. t he

nor mal t o t he sur f ace el ement d.S

p = t he di st ance bet ween t he sur f ace el ement and t he

sat el l i t e

The geomet r y of t he ear t h- t o- sat el l i t e r adi at i on pr ocess i s shown

i n Fi g. 3.

Si nce t he sat el l i t e shape under consi der at i on has cyl i ndr i cal

symmet r y onl y, each sur f ace el ement of t he ear t h wi l l see a di f f eren

pr oj ect ed ar ea of the sat el l i t e. Thus, t he angl e of or i ent at i on

wi l l be a var i abl e i n t he subsequent i nt egr at i on of dl c .2

Let dS cos a be t he sur f ace el ement of a sphere of r adi us p.

Then

d S c o s a = p 2 s jn 7 7 d ^ d w

wher e 77 and \jr ar e spher i cal pol ar coordi nat es about t he cent er of

t he sat el l i t e wi t h t he pol ar axi s coi nci di ng wi t h t he di r ect i on of

t he angul ar moment um vect or of t he body. Rewr i t i ng Eq. (3) i n t erms

of r]} and gi ves

d 1^ = - aj i cos y sin r ] d 77j, d02 a t

wher e y i s def i ned as t he angl e bet ween t he di r ect i on of t he sun and

t he nor mal t o the sur f ace el ement p^ si n - d. T d)]/ .

Wi t h t he hel p of Fi g. 4, i t can be seen t hat

cosy= cos [cos - sin (t70-7]j ) ctn T]0] + cos r)s sin (Vq~Vi ^ esc rj0

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wher e

0g = t he angl e bet ween t he r adi us vect or f r om t he cent er o

t he ear t h t o t he sat el l i t e and t he di r ect i on of t he s

7 2 = t he angl e bet ween t he di r ect i on of t he angul ar

moment um vect or of t he sat el l i t e and t he di r ect i on of

t he sun

t j q = t he angl e bet ween t he di r ect i on of t he angul ar moment

vect or of t he sat el l i t e and a r adi us vect or f r om t he

cent er of t he ear t h to t he sat el l i t e

The assumpt i on has been made t hat i i s i ndependent of a; t hat i

t hat t he r ef l ect i on f r om t he ear t h i s per f ect l y di f f use.

The t ot al power r ecei ved by t he sat el l i t e t hr ough r ef l ect i on ma

now be wr i t t en as

wher e t he l i mi t s of i nt egr at i on over \Jr depend on 77^ and t?q

I nt egr at i on wi t h r espect t o \]/ i s i mmedi ate; however , t he

mat hemat i cal f or m of t he r at i o Ag/ Ay as a f unct i on of r j , i s t oo

compl ex to per mi t anal yt i cal i nt egr at i on. Ther ef or e, t he i nt egr at i on

wi t h r espect to 77 must be car r i ed out numer i cal l y.

s22 a

10

rr

/0

+ cos 775 sin (7?q "?71 ) cscT q} drj^d\p

77= 7 T f o r V j < - t j 0

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I n t he above i nt egr at i on, i t has been assumed t hat t he ear t h i s

f l at ; hence, t he ear t h as seen f r om t he sat el l i t e cover s hal f of t he

sky. I n an ear l i er st udy by Dr . A. R. Hi bbs of t he J et Pr opul si on

Labor at or y ( Ref . l ) t he t ot al power r ecei ved by a spher i cal sat el l i t e

t hr ough r ef l ect i on was f ound to be

I s = 2772a2 (Xj i ( 1- x/2y) cos &s

t hr ough t he f i r st or der i n y, wher e

y = h/ r 0

h = hei ght of t he sat el l i t e above t he ear t h s sur f acer Q = r adi us of t he ear t h

The f act or ( l - / 2y) cut s down t he f r act i on of t he sky f i l l ed by t he

ear t h, and can be t hought of as t he al t i t ude ef f ect .

Ass umi ng t hat t he al t i t ude ef f ect i s i ndependent of t he shape

of t he sat el l i t e, t he r esul t s of t he i nt egr at i on of Eq. (4) are

cor r ect ed by t he f act or ( l - J 2 y) .

I f t he i nt egr al over t he t er m wi t h t he coef f i c i ent cos 0g i s

cal l ed A ( l - V 2y) \ and of - t he i nt egr al over t he t er m wi t h t her l ,

coef f i c i ent cos 775 i s cal l ed Ar 2( l - ' / 2 y) , t hen t he r esul t f or the

power r ecei ved f r om sunl i ght i s

[S 2 = al l!77 cs 8S +A r2 cos 775] (

Ref er r i ng t o Fi gs. 3 and 4, i t can be seen t hat

COS 8 g = COS 8 C O S

COS 775 = COS COS (t] q - 8 )

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Jet Prop u ls ion Labo ra t o r y Ext er nal Publ i cat i on No. 6

wher e

0 = pol ar angl e of t he sat el l i t e i n i ts or bi t measur ed

f r om noon t r ansi t

cp = t he angl e bet ween a r adi us vect or f r om t he cent er of t

ear t h t o t he sun and t he pl ane of t he sat el l i t e or bi t

Subst i t ut i ng t hese r el at i onshi ps i n Eq. (5) gi ves

fr - a, i 7Tcos \A . cos 9 +A . sin 6 ] 2 3 4

wher e

\ = \ +Ar2 CO.*,,,

Ar4 = \ Si" V

The f unct i on i ( a) , appear i ng i n Eq. ( 3) , i s def i ned f or t he sun

ver t i cal l y above a par t i cul ar sur f ace el ement . Wi t h t hi s def i ni t i on

t he t ot al power r adi at ed f r om a par t i cul ar sur f ace el ement i nt o a

hemi spher e can be obt ai ned wi t h a si mpl e i nt egr at i on. The r esul t i s

% 77Ti = E

I f t he coef f i ci ent f or di f f use r ef l ec t i on f rom the ear t h i s r , theb

equat i on becomes

7ri = SrE

Act ual l y, r i s not a const ant f or al l sur f ace el ement s on t he ear t hE

For t hi s s t udy an average val ue over t he ear t h s sur f ace, whi ch i s

appr oxi mat el y 0. 4 ( Cf . Ref . 2), i s used.

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Jet Propu l sion Labo ra t o r y Ext er nal Publ i cat i on No. 6

The t ot al power cont r i but i on f r om sol ar r adi at i on may now be

wr i t t en as

Ther mal r adi at i on f r om t he ear t h i s r ecei ved by t he sat el l i t e a

t he r ate 1 . Thi s t er m may be eval uat ed i n t he same manner as that

empl oyed i n det er mi ni ng t he power cont r i but ed f r om r ef l ect ed sol ar

r adi at i on. I t i s not necessar y t o consi der t he posi t i on of t he sun;

t her ef or e, t he angl es 0^ and r/ do not appear i n t he r esul t of t he

i nt egr at i on. Use of t he St ef an- Bol t zmann l aw yi el ds t he f ol l owi ng

re sui t :

Ag = t he t ot al pr oj ect ed ar ea of t he body f or r ecei pt of

t hermal r adi at i on f r om t he ear t h (based, on an i nt egr al

si mi l ar t o t hat of Eq. 4)

a - t he St ef an- Bol t zmann const ant

T^ =. t he ef f ect i ve t emper at ur e of t he ear t h = 250K ( Ref . 3

ccq = t he coef f i ci ent of absor pt i vi t y of t he body f or r ecei p

of t her mal r adi at i on at 250K

The t her mal r adi at i on f r om t he sat el l i t e may be wr i t t en as

wher e

R = /I j- e gcr Tp

wher e

A j = t he t ot al sur f ace ar ea of t he body

e 2 the coef f i c i ent of emi ssi on for t her mal r adi at i on fr om

the sat el l i t e

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20/58


For a par t i cul ar wave l engt h of r adi at i on Ker chof f ' s l aw state:

a

We expect t he sat el l i t e to be at appr oxi mat el y the same t emper a

t ur e as t he ear t h. Theref ore, t he i mpor t ant wave l engt h r egi on of

i t s r adi at i on shoul d be approxi mat el y t he same as t hat of t he t her ma

r adi at i on f r om t he ear t h, so t hat t o a good appr oxi mat i on

The equat i on f or t he r at e of change of t he t emper at ur e of t he

sat el l i t e shel l may now be r ewr i t t en i n t he f ol l owi ng manner

( 2)"dTr

dt

CL^S + eraC (

and t he meani ng of t he super scr i pt s i s as f ol l ows:

Ter m ( l ) i s t he di r ect sol ar r adi at i on t er m and i s t o be i ncl ud

onl y when t he sat el l i t e i s i n t he sun. That i s, t he t er m i s t o be

i ncl uded onl y when 9 l i es bet ween t he angl es ( 2 n - 1 / 2 ) tt - 0 2 and

( 2 n + 1 / 2 ) t t + 0 2 w er e

0, = si n " ( s i n 0 / cos cp)j f or cp< (tt/ 2 - 0 )

2tt/ 2 f or 9 >(ir/ 2

- 1V

= cos [r l/ ( r 0 >]I t has al r eady been not ed t hat t he cal cul at i on of t he r ef l ect ed

sunl i ght cont r i but i on was made f or a f l at ear t h as seen f r om t he

sat el l i t e t o l ess t han hal f of t he sky. However , one addi t i onal


21/58

Jet P ropu lsion Labo ra t o r y Ext er nal Publ i cat i on No. 6

ef f ect of t he ear t h' s cur vat ur e st i l l r emai ns. I t has been assumed

t hat al l of t he ear t h seen by t he sat el l i t e i s i l l umi nat ed. Act ual l

as t he sat el l i t e appr oaches t he t wi l i ght zone, t hi s i s not t he case.

For t unat el y, t he r esul t i ng er r or i s smal l , and can be easi l y t aken

car e of , at l east t o a ver y good appr oxi mat i on.

The r ef l ect ed sunl i ght t erm, wi t h t he super scr i pt ( 2) , i s t o be

i ncl uded onl y wher e 0 l i es bet ween t he angl es ( 2 n - 1 / 2 )7r and

( 2n + l / 2 )7r. Thus, t he r ef l ect ed sunl i ght t er m i s cut of f as t he

sat el l i t e passes over t he t er mi nat or . I ncl usi on of t he compl et e t er

on t he sunl i t si de of t he t ermi nat or i mpl i es t oo much r ef l ect ed l i gh

Dr oppi ng t he t er m compl et el y on t he ot her si de i mpl i es t oo l i t t l e

r ef l ect ed, l i ght . The t wo er r or s near l y cancel out .

B. Ef f ect of Sur f ace Char act er i st i cs/

I f t he sat el l i t e wer e al ways i n t he shadow of t he ear t h, i t s

t emper at ur e woul d appr oach t he equi l i br i um val ue Tn = Tr ( A / A_ )1/ / 4,P b b T

i ndependent of t he sur f ace char act er i st i cs. But , si nce t he sat el l i t

spends over hal f of i t s l i f e i n t he sun, t hi s l ower l i mi t i s never

r eached. The act i on of t he sunl i ght r ai ses the t emper at ur e.

The ef f ect i veness of sunl i ght i n r ai si ng t he aver age t emper at ur

can be eval uat ed i n t he f ol l owi ng way. Suppose t he f act or a ? i s

di vi ded out of t he r i ght - hand si de of Eq. ( 10) . The t wo l ar ge

f act or s on t hi s si de are compet i ng f or ci ng f unct i ons. The f i r st , no

wi t h t he coef f i ci ent (ccj / a ) S, i s posi t i ve, but acts onl y par t of

t he t i me. The second, now wi t h onl y o' as a coef f i ci ent , i s negat i ve

and .is al ways pr esent .

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Jet P ropu ls ion Labo ra t o r yExter nal Publ i cat i on No. 6

The r esul t i s a cycl i c f l uct uat i on of t emper at ur e, whose det ai l

can be cont r ol l ed onl y by cont r ol l i ng t he r at i o aj _/a2 once t he shap

of t he sat el l i t e has been det er mi ned. The cor r ect choi ce of t hi s

r at i o f or t he sat el l i t e sur f ace i s cr i t i cal f or t emper at ur e cont rol .

Act ual l y, si nce t he sat el l i t e i s spi nni ng wi t h a per i od much

shor t er t han any of t he i mpor t ant t hermal t i me const ant s, onl y t he

average val ue of ctj /ccp over t he sur f ace i s i mpor t ant . For t hi s

r eason, i t i s not necessar y t o f i nd a si ngl e mat er i al wi t h t he

cor r ect r at i o ci j Va2 f or t he whol e sur f ace. I f t wo mat er i al s can be

f ound whose r at i os of aj _/a2 br acket t he desi r ed val ue, t hen t he

sur f ace may be coat ed wi t h a pat t er n of t hese t wo mat er i al s.

Sel ect i on of t he pr oper f r act i on of t he sur f ace to be cover ed by eac

wi l l t hen per mi t t he cor r ect aver age rat i o t o be achi eved.

Two sur f ace mat er i al s have been cons i der ed; st eel ( si nce t he

sat el l i t e shel l i s made of st eel ) and Roki d. e , a cer ami c mat er i al ,

( si nce t he sat el l i t e i s exposed t o aer odynami c heat i ng dur i ng t he

l aunch phase). A st eel sur f ace accept s a r el at i vel y l ar ge amount of

power f r om sol ar r adi at i on ( hi gh val ue of a / a ) } whereas a Roki de-

coat ed sur f ace accept s a r el at i vel y smal l amount of such power ( l ow

val ue of 0 / 0 2 ). The val ue of a / cc2 f or t he sur f ace mat er i al s t o be

used must be car ef ul l y measur ed i f accur at e t emperat ur e pr edi ct i ons

ar e r equi r ed. Such measur ement s have been made f or st eel and Roki de

sur f aces f or t he J et Pr opul si on Laborat or y by t he Mechani cal Engi nee

i ng Depar t ment of t he Uni ver si t y of Cal i f or ni a at Ber kel ey. A

di scussi on of t hese measur ement s may be f ound i n Ref . 4.

ORoki de A, al umi num oxi de appl i ed by a pat ent ed pr ocess of t he

Mor t on Co. , Worcest er , Mass.

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23/58


Br i ef l y, the rat i o of a 1/ 0.2 f r Roki de was found, t o be 0. 437.

Two t ypes of st eel wer e used wi t h t wo di f f er ent sur f ace pr epar at i ons.

For t he st eel used on t he cyl i nder a / a 0 i s 1. 92; wher eas, f or t he

st eel used i n t he nose cone the rat i o i s 4. 12.

I I I . AVERAGE TEMPERATURES OF THE SATELLI TE SHELL

The aver age t emper at ur e of t he sat el l i t e shel l may be det er mi ned

by numer i cal i nt egr at i on of Eq. ( 10) . I t i s necessar y t o speci f y t he

t i me of l aunch, t he angl e bet ween t he pl ane of t he orbi t and t he

di r ect i on of t he sun, t he char act er i st i cs of t he or bi t , t he sur f ace

char act er i st i cs of t he sat el l i t e, and t he t ot al heat capaci t y of t he

sat el l i t e payl oad. . A number of such i nt egr at i ons have been car r i ed

out t o i l l ust r at e the ef f ect of t he var i ous par amet er s- upon t he

t emper at ur e of t he sat el l i t e shel l . Exampl es of t he aver age t emper a

t ur es obt ai ned, f r om t hese i nt egr at i ons ar e di spl ayed i n Fi gs. 5

t hr ough8

, wher e

h = t he al t i t ude of t he c i r cul ar or bi t i n mi l es

cp = t he angl e bet ween the pl ane of t he or bi t and t he

di r ect i on of t he sun

6 = t he angl e ar ound t he ci r cul ar or bi t measur ed f r om t he

l aunchi ng poi nt

EXPLORER I i s appr oxi mat el y 80 i n. l ong and 6 i n. i n di amet er

( see Fi g. 9) and. i s composed of t hr ee sect i ons: t he nose cone, t he

cyl i ndr i cal sect i on t o whi ch t he nose cone i s at t ached, and t he

empt y f our t h- st age mot or case. E?ch of t he t hr ee sect i ons i s t her mal

i nsul at ed, f r om t he ot her s so t hat t he t emper at ur e of each sect i on may

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Jet Prop u ls ion Labo r a t o r y Ext er nal Publ i cat i on No. 6

be consi dered i ndependent l y. Cont r ol of t he t emper at ur e i s necess a

f or onl y t he f i r st t wo sect i ons si nce t hey cont ai n t he el ect r oni c

equi pment .

For t hi s st udy, i t was assumed t hat t he t hi ckness of t he sat el l

nose cone shel l was 3 mm at t he t i p and 0. 8 mm over t he rest of t he

body. The t ot al heat capaci t y of t he nose cone shel l was det er mi ned

f r om t he wei ght of t hi s sect i on of t he shel l ( 352. 2 g) and t he

speci f i c heat capaci t y of st eel ( 0. 127 cal / g/ C) ( Cf . Ref . 5) t o be

44. 73 cal / C. The t ot al sur f ace ar ea f or t he conf i gur at i on shown

oi n Fi g. 1 was f ound t o be 136. 097 i n. Bot h of t hese val ues wer e use

i n t he numer i cal i nt egr at i ons per f or med.

A second set of average t emper at ur es was obt ai ned f or t he

cyl i ndr i cal sect i on of t he shel l , wi t h t he di mensi ons shown i n Fi g.

Bot h ends of t he cyl i nder were assumed t o be i nsul at ed f r om t he

r emai nder of t he payl oad and t o act as r adi at i on shi el ds. Sampl e

aver age t emper at ure cur ves f or t hi s conf i gur at i on ar e shown i n Fi gs.

and 8 . Thi s cyl i ndr i cal conf i gur at i on has a t ot al sur f ace ar ea of

376. 991 i n. * and a t ot al heat capaci t y of 140. 6 cal / C.

On t he basi s of t hese cal cul at i ons, a r at i o of 25% Roki de was

sel ect ed f or t he cyl i ndr i cal secti on, gi vi ng an aver age aj _/ a2 of 1. 3

and a r at i o of 30% Roki de was chosen f or t he nose cone, gi vi ng an

aver age a / ccp of 1. 61.

I V. TEMPERATURE PREDI CTI ONS

I t i s essent i al t o pr ovi de t he pr oper t emperat ur e envi r onment f

t he r adi o equi pment car r i ed by t he sat el l i t e f or at l east t he l i f et i

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Jet P ropu lsion Labo ra t o r y Ext er nal Publ i cat i on No. 6

of t he bat t er i es power i ng t hi s r adi o equi pment . I t i s possi bl e t o

choose t he i ni t i al t emper at ur e of t he sat el l i t e shel l , aver aged over

t he f i r st f ew or bi t s, wi t hi n t he pr oper bounds. Thi s t emper at ur e wi

var y wi t h t i me due t o t he pr ecessi on of t he sat el l i t e or bi t caused b

t he obl at eness of t he ear t h and al so due to t he change i n or i ent at i o

of t he sat el l i t e wi t h r espect t o t he sun. The pr ecessi on of t he or b

may be regarded, as a change i n t he angl e bet ween t he di r ect i on of t h

sun and t he pl ane of t he or bi t (9 ). Changes i n t he sat el l i t e' s

or i ent at i on wi t h r espect t o t he sun may be account ed f or by var yi ng

t he or i ent at i on angl e Si nce t he t emper at ur e of i nt er est i s t hati nsi de t he sat el l i t e, onl y t he mean val ue of t he shel l t emper at ur e

over a cycl e i s consi dered.

1958 ALPHA was i nj ected, i nto or bi t at 3 hr 55 mi n 5 sec Gr eenwi

Mean Ti me on Febr uar y 1, 1958. The average al t i t ude of t he orbi t i s

appr oxi mat el y 900 st at ut e mi l es, and t he angl e of i ncl i nat i on of t he

or bi t t o t he ear t h' s equat or i s 33. 34 deg. Thi s set of l aunchi ng

condi t i ons gi ves i ni t i al val ues of = 107 deg, and 9 = 0 deg.

As poi nt ed out i n Sec. I I , t he or i gi nal at t i t ude of t he axi s of

symmet r y was not mai nt ai ned. Wi t hi n a shor t per i od of t i me t he

sat el l i t e had pr ecess ed t hrough 90 deg and was t umbl i ng about i t s

or i gi nal spi n axi s wi t h a per i od of appr oxi mat el y 7 sec. Thus, t he

expect ed t emper at ur e- t i me hi st or y f or 1958 ALPHA must ut i l i ze a

pr oj ect ed ar ea averaged over t he t umbl i ng per i od. The assumpt i on wi

be made t hat t he pr ecess i on of t he sat el l i t e' s axi s of symmet r y

occur r ed i n appr oxi mat el y one day. Thus, on Febr uar y 2 t he sat el l i t e

i s t umbl i ng i n a pl ane appr oxi mat el y 16 deg away f r om t he di r ect i on

t he sun and t he ef f ect i ve pr oj ect ed ar ea f or t he r ecei pt of sol ar

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26/58


r adi at i on cor r esponds t o an aver age angl e of or i ent at i on of 116 deg.

Pr edi ct ed i nt er nal t emper at ur es f or t hi s geomet r i cal si t uat i on have

been pr epar ed f or t he nose cone and t he cyl i nder. These pr edi ct ed

i nt er nal t emperat ur es are pl ot t ed wi t h t he obser ved t emperat ur e dat a

i n a l at er Sect i on of t hi s Publ i cat i on.

V. TEMPERATURE FOR 1958 ALPHA

Four di r ect t emper at ur e measur ement s ar e made usi ng r esi st ance

t her momet ers. These r esi st ance t her momet er s are pl aced as f ol l ows:

1. The st agnat i on- poi nt t emper at ur e measur ed at t he t op of

t he nose cone and capabl e of cover i ng a r ange of - 50C

t o +450C. The approxi mat e accur acy of t hi s measur emen

i s 20C.

2. The nose- cone ski n t emper at ur e measur ed j ust f or war d of

t he ant enna gap and. capabl e of cover i ng a. r ange of

- 50C t o +220C. At 50C t he accur acy of t hi s measur e

ment i s 16C. At 0C t he accur acy i s 18C.

3. The cyl i nder ski n t emper at ure measur ed af t on t he

cyl i nder and capabl e of cover i ng a r ange of - 50C t o

+110C. Over t he r ange of - 10C t o +80C t he accur acy

of t hi s t emper at ure data i s 4C.

4. The i nt ernal t emperat ur e of t he cyl i nder measur ed i n t h

hi gh- power ed t r ansmi t t er and. capabl e of cover i ng a r ang

of - 60C t o +110C. The accur acy of t hi s measur ement

r anges f r om 2C at T = 0 t o 30C t o 20C at T = 90C.

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I n addi t i on t o t hese di r ect t emper at ur e measurement s, i ndi r ect

measures of i nt er nal t emper at ur e ar e avai l abl e. The i nt er nal t emper

t ur e of t he nose cone may be i nf er r ed by obser vi ng t he f r equency l eve

of t he cosmi c- r ay measur ement channel . Cal i br at i ons of t he subcar r i e

osci l l at or i ndi cat e t hat t he i nt er nal t emper at ur e of t he nose cone i s

known to 12C f or T = 0 t o 25C and to 6 C f or T = 25 t o 50C.

Ther e i s cont i nuous t r ansmi ssi on of al l t el emet r y dat a. The

st agnat i on poi nt t emper at ur e and t he nose- cone ski n t emper at ure

measur ement s ar e t r ansmi t t ed, by t he l ow- power ed t r ansmi t t er . The

i nt er nal and ski n t emper at ur es of t he cyl i nder are t r ansmi t t ed by t he

hi gh- power ed t r ansmi t t er . The dat a ar e r ecor ded at t he f ol l owi ng

l ocat i ons :

Pat r i ck Ai r For ce Base 28N Lat i t ude

Ear t hquake Val l ey 33N Lat i t ude

San Gabr i el 34N Lat i t ude

Ni ger i a 10N Lat i t ude

Si ngapore 2N Lat i t ude

Pat r i ck Ai r For ce Base, Ear t hquake Val l ey, and San Gabr i el r ecei

appr oxi mat el y f our passes a day; Ni ger i a and Si ngapor e recei ve about

seven passes a day. Dat a f r om t he l ow- power ed, t r ansmi t t er ar e r ecei v

at al l st at i ons. I nf or mat i on f r om t he hi gh- power ed t r ansmi t t er i s

r ecei ved, at Pat r i ck Ai r For ce Base and San Gabr i el onl y.

The t el emet r y dat a f r om some seven hundred, and t hi r t y- t wo passeshave been r educed and pl ot t ed agai nst t i me. The t i me per i od cover ed

i s f r om Febr uar y 1, 1958, t o Apr i l 14, 1958. I ndi vi dual f i gur es have

been prepar ed f or each of t he t emper at ur e measur ement s. The pr edi ct e

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i nt er nal t emper at ur e f or t he nose cone and f or t he cyl i nder has been

added t o t he pl ot s of t hese quant i t i es. These dat a ar e shown i n

Fi gs, 10 t hr ough 29.

Bot h t he measur ed i nt er nal t emperat ure i n t he cyl i nder and t he

i ndi r ect measur e of i nt er nal t emper at ure i n t he nose cone show a r a

of 35C. Thi s range i s t r aver sed semi per i odi cal l y wi t h an apparent

per i od of appr oxi mat el y 2 1/ 2 days. However , i t i s ver y pr obabl e t h

t hi s t emper at ur e r ange i s exper i enced dur i ng each or bi t . I t shoul d

be r emember ed t hat t he maxi mum f r act i on of an orbi t over whi ch dat a

r ecor ded i s appr oxi mat el y 2 b % . The r ecor ds show an i nt er nal f l uct u

t i on f r om 0C t o 35C i nsi de t he cyl i nder and f r om 5C t o 40C i nsi d

t he nose cone.

I n compl et i ng t he t emper at ur e pr edi ct i ons some al l owance was

made f or t he r emai ni ng uncer t ai nt i es, such as unpr edi ct ed. var i at i ons

i n at t i t ude and al t i t ude. I n maki ng t hi s al l owance, a conservat i ve

approach was used consi st ent l y based, on t he requi r ement t hat i n no

case was t he t emper at ur e t o exceed +80C, t he val ue at whi ch t he

el ect r oni c equi pment suf f er s per manent damage. I t was est i mat ed t ha

t hi s al l owance mi ght cont r i but e as much as 15C t o the si mpl er pr e

di ct i on. I t i s t hi s conser vat i ve pr edi ct i on whi ch i s shown i n t he

Fi gur es of t hi s r epor t .

Thus, bef or e t he f i r i ng, i t was est i mat ed t hat t he act ual t empe

t ur es mi ght r un as much as 15 bel ow t he conser vat i ve pr edi ct i ons.

The dat a show t hat t he t emper at ur es wer e gener al l y about 10 bel ow

t hi s conser vat i ve pr edi ct i on.


29/58


Shel l t emper at ur es r angi ng f r om - 25C t o 75C have been obser ve

An i nspect i on of Fi gs. 5 t hr ough 8 i ndi cat es t hat a t emper at ur e

var i at i on of 80 t o 90C dur i ng one or bi t woul d be expected.

VI . THE PI ONEER PROBES

The t emper at ur e- cont r ol pr obl em f or t he moon pr obes, PI ONEERS I

and I V, di f f er ed i n sever al ways f r om t he pr obl em f or t he EXPLORER

sat el l i t es . Fi r s t , i t i s not possi bl e to r egul at e t he t i me of f i r i n

i n accor dance wi t h t he r equi r ement s of t emper at ur e cont r ol . Ti me of

f i r i ng i s di ct at ed by t r aj ect or y r equi r ement s. Second, t he ear t h

does not ent er , i n a si gni f i cant way, i nt o t he t emper at ur e pr obl em

dur i ng t he i mpor t ant por t i ons of the f l i ght . Thus, r adi at i on f r om t

ear t h can be negl ect ed, and a st eady- st at e t emper at ur e. can be assume

f or the cal cul at i ons, i f t he at t i t ude can be hel d f i xed. Thi r d, t he

amount of heat gener at ed i nt er nal l y by t he t r ansmi t t er and ot her

el ect r oni c equi pment of t he PI ONEERS i s not a negl i gi bl e sour ce as i

was f or t he EXPLORERS. Four t h, dur i ng t he f l i ght t hr ough t he at mos

pher e of t he l aunchi ng vehi cl e, t he payl oad i s pr ot ect ed by a. shr oud,

t hus maki ng possi bl e t he use of sur f ace mat er i al wi t hout t he r est r i c

t i on of abi l i t y to wi t hst and aer odynami c heat i ng. Fi f t h, t he

t emper at ur e ext r emes per mi t t ed f or t hi s payl oad wer e somewhat

nar r ower t han t hose per mi t t ed f or t he EXPLORER payl oad.

Fi gure 27 shows a pr of i l e of t he payl oad used i n PI ONEERS I I I

and I V. The Fi gur e shows f our r ef er ence ar eas: The nose cone; t he

cyl i ndr i cal wr appi ng ar ound t he bat t er y pack ( i ) ; t he annul ar base o

Page


30/58


t he bat t er y pack ( I I ); and t he r emai ni ng por t i on of t he payl oad' s

base ( i l l ) . To achi eve t emper at ur e cont r ol , each one of t hese ar eas

was gi ven a di f f erent sur f ace t r eat ment .

The successf ul oper at i on of t he payl oad r equi r es t hat t he t empe

t ure l i e bet ween t he l i mi t s of 20C and 50C. I t was deci ded t o mak

each of t he above- l i st ed areas separ at el y mai nt ai n a. t emper at ur e as

cl ose as possi bl e t o t he mi dpoi nt of t he l i mi t s, 35C. I t was f or

t hi s r eason t hat each of t he ar eas r ecei ved a di f f erent sur f ace

t r eat ment .

The dependence of t emper at ur e upon at t i t ude angl e 17 coul d not b

overcome by cont r ol l i ng t he t i me of l aunch, as was done f or t he

EXPLORER sat el l i t es, si nce t he t r aj ect ory r equi r ement s f or a moon

pr obe speci f y t he t i me of l aunch t o wi t hi n t he near est f ew mi nut es.

Sever al t i mes of l aunch on a ser i es of days were s el ect ed f or t he

vehi cl e. I n t hi s way, al l owance was made f or t he possi bi l i t y of

l ast - mi nut e del ays i n t he f i r i ng schedul e. I n t ur n, t hi s r equi r ed

t hat t he sur f ace coat i ng be changed day by day i f such post ponement s

became necessary si nce each new days f i r i ng r esul t ed i n a di f f erent

angl e, 17 .

The nose cone was made of f i ber gl ass, and i t s out er sur f ace was

covered wi t h a gol d wash. For PI ONEER I I I , 4 4 % of t hi s sur f ace was

t hen st r i ped wi t h whi t e pai nt . Ar ea 1 was const r ucted, of a gol d-

pl ated. al umi num- f oi l shi el d. , wi t h 40% of t he area, pai nt ed, bl ack.Ar ea 3 was gol d, pl ated, and unpai nt ed. Ar ea 4 was sprayed, wi t h

al umi num pai nt . I nt ernal const r uct i on was so desi gned, t hat t he 3 wa

of i nt er nal l y gener at ed heat was conduct ed, pr i nci pal l y to Ar ea 4 f or

r adi at i on out i nt o space.

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Jet P ropu ls ion Labo ra t o r y Ext er nal Publ i cat i on Mo. 6

The obser ved payl oad t emper at ur e dur i ng t he f l i ght of PI ONEER I

i s shown i n Fi g. 28. The t emper at ur e r ose st eadi l y dur i ng t he f i r st

sever al hour s of f l i ght as t he payl oad moved out f r om t he shadow of

t he ear t h and r eached a st eady st ate val ue of approxi mat el y 37C.

Based on t r aj ect or y and si gnal - st r engt h i nf or mat i on, i t i s est i mat ed

t hat t he angl e 77 gi vi ng t he at t i t ude bet ween t he payl oad axi s and t h

sun was appr oxi mat el y 91 deg. Thi s angl e was consi der abl y gr eat er

t han had been expect ed. As a r esul t , t he nose cone was somewhat

cool er t han expect ed and the r emai ni ng ar ea somewhat war mer t han

expect ed.

As a r esul t of t he sur f ace t emper at ur e di f f erences bet ween

var i ous sect i ons of t he payl oad, a heat f l ux occur r ed bet ween t he

payl oad i nst r ument sect i on and t he nose- cone shel l . Usi ng a

r easonabl e assumpt i on f or t he r adi at i ve t r ansf er bet ween t he f or war d

sect i on of t he i nst r ument port i on and t he i nt er i or of t he nose shel l

t he obser ved t emper at ur e appear s t o be al most exact l y t hat expect ed

on t he basi s of t he sur f ace char act er i st i cs.

The expect ed at t i t ude angl es f or t he t r aj ect or i es of PI ONEER I V

wer e di f f er ent f r om t hose of PI ONEER I I I . As a r esul t , f or the

act ual f l i ght day, t he gol d- cover ed, nose shel l was pai nt ed 4 4 % bl ack,

t he gol d- pl at ed- al umi num shi el d of Area. 1 was pai nt ed 43/o whi t e, and

Ar eas 2 and 3 wer e t he same as i n t he case of PI ONEER I I I .

The expect ed i ncl i nat i on angl e was 103. 5 deg and t r aj ect or y and

si gnal - st r engt h measur ement s i ndi cat ed t hat t hi s angl e was obt ai ned

i n f l i ght . The measur ed t emper at ur e f or PI ONEER I V i s shown i n

Fi g. 29.

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Jet Propu ls ion Labo ra t o r y Ext er nal Publ i cat i on No. 6

The measur ement s i ndi cat e an equi l i br i um t emper at ur e of 42C.

Cal cul at i on of t he expect ed equi l i br i um t emper at ur e f or t he at t i t ude

angl e of 103. 50 r esul t i n an expect ed t emper at ure of appr oxi mat el y

35C, whi ch i s 7C l ower t han measured.

Thi s 7C di scr epancy bet ween cal cul at ed and obser ved t emper at ur

i s wi t hi n t he uncer t ai nt i es expect ed. These uncer t ai nt i es ar i se f r o

many causes, but t he pr i nci pal f act or i s a l ack of compl et e i nf or ma

t i on on t he r adi at i ve pr oper t i es of sur f ace mat er i al s and pai nt s use

f or t emperat ur e cont r ol .

VI I . CONCLUSI ONS

From t he r esul t s obt ai ned i n t he f l i ght s of t he EXPLORER sat el

l i t es and t he PI ONEER I I I and I V moon pr obes, i t appear s t hat passi ve

t echni ques f or t emper at ur e cont r ol ar e possi bl e at l east f or t r a

j ect or i es whi ch do not car r y t he body so f ar away f r om t he ear t h' s

or bi t t hat t he sol ar const ant i t sel f i s changed appr eci abl y. I n

or der t o achi eve adequat e cont r ol by passi ve t echni ques, i t i s

necessar y t o have excel l ent i nf or mat i on on t he r adi at i ve pr oper t i es

of t he mat er i al s used f or surf ace pr epar at i on. I t i s al so necessar y

t o prevent any change i n t he nat ure of t he sur f ace bet ween t he t i me

i t i s pr epar ed and t he t i me t hat t he space pr obe l eaves t he at mos

pher e. Even t hen, af t er t he best i nf or mat i on has been obt ai ned on

sur f ace pr oper t i es, and af t er t he gr eat est car e has been t aken t o

ensur e t hat t hese sur f ace pr oper t i es wi l l be pr eser ved t hr oughout t he

l aunchi ng phase of t he f l i ght , di scr epanci es ar e st i l l f ound bet ween

cal cul at ed and obser ved t emperat ures.

Page 2


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Jet P ropu ls ion Labo ra t o r y Ext er nal Publ i cat i on Ho. 6

When t he t emper at ur e cont r ol l i mi t s are est abl i shed by

el ect r oni c equi pment , t he magni t ude of t he di scr epanci es so far-

obser ved i s suf f i ci ent l y smal l t hat no gr eat danger exi st s of causi n

t he f ai l ur e of a payl oad by unf or seen t emperat ur e var i at i ons. How

ever , when bi ol ogi cal sampl es are i nt r oduced i nt o t he payl oad, or

when t he f l i ght t r aj ect or y t akes t he payl oad ei t her much cl oser t o o

much f ur t her f r om t he sun, or when t he at t i t ude of t he payl oad can

nei t her be cont r ol l ed nor compensat ed f or , passi ve t emperat ur e

cont r ol t echni ques wi l l be of much l ess val ue. Cer t ai nl y, as t he

pr ogr am f or t he expl or at i on of space devel ops and t he payl oads t o

car r y out t hi s expl or at i on become i ncr easi ngl y compl ex, i t i s

essent i al t o l ook f or war d t o t he necessi t y of i nt r oduci ng acti ve

t emper at ur e- cont r ol schemes.


34/58

Jet Prop u lsion Labo ra t o r y External Publication No. 6

THERMALLYINSULATED

D IV IDER

t) =A N G L E O F O R I E N T A T IO N

r = 3 INC HE S

= 2 INC HE S

Z z= 10 INCHES=20 INCHES

THERMALLY

INSULATED BASE

- - - SOURCE OF

RADIATION

Fig. 1 . Dimensions andOrientation of Payload

r ) , deg

Fig. 2. The Ratio of Ag/Aj for the Conical

Section of the Payload

Page


35/58

Jet P ropu ls ion Labo ra t o r y External Publication No. 6

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