8/12/2019 Astronomical Wrubel

1/10

T h e E l e c t r o n i c C o m p u t e r a s a n s t r o n o m i c a l I n s t r u m e n tM A R S H A L H W R U B E L

Indian a U nivers i ty , Bloomington, Indiana , U.S.A.SUMM RYThe enormous potent ia l of the e lec t ronic computer as an ins t rument of observa t iona l and theore t ica lr e s e a r c h is emphasized. Astronomical exam ples are used to i l lustrate the co ncept of prog ramm inga n d the f lexibili ty of electronic com puters. S pecific recom men dations are ma de for the effective u s eof these devices in astronomy.

1. INTRODUCTIONT H ER E a r e v e r y f e w a s t r o n o m e r s f o r t u n a t e e n o u g h t o w o r k w i t h p a p e r a n d p e n c i la l o n e. F o r m o s t o f u s , th e r e i s a l o n g p a t h t o b e f o ll o w e d , f r o m o b s e r v a t i o n s t o c o n -c lu s io n s , o r f r o m t h e o r y t o p r e d i c t io n , b e f o r e o u r w o r k c a n b e u s e f ul t o o u r s e l v e sa n d o t h e r s . I n s o m e c a se s t h e d a t a o b t a i n e d i n o n e n i g h t o f o b s e r v a t i o n s m a y t a k ew e e k s t o a n a l y s e . T h i s p r o c e s s m a y b e so t i m e - c o n s u m i n g t h a t f r e q u e n t l y o n l y af r a c t i o n o f t h e d a t a a r e r e d u c e d b e f o r e t h e a s t r o n o m e r is d i v e r t e d b y n e w p r o b l e m s .A s a r e s u l t m u c h u s e f u l i n f o r m a t i o n g a t h e r s d u s t a n d n e v e r a p p e a r s i n t h e l i t e ra t u r e .

W h a t c a n b e m o r e d e t r i m e n t a l t o a s t r o n o m i c a l e n t h u s i a s m t h a n r o u t i n e , d u ll ,l a b o r i o u s c o m p u t a t i o n I t h a s s t r a n g l e d s o m e l a rg e p r o g r a m m e s , i t h a s d e l a y e d o t h e r sa n d i t f re q u e n t l y d r iv e s p r o m i s i n g g r a d u a t e s t u d e n t s c o m p l e t e l y a w a y f r o m a s t r o -n o m y . U n l e s s a l a rg e f o r c e o f d e s k c a l c u l a t o r o p e r a t o r s i s a v a i l a b l e ( a n d t h i s i s u n -l i k e l y w h e n a s t r o n o m e r s m u s t h i r e a s s is t a n t s in c o m p e t i t i o n w i t h i n d u s t r y ) , t h ea s t r o n o m e r m u s t do t h e w o r k h i m s e l f a n d s p e n d v a l u a b l e h o u r s a t m e n i a l t a s k s ,i n s t e a d o f i n c r e a t i v e t h o u g h t .

W i t h t h i s o b s t a c le in th e p a t h , o n e w o u l d t h i n k t h a t a s t r o n o m e r s w o u l d l e a p a t t h ep r o s p e c t o f u s i n g h i g h - s p e e d c o m p u t e r s . T h i s h a s n o t b e e n th e e a s e. ( A s t r o n o m e r sa r e i n n a t e l y a s c o n s e r v a t i v e a g r o u p o f s c i e n t i s ts a s o n e c a n f in d . ) W i t h t h e e x c e p -t i o n o f a f ew w i d e l y d i s s i m i l a r f ie ld s t h e u s e o f c o m p u t e r s h a s b e e n t i m i d a n d s p o r a d i c .

B y a n d l a rg e , th e p r i n c i p a l re a s o n h a s b e e n i n e rt ia . A s t r o n o m e r s a r e v a g u e l y a w a r eo f w h a t e l e c t ro n i c c o m p u t e r s c a n d o t o h e l p t h e m , b u t f e w h a v e t a k e n t h e t r o u b l et o i n v e s t i g a t e f u r t h e r . F o r s o m e r e a s o n , e l e c t ro n i c m a c h i n e s a r e r e g a r d e d e i t h e r a sm y s t e r i o u s o r d i f fi c u lt t o l e a r n t o u s e . I n r e a l i t y , w i t h a l i tt l e g u i d a n c e , a n y o n ef a m i l i a r w i t h d e s k c a l c u l a to r s c a n b e p r o d u c i n g u s e f u l r e s u l t s w i t h a h i g h - s p e e dm a c h i n e i n a m a t t e r o f s ix w e e k s o r l es s. W h i l e t h i s m a y a p p e a r t o b e a lo n g t i m e t od e v o t e t o l e a rn i n g a n e w t e c h n i q u e , i t i s a n i n v e s t m e n t w h i c h s a v e s f a r m o r e t i m ei n t h e e n d .

N a t u r a l l y , a s t r o n o m e r s c a n n o t b e e x p e c t e d t o c h a n g e t h e ir m e t h o d s o v e r n i g h t .I t w i ll b e t h e y o u n g a s t r o n o m e r , a c c u s t o m e d t o le a r n i n g n e w t h i n g s , w h o w i ll a c c e p te l e c t r o n i c c o m p u t a t i o n i n h i s s tr i d e . I t i s to t h e s e m e n , es p e c i a l ly , t h a t t h i s a r t ic l e isa d d r e s s e d .

107

8/12/2019 Astronomical Wrubel

2/10

108 The ele

8/12/2019 Astronomical Wrubel

3/10

MARSHAL H WRUBEL 109A s in g l e a s t e r i s k in d i c a t e s m u l t i p l i c a t i o n , a d o u b l e a s t e r i s k is e x p o n e n t a t i o n , a n dC O S F i n d i c a te s t h a t t h e c o s in e f u n c t i o n o f t h e a r g u m e n t T H E T A is d e s ir e d.

W h e n F O R T R A N is u s ed , th e e n t i r e p r o g r a m m e i s w r i t t e n in F O R T R A N l an -g u a g e a n d f e d i n t o t h e m a c h i n e . T h e c o m p u t e r i t se l f t h e n d e c id e s h o w t o e x p r e s st h e F O R T R A N p r o g r a m m e i n i ts o w n b as ic c o d e a n d p r o d u c e s a d e c k o f c a r d sw h i c h c a n b e u s e d in t h e f u t u r e t o r u n t h e p r o b l e m w i t h a p p r o p r i a t e d a t a .

I n t e r p r e t i v e s y s t e m s a r e a ls o w i d e l y u s e d. H e r e w e s u b s t i t u t e a s i m p l er a n dm o r e v e r s a t il e l a n g u a g e f o r t h e o n e b u i l t in t o t h e m a c h i n e , a n d h a v e t h e m a c h i n et r a n s l a t e e a c h i n s t r u c t io n i m m e d i a t e l y b e f o r e e x e c u t i n g it . A t y p i c a l i n t e r p r e t i v e

c o d e is t h e o n e d e v e l o p e d a t B e l l T e l e p h o n e L a b o r a t o r i e s f o r t h e I B M T y p e 6 50 .1T h e e x a m p l e , g i v e n a b o v e , n o w is e x p r e s s e d b y t h e f o l lo w i n g s e ri es o f i n s t r u c t i o n s :

3 2 I 2 I 6 0 13 2 0 2 2 0 2 6 0 20 3 0 4 2 0 3 6 0 33 603 201 6O43 6 0 4 2 0 2 6 0 51 6 0 1 6 0 2 6 0 62 6 0 6 6 0 3 6 0 7

T h i s a p p e a r s t o h a v e l i t t l e r e l a t i o n t o t h e f o r m u l a i t is i n t e n d e d t o r e p r e s e n t , b u t w ew i ll s o o n s ee t h a t i t i s e n t i r e l y l o g ic a l. ( A l t h o u g h n o t p r o g r a m m e d a s e f fi c ie n t ly a sp o s s i b l e , t h i s w i l l s e r v e a s a s u i t a b l e e x a m p l e . )

E a c h l in e r e p r e s e n t s o n e i n s t r u c t i o n a n d e a c h i n s t r u c t i o n c o n s is t s o f l 0 d i g i ts :f i r s t o n e d ig i t, t h e n t h r e e g r o u p s o f t h r e e . T o u n d e r s t a n d t h i s p r o g r a m m e i t isn e c e s s a ry t o k n o w a li t t le a b o u t t h e m e m o r y u n i t u s e d b y t h i s s y s t e m . I t c o n s is ts o fo n e t h o u s a n d l o c a t io n s , w i t h a d d r e s s e s 0 0 0 t o 9 9 9 . I n e a c h l o c a t i o n o n e 1 0 - d ig i tw o r d c a n b e s t o r e d .

I n f o r m a t i o n c a n b e s e n t to o r f r o m a n y l o c a t i o n b y s p e c i f y in g it s a d d re s s a t a na p p r o p r i a t e p l a c e in a n i n s t r u c t i o n . W h e n n e w i n f o r m a t i o n i s s e n t t o a p a r t i c u l a rl o c a t i o n t h e o l d i n f o r m a t i o n i s a u t o m a t i c a l l y e r a s e d ; b u t i n f o r m a t i o n c a n b e c a ll edf o r f r o m a n y l o c a t i o n w i t h o u t a f f ec t in g th e i n f o r m a t i o n s t o r e d t h e r e . T h a t i s, w h e nw e s e n d i n f o r m a t i o n t o l o c a t i o n 6 0 1 , t h e n u m b e r p r e v i o u s l y i n 6 01 is l o s t ; b u t w h e nw e c a ll f o r i n f o r m a t i o n f r o m 6 0 1, t h e n u m b e r i n 6 01 r e m a i n s t h e r e . P r i o r t o e x e c u t i n gt h e i n s t r u c t i o n s g i v e n a b o v e , w e w i ll a s s u m e t h a t a , b , a n d ~ h a v e b e e n s t o r e d i nl o c a t i o n s 2 0 1 , 2 0 2 a n d 2 0 3 r e s p e c t i v e l y .

T h e f i r s t i n s t r u c t i o n r e a d s3 2 0 1 2 0 1 6 0 1

T h e f i rs t d i g i t , 3 , i n d i c a t e s t h a t a m u l t i p l i c a t i o n i s t o b e p e r f o r m e d . T h e m u l t i p l i e ri s i n 2 0 1 , t h e m u l t i p l i c a n d i s a l so i n 2 0 I , a n d t h e p r o d u c t i s t o b e s t o r e d i n 6 0 1 .T h e i n s t r u c t i o n , t h e r e f o r e , c o m p u t e s a 2 a n d s t o r e s t h e r e s u l t i n 6 0 1 .

I n a s i m i la r w a y , t h e s e c o n d i n s t r u c t i o n c o m p u t e s b 2.T h e i n t e r p r e t a t i o n o f t h e t h i r d i n s t r u c t i o n i s s o m e w h a t d i f f e re n t . S i n c e t h e f i r st

d i g i t is z e ro , i t i n d i c a t e s t h a t t h e f i rs t g r o u p o f t h r e e d i g i ts i s n o t a n a d d r e s s , t h ew a y i t w a s i n t h e p r e v i o u s i n str uc tio r_ .% b u t i n s t e a d is a n i n s t r u c t i o n c o d e . I n t h i sc a se , 3 0 4 i n d i c a t e s t h a t t h e c o s in e o f t h e n u m b e r i n l o c a t i o n 2 0 3 is t o b e t a k e n a n d

1 IBM Technical New sletter No. 11.

8/12/2019 Astronomical Wrubel

4/10

1 1 T h e e l e c t r o n i c c o m p u t e r a s a n a s t r o n o m i c a l i n s t r u I n e n tstored in 603. This is multiplied by a in the next instruction and stored in 604; andby b in the next and stored in 605.

Finally, once we know th at the code 1 is addition, and 2 is subtraction, thelast instructions should be easily understood. The final result can be found in loca-tion 607.

By way of contrast, consider the programme for the same calculation using asystem called SOAP on the IBM Type 650:

BEGIN RAU AMPY ASTU ASQRAU BMPY BSTU BSQRAU THETALDDMPY ARAU 8003MPY BSTU TEMPRAU ASQAUP BSQSUP TEMPSTU Y

COS

ENDNote how much more has to be written in comparison with either FORTRAN orthe Bell interpretive system. This is a very flexible programming procedure, but itis also somewhat complicated.

Without going into much detail, a few things can be pointed out. Every instruc-tion begins with a thr ee-le tter mnemonic code. Memory locations are also givensymbolic codes. The first three i nstruction s calculate and store a 2. RAU meansReset Ad d Uppe r acc umula tor ( part of the a rithme tic unit). The effect is to clearthe arithmetic unit and set up the multiplier, a. The second instruction carries outmultiplication by a; the third instruction, STU, means STore Upper accummulator,and it stores the produc t in the symbolic location ASQ. To explain the rest of thisprogr amme is beyo nd the scope of this article.

Brief thoug h our description has been, it should at least indicate th at using atechniq ue such as FO RTR AN , or the Bell Laboratori es inter preti ve code, is notbeyond the capabilities of any astronomer.

3. THE ROUTINE USE OF COMPUTERSSuppose we have become reasonably proficient programmers; what then? To

what sort o f problems could this techniqu e be applied? To begin with one couldautomatize all the standard computations that are being done at an observatory:radial velocities, photoelectric reductions, least squares solutions, plate reductions,radio telescope reductions, statistical analyses, etc.

The process begins by making a broad outline of the co mputa tion in the form of aflow diagram . The entire computati on is divided into boxes ; each box repre-sents a separate phase of the problem, frequently complete within itself. The boxes

8/12/2019 Astronomical Wrubel

5/10

MARSHAL H. WRUBEL 111a r e l in k e d b y f l ow l in e s w h i c h i n d i c a t e t h e p a t h t h e c o m p u t a t i o n s h o u l d f o ll o w . T h em a c h i n e c a n b e i n s t r u c t e d t o c h o o s e b e t w e e n a l t e r n a t e p a t h s ; f o r e x a m p l e , d i ff e r e n tp r o c e d u r e s m a y b e n e e d e d d e p e n d i n g u p o n t h e s ig n o f a re s u l t, o r p e r h a p s a p a r -t i c u l a r f u n c t i o n i s b e s t r e p r e s e n t e d b y o n e e x p a n s i o n f o r l a r g e v a l u e s o f t h e a r g u m e n ta n d a n o t h e r f o r s m a ll v a lu e s . T h e c o m p u t e r c a n b e p r o g r a m m e d t o m a k e d e c is io n so f th i s k i n d .

T h e p r o b l e m i s u s u a l l y p r o g r a m m e d o n e b o x a t a t im e . E a c h l a rg e b o x m a y b ef u r t h e r s u b d i v i d e d i n t o s m a l le r b o x e s , d e p e n d i n g u p o n i t s c o m p l e x i t y . B y u s i n g af lo w d i a g r a m , t h e p r o g r a m m i n g c a n b e d o n e i n a n o r d e r l y w a y a n d t h e i n t e r r e la t i o no f a l l t h e p a r t s i s c l e a r l y v is i b le . I n e x p l a i n i n g a p r o b l e m t o s o m e o n e e l se , e i t h e r a na s t r o n o m e r o r a c o m p u t e r e x p e r t , i t is m u c h e a s ie r t o t a l k i n t e r m s o f t h e f l o wd i a g r a m t h a n i n t e r m s o f t h e p r o g r a m m e . T h e p r o g r a m m e is c lu t t e r e d w i th d e t a il so f l it tl e i n te r e s t t o a n y o n e b u t t h e p r o g r a m m e r , b u t a p r o p e r l y p r e p a r e d f lo w d i a -g r a m g i v e s th e e s s e n c e o f t h e c a l c u la t io n .

Fro. 1. Definitions for line profile computatio n.

C o n s i d e r th e f o ll o w in g e x a m p l e f r o m t h e t h e o r y o f a b s o r p t i o n l in e s. S u p p o s e w ew a n t t o f i n d t h e p r o f i le s o f li n e s f o r m e d b y s c a t t e r i n g a c c o r d i n g t o t h e S CH U ST ER -SCHW RZSCHILDm o d e l. T h e p a r a m e t e r s o f t h e p r o b l e m a r e:1 ) t h e a b u n d a n c e f a c t o r , r 0 ;2 ) t h e l i m b d a r k e n i n g , I O ) / I 1 ) ; a n d

3 ) t h e d a m p i n g , a .T h e l in e p r of il e is b u i l t u p p o i n t b y p o i n t u s i n g t h e v a r i a b le , v , t o m e a s u r e t h e d i s t a n c ef r o m t h e c e n t r e o f th e l in e . T h e o b j e c t o f t h e c a l c u l a ti o n i s t o c o m p u t e R v ) , t h er e s i d u a l i n t e n s i t y a t t h e p o i n t , v , i n u n i t s o f t h e c o n t i n u u m F i g . 1) .

C H A N D R A S E K H A R h as g i v en t h e so l u t i o n fo r R v ) , a n d i s h a s b e e n w r i t t e n f o rp u r p o s e s o f c o m p u t a t io n 3 a s

.~ + K yR - : ~ + T l + 2 y

w h e r e y i s t a b u l a t e d a s a f u n c t i o n o f e -~ 1, a n d4K = 3 I O ) / I 1 ) + 2

d e p e n d s o n l y o n t h e l i m b d a r k e n i n g .C~A~DRASEKH.~ S. an d ELBERT DONNA in A p . J . 115 26-9 1952.

a WRUBEL M. H. in A p . J . 119 51 1954.

8/12/2019 Astronomical Wrubel

6/10

1 1 2 T h e e l e c t r o n ic c o m p u t e r a s a n a s t r o n o m i c a l i n s t r u m e n tT h e q u a n t i t y ~1 d e p e n d s u p o n a , v, a n d 0, a n d c a n b e fo u n d f r o m t h e t h e o r y o f

t h e a b s o r p t i o n c o e ff ic i en t . I t i s g i v e n b y t h e r e l a t i o n~ ] ( a , v ) = ~ 0 H ( a , v ) .

H A R R I S4 h a s t a b u l a t e d t h e f u n c t i o n s H ~ ( v ) , n e c e s s a r y to e v a l u a t e4

H ( a , v ) = ~ _~ a i H l ( v ) .i = o

W e h a v e g i v e n a b o v e e v e r y t h i n g n e c e s s a r y to c o m p u t e p r of ile s , b u t w e h a v e n o tp u t t h in g s i n a l og i ca l o r d e r f o r c o m p u t a t i o n . O b v i o u s l y y m u s t b e k n o w n b e f o r e w ec a n f in d R , a n d r l m u s t b e k n o w n b e f o r e w e c a n f i n d y .

T h e f lo w d i a g r a m o f F i g . 2 i n d i c a t e s t h e o r d e r i n w h i c h t h e c a l c u l a t i o n s m u s t b ec a r r i e d o u t to c o m p u t e a l in e p r o fi le a u t o m a t i c a l l y . T h e t e r m R e a d m e a n s t h a t

1.

1 23 .

7 ~ 45.

1 61 7[ 81 9

R e a d a ]

R e a d I ( ' ) ] I ( 1 ) ]

R e a d ]

R e a d v , H i ( v ) ( i = 0 . . . . . 4 )

C o m p u t e 7 1 : To ~ a i H i ( v )I z

C o m p u t e e - r l I

I n t e r p o l a t e i n t a b l e t o fi n d y IlC o m l ) u t e R ( ~ ) ]P u n c h a , I ( ) / I( 1 ) , t o , v , R ( v ) ]

F i o . 2 . F l o w d i a g r a m f o r S CH U ST ER -S cH 'v VA R ZS CH IL D m o d e l l i n e p r o f i l e s .a c a r d e n t e r s th e i n p u t , a n d t h e i n f o r m a t i o n p u n c h e d o n t h e c a r d i s s t o r e d in t h em e m o r y u n i t . ( I n b o x 4 t h e v a l u e s o f v a n d H 0 to H 4 a r e al l o n o n e c a r d .) P u n c hm e a n s t h e re s ul ts , a n d s o m e i d e n t i fy i n g i n f o r m a t i o n a r e p u n c h e d o n a c a r d b y t h eo u t p u t u n i t .

A f t e r t h e r e s u l t h a s b e e n c a l c u l a t ed a n d p u n c h e d f o r on e v a l u e o f v , t h e m a c h i n ea u t o m a t i c a l l y r e a d s t h e n e x t v a l u e . T h i s p r o c e s s c o n t i n u e s u n t i l t h e l a st v a l u e o f vis r e a d . I t i s t h e n p o s s i b l e to r e a d n e w v a l u e s o f a , I ( O ) / I ( 1 ) , o r ~ 0, i f d e s i r e d .

A s a n o t h e r e x a m p l e , c o n s id e r t h e r e d u c t i o n o f p h o t o e l e c t r ic o b s e r v a t i o n s . O n ep r o c e d u r e h a s b e e n p r o g r a m m e d f o r t h e I B M 6 5 0 b y E DW A RD C . O L SO N f o r t h eN a t i o n a l A s t r o n o m i c a l O b s e r v a t o r y , f o l l o w i n g a m e t h o d d u e t o H A RO LD L . JO HN SO N.

I n o r d e r t o r e d u c e o b s e r v a t i o n s t o t h e U , B , V , s y s t e m , i t is n e c e s s a r y t o o b t a i n4 H A R R IS , D . L . , I I I ; i n A p . J . , 108 , 112 , 1948 .

8/12/2019 Astronomical Wrubel

7/10

M A R S H AL H . W R U B E L 1 1 3the extinction of the atmosphere and the transfor mation of the instr umental coloursystem to the standard system.

For example, assume that the B-V colour is related to the instrumental yellowcolour outside the atmosphere, Cy by the linear transformation:

B - V = A1T A2Cy.Cy is foun d from the raw colour, Cyo by using a n e xtinct ion coefficient to remove theeffect of the atmosphere:

Cy0 - /c l sec zC y = 1 + 0.032 sec zIn turn , the raw colour is found from th e yellow and blue deflections, y1 and B 1,together with the amplifier-gain step-calibrations, Sr and SB :

Cyo = 2.5 log (Y1/B1) : SB -- S t.If four or more standard stars of known B-V are observed, the values of A1, Au andkl, can be found by least squares. This will involve setting up three linear normalequations which are solved simultaneously by stand ard procedures. The flow dia-gram is given in Fig. 3.

1 . R e a d C o o r d i n a t es a n d c o lo r s o f s t a n d a r d s t a r s 11 2 . R e a d A m p l i fi e r g a i n s t e p c a l i b r a t i o n s I

3 . R e a d : H o u r a n g l e a n d d e f le c ti o n s f o r s t a n d a r d s t a r s o b s e r v e d I1 4 . C o m p u t e s e e z I1 5 . C o m p u t e r a w y e l lo w c o l o r ]I 6 . C o m p u t e c o e f f ic i e n ts o f l i n e a r s y s t e m I] 7 . C o m p u t e s o l u t i o n o f l i n e a r s y s t e m ]I 8 . P u n c h A 1 A ~ a n d k l ]

F ic . 3 . F l o w d i a g r a m f o r o b t a i n i n g B - V t r a n s f o r m a t i o n a n d e x t i n c t i o n f a c t o r s .

A similar procedure is used to obtain the constants needed to go from ultra andyellow deflections to U-B and V. The individual formulae are somewhat different,but eventua lly the problem reduces to the solution of a system of simultaneouslinear equations. This suggests th at we can use the same program me for solving eachlinear system. Bo x 7 can therefore be removed fro m the general flow of the problemand trea ted separately, as a subro utine . Whenever we need to solve a linearsystem, we execute the subroutine. When the solution is found, the normal flow ofthe computation is resumed.

A flow diagram for computing the three groups of transformation coefficients isgiven in Fig. 4.

8/12/2019 Astronomical Wrubel

8/10

1 1 4 T h e e l e c tr o n ic c o m p u t e r a s a n a s t r o n o m i c a l i n s t r u m e n tT h e m a i n f lo w i s i n t er r u p t e d t h r ee t im e s t o e x e c u t e t h e s a m e s u b r o u t i n e e a c h

t i m e o f c o u r s e w i t h d i ff e r en t d a t a .I d o n o t m e a n t o m i n i m i z e t h e s t e p s t h a t l i e b e t w e e n t h e f l o w d i a g r a m a n d t h e

f i n a l p r o g r a m m e b u t t h e f lo w d i a g r a m i s h a l f t h e b a t t l e . W i t h t h e a i d o f a f l o wd i a g r a m t h e a s t r o n o m e r s h o u l d b e a b le t o d es c ri b e h is c o m p u t a t i o n t o t h e p r o -g r a m m e r . I f t h e a s t r o n o m e r k n o w s p r o g r a m m i n g a s w e ll t h e b a t t l e i s w o n .

1 . R e a d d a t a ( a s a b o v e ) ]2 , C o m p u t e3 . C o m p u t e4 . C o m p u t e

s e e z Ir a w y e l l o w c o l o r ]c o e f f i c ie n t s o f l i n e a r s y s t e m [

[ e n t e r s u b r o u t i n e t[ l e a v e s u b r o u t i n e ]

t r a n s f o r m a t i o n c o e f fi c ie n t s f o r B - V ]. P u n c h6 . C o m p u t e7 . C o m p u t e c o e f f i c ie n t s o f l i n e a r s y s t e m ]

] e n t e r s u b r o u t i n e II l e a v e s u b r o u t i n e ]

8 . l ) u n c h t r a n s f o r l n a t i o n c o e f fi c ie n t s f o r U - B ~[ 9 . C o m p u t e r a w y e l l o w m a g n i t u d e ]

1 0 . C o m p u t e

r a w u l t r a c o l o r ]

i l . P u n c h

c o e f f i c ie n t s o f l i n e a r s y s t e m ]I e n t e r s u b r o u t i n e ]I le a v e s u b r o u t i n e I

t rans f ormat ion coe f f i c i en t s f or V [~IG, 4 .

4 . T H E ] M A G I N A T IV E U S E O F C O M P U T E R SI f e le c tr o n ic c o m p u t e r s d i d n o t h i n g b u t t h e r o u t i n e re d u c t i o n s a s s o c ia t e d w i t h a n

o b s e r v a t o r y t h e y w o u l d b e v e r y u s e fu l . B u t t h e ir p o t e n t i a l is f a r g r e at e r t h a n t h a t .A s o n e b e c o m e s m o r e f a m i li a r w i t h c o m p u t e r s t h e y i l l u m i n a t e n e w w a y s o f a p p r o a c h -i n g o l d p r o b l e m s ; a n d w h i c h i s c e r ta i n ly m o r e i m p o r t a n t t h e y b r i n g o b s e r v a t i o n a l

8/12/2019 Astronomical Wrubel

9/10

M A R S H A L H . W R U B E L 1 1 5a n d t h e o r e t i c a l p r o b l e m s t h a t w e r e a t o n e t i m e b e y o n d o u r r e a c h i n t o t h e r e a l m o fp o s s i b il i ty . F o r e x a m p l e , s e q u e n c e s o f s t e ll a r m o d e l s d e s c r i b in g t r a c k s o f e v o l u t i o ni n t h e H - R d i a g r a m r e q u i r e s u c h an e n o r m o u s a m o u n t o f c o m p u t a t i o n th a t h ig h-s p e e d m a c h i n e s a r e a b s o l u t e l y n e c e s s a r y to c a l c u l a t e t h e m i n a r e a s o n a b l e t i m e .

T o s h o w h o w a s i m p l e p r o b l e m c a n g r o w i n g e n e r a l i t y w h e n a n e l e c t r o n i c co m -p u t e r i s a v a i la b l e , c o n s i d e r t h e f l o w d i a g r a m o f F i g . 2 a g a in . T h i s w a s a s c h e m e f o rc a l c u l a ti n g l in e p r o fi le s a c c o r d i n g t o t h e S c h u s t e r - S e h w a r z s c h i l d m o d e l . I f w ee x a m i n e i t c l o s e ly , h o w e v e r , w e s e e t h a t i t c a n b e d e s c r i b e d i n m o r e g e n e r a l t e r m s(Fig. 5) .

R e a d p a r a m e t e rsB o x e s l , 2 a n d 3 ) ]

U se theorY BoxesOfb s o r p t i o n 4n d 5 ) c e f f i c i e n t ]/

U s e so l u t io n o f t r a n s f e r e q u a t i o n /B o x e s 6 , 7 a n d 8 ) _ _ _

P u n c h r e s u l t s(Box 9)F I G . 5 .

I n o u r o r i g in a l a p p l i c a t i o n w e u s e d t h e r e s u l t s o f t h e s o l u t i o n o f t h e t r a n s f e rpr ob le m fo r the SCHUSTER-SCHWARZSCHILDm o d e l i n b o x e s 6 , 7 a n d 8 . W e c o u l d e a s i l ys u b s t i t u t e t h e s o l u t io n f o r t h e M IL NE -E DD IN G TO N m o d e l , k e e p i n g t h e p r o g r a m m e f o rb o x e s 1 t o 5 a n d b o x 9 i n t a c t ; o r w e c o u ld s u b s t i t u t e a n y o t h e r a s s u m e d r e l a ti o nb e t w e e n t h e r e s i d u a l in t e n s i ty a n d t h e p a r a m e t e r s .

W e c o u l d f u r t h e r c h a n g e b o x e s 4 a n d 5 i f s o m e o t h e r t h e o r y o f t h e a b s o r p t io nc o e f fi c ie n t w e r e p r e f e r a b l e - - s a y , i n c o n si d e ri n g t h e S t a r k b r o a d e n i n g o f h y d r o g e nl in e s . I n t h i s w a y w e m a y r i n g t h e c h a n g e s o n a n e x i s t in g p r o g r a m m e , p r e s e r v i n go r r e p l a c i n g s e c t i o n s a s t h e s i t u a t i o n d e m a n d s .

A c t u a l l y , e l e c t r o n i c c o m p u t e r s m a k e i t f e a s i b l e t o g o b e y o n d i d e a l i z e d m o d e l s i nw h i c h t h e p a r a m e t e r s a r e c o n s t a n t w i t h d e p t h , t o c o m p u t e l in e p r o fi le s f o r m o d e la t m o s p h e r e s i n w h i c h i o n iz a t io n , d a m p i n g , e t c . , v a r y w i t h d e p t h . A l t h o u g h t h is i sp o s s i b le w i t h d e s k c a l c u l a to r s a s w e l l b y u s i n g w e i g h t f u n c t i o n s o r s i m il a r t e c h n i q u e s ,t h e e a s e w i t h w h i c h th e s e c o m p u t a t i o n s c a n b e c a r ri e d o u t o n a n e l e c tr o n ic m a c h i n em a k e s i t r e a s o n a b l e t o e x p l o r e a m u c h w i d e r r a n g e o f p o s s ib i li ti e s. F o r e x a m p l e , i tw o u l d b e p o s s ib l e to p e r f o r m n u m e r i c a l e x p e r i m e n t s o n t h e e f f e c t o f b l e n d i n g o rb l a n k e t i n g .T h i s f l e x ib i li ty o f p r o g r a m m e s i s n o t r e s t r i c t e d t o t h e o r e t i c a l p r o b l e m s . I n t h ee x a m p l e w e d i s c u s s e d c o n c e r n in g t h e r e d u c t i o n o f o b s e r v a t i o n s o f s t a n d a r d s t a r s too b t a i n e x t i n c t i o n a n d c o l o u r s y s t e m t r a n s f o r m a t i o n s , w e a s s u m e d a l in e a r r e la t i o nb e t w e e n t h e i n s t r u m e n t a l a n d B - V c o lo u rs . T h is a s s u m e s th e s y s t e m s a r e n o t v e r yd i f f e re n t ; b u t i f t h e y w e r e , t h e m a c h i n e c o u l d b e p r o g r a m m e d t o i n c lu d e n o n - l in e a rt e r m s a s w e l l .A s t r o n o m e r s h a v e s c a r c e l y b e g u n t o e x p l o r e t h e p o s s i b il it ie s o f e x i s ti n g c o m p u t i n ge q u i p m e n t , b u t w e m i g h t m e n t i o n s o m e o f t h e a d v a n c e s t h a t p r o b a b l y li e a h e a d .

8/12/2019 Astronomical Wrubel

10/10

1 16 T h e e l e ct r o ni c c o m p u t e r a s a n a s t r o n o m i c a l i n s t r u m e n tOne particularly promising application of computer techniques is in selecting, froma large memory, information which fits particular requirements. If a suitable deviceis perfected to transcribe a printed page directly to magnetic tape, it would becomepractical to record volumes of inform ation, such as the He nry Draper Catalogue, in aform machines can easily use. This could simplify the planning of observing pro-grammes, because it would the n be possible to ask the machine to find the co-ordin-ates of all A stars brighter t ha n 10th magn itud e tha t can be observed from McDonaldObservatory in March .Going one step further, it may one day be possible to search the literature bymachine to find all references to a particular object. And, of course, there is thepossibility of translation by machine, an E1 Dorado so many are seeking, and whichwill be of profit to the astronomer as well as every other scientist when found.

5 C O N C L U S I O N S A N D R E C O M M E N D A T I O N SFew observatories have enough routine reductions to keep a high-speed machine

busy, even for an 8-hour day. Therefore, if the y do not have a theoretical depar tmentinterested in machine computations they cannot justify the rental or purchase of alarge calculator. Observatories connected with universities may be fortunate inhaving a computer facility accessible on the campus which they can share withother departments. In other cases, nearby industrial installations may be generousin offering comput ing time in th e wee hours of the morning. (This should not d isturban astronomer.)

The success of the connection between an observatory and an electronic com-puter will largely depend upon the accessibility of the machine. It must be nearenough so that it can be used without spending a disproportionate amount of timegetting to it. It ought to be a machine for which a large programme library of stand-ard m etho ds is alre ady available. (This is the case for most of the widely distribute dmachines and also for a few one of a kin d machines at active research installations.)The observatory should hire a part-time programmer who would be responsible forco-ordinating the ob serv atory's use of the machine. He would also have t he responsi-bility of running the programmes on the machine.

Finally, at least one astronomer on the observatory staff should acquire, throughexperience, a knowledge of machine techniques. Otherwise, the connection betweenthe observatory and the computer will be too remote to be effective.

The electronic computer is an important research tool. Now it is up to the astrono-mer to use it.