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a s s e m b le d in to o n e p ro g ra m . B y B ra d le y E . S c h a e fe r

'I 'A R L I G H T , S T A R A R I G H I , I I R S T

s ta r I se e to n ig h t. M a n y o f u sh a ve w ish e d u p o n th e firs t s ta rsp o tte d in th e e ve n in g tw ilig h t. I

ha ve o fte n trie d to use m y know le dge a s a na stronom e r to ga ir- r a n a dva nta ge a t know -ing w he re a nd w he n to se e the first s ta r.

L o n g - t im e re a d e rs o f th is d e p a rtm e n tw ill k n o w m y p ro g ra m s fo r p re d ic t in gth e v is ib ility o f s ta rs u n d e r m a n y c o n d i-t io n s . C e n tra l to a ll th e s e a p p lic a tio n s isd e te rm in in g th e e x tin c tio n o f l ig h t ( in -te n s ity re d u c tio n ) b y th e a tm o s p h e rea n d th e s k y b r ig h tn e s s u n d e r a w id era n g e o f c o n d it io n s . I n p a rt ic u la r , th egre a te st unce rta in ty in m ost o f m y re -su lts a rise s from the a ccura cy to w h ichthe ha z ine ss o f the a ir ca n be e stim a te d .C onse que ntly , I ha ve spe nt m uch re -s e a rc h t im e d e r iv in g e q u a tio n s th a t c a npre d ict e xtinction for a nyw he re in thew orld a nd sky brightne sse s for a ny illu -m in a tio n c o n d it io n s . T h e re s u lt is a u s -a b le se t o f e qua tions tha t cove rs m oon-ligh t, tw iligh t, a nd da yligh t fo r the firsttim e . R e ce ntly , I ha ve e xte nde d the sefrom the v isua l ba nd to the e n tire optica lra nge .

E xtinction a nd sky brightne ss a re both$ ro n g ly re la te d w ith m a n y e n v iro n -m e nta l cond itions, m a king re a sona b lee stim a te s fe a sib le . M ost o [ the se re la -tions a re from know n physica l la w s,w hile som e a re m e re ly e m pirica l.T a king the m toge the r, I ca n tra ns-la te in form a tion a bout a s ite 's la ti-tude , a ltitude , te m pe ra ture , re la tivehum id ity , a nd the tim e o f ye a r in toa cce pta b le pre d ictions o f the a tm os-phe ric ha z ine ss for a ny optica l filte r.W ith the se e xtinction va lue s, the sta geof so la r a ctiv ity , the pha se o f the M oon,the M oon 's a ltitude a nd d ista nce fromthe d ire ction o f in te re st, the a ltitude a nda ngula r d ista nce to the S un , a nd the a lti-tude tha t the te le scope is po in ting , I ca n

ca lcu la te the sky brightne ss unde r a nycle a r cond itions for a ny optica l filte r.

T h e P ro g ra mA s p u b lis h e d h e rc , th e p ro g ra m in c o rp o -ra te s Q pica l va lue s for the ca se of a da rkn ight sky in southe rn A riz ona . F or pa ra m -e te rs tha t you w ill fre que ntly va ry, line sca n e a sily be cha nge d from dire ct va lue s toIN P U T sta te m e nts (such a s line 2 2 0 ) .

M y m ode l for e xtinction a nd sky bright-

a s tro n o m ica l co m p u tin g I

ne ss is im ple m e nte d a s tw o subroutine s.T h e s e c h u n k s o f c o m p u te r in s tru c tio n sc a n b e in c lu d e d in e a r l ie r p ro g ra m s -fo r te le s c o p ic lim it in g m a g n itu d e s ( S & T :N o v e m b e r 1 9 8 9 , p a g e 5 2 2 ) , h e lia c a l r is -in g ( S & ? i S e p te m b e r 1 9 8 5 , p a g e 2 6 1 ) ,lu n a r o c c u lta t io n s ( S & T . fa n u a ry 1 9 9 3 ,p a g e 8 9 ) , a n d e x tin c tio n a n g le s ( S & IA pril 1 9 8 7 , pa ge 4 2 6 ) - to y ie ld m orea ccura te re su lts .

T h e m a in p ro g ra m c o n s is ts o f p a ra m -e te r in p u t, c a lls to th e tw o s u b ro u tin e s ,a n d o n e c a lc u la t io n fo r th e v is u a l l im it-in g m a g n itu d e . T h e b a s ic e q u a tio n fo rth is c a lc u la t io n ( lin e s 3 1 0 a n d 3 2 0 ) is th e

S k y & T e le s c o p e M a y 1 9 9 8 5 7

I

L e t m e p re se n t o n e co m p le te ly w o rke de x a m p le to d e m o n s tra te th e ty p ic a l v a l-u e s irs w e ll a s to h e lp yo u d cb u g typ in gcrro rs . T h e sa rr- rp le ca se w ill b c fo r ir n o r-m a l o b s e rv e r f ro m th e A m e r ic a nS o u th w e s t o n a d a rk n ig h t in F e b ru -a ry 1 9 9 8 lo o k in g h a lf i^ra y u p th es k y ( 4 5 ' a w try fro m th e z e n ith ) ,w ith in p u t a s g iv e n in th c a c c o m -p a n y in g lis t in g . T h e a ir m a s s rsL 4 I tb r th e v a r io u s e x t in c t io uc o rn p o n e n ts . T h e e x t in c t io nco e ffic ie n ts in th e U , B ,V , R , a nd I w a ve ba ndsa re , re spe ctive ly , 0 .6 2 ,0 . 3 2 , 0 . 1 9 , 0 . 0 9 , a n d0 . 0 5 m a g r. r itu d e p e ra ir m a s s w ith to ta le x tin c tio n s o f 0 . U 7 ,0 . 4 6 , 0 . 2 7 , 0 . 1 3 , a n d0 .0 7 m a gnitude . A t the sew a v e b a n d s , th e s k y lu m r-n o s i ty is 3 . 1 x l0 ' ' , 4 . 0 x l0 ' ' ,

1 . 0 R E M V I S L I M fT . B A S v is u a L L im its

2 0 R E I{ by B ra dle y E . S cha e fe r

3 0 F O R I = 1 T O 5 : R E A D W A ( I ) : N E X T I

4 0 D A T A O . 3 6 5 , 0 . 4 4 , 0 . 5 5 , 0 , 7 , 0 . 9

5 0 F O R I :1 T O 5 : R E A D U O ( I ) : N E X ! I

5 0 D A T A - 1 0 . 9 3 , - 1 0 . 4 5 , - 1 1 . 0 5 , - tL . 9 0 , - 1 2 , 7 0

7 0 R D . 3 . 1 4 1 5 9 / 1 8 0 . 0

8 0 R E M Input fo! I {oon a nd S us

9 0 A lil= 1 - 8 0 , 0 ! R E !. { l ' lo o n p h a s e ( d e g . r 0 = F !{ , g o c F Q / L Q ,

1 8 0 = N M )

1 0 0 Z l:= 1 8 0 , 0 | R E I ! Z e D ith d L e ta c e o f :{o o n ( d e g , )

1 1 0 R ]il= 1 8 0 . 0 : R E U A n g u la r d is ta n c e to M o o n ( d . e g . )

1 2 0 z s = 1 8 0 . 0 ! R E !{ z e n L th d is ta c e o f S u r ( d e g r . )

1 3 0 R S = 1 8 0 . 0 : R E M A 4 g u 1 a r d is ta c e to S u n ( a le g . )

1 4 0 R E !! fnput for tbe S itse , D a te , O b8 e rye r

1 5 0 R H = 4 0 . 0 : R E U re la t iv e b m id ity ( e ")

1 5 0 T E = 1 5 . 0 : R E M A ir te r4 ) e ra tu re ( a te g . C )

L 7 0 L A = 3 0 . 0 ! R E M L a titu d e ( a le g . )

1 8 0 A t= 1 . 0 0 0 . 0 | R E lt . A lt itu d e a b o v e e e a 1 e v e 1 ( m )

1 9 0 M = 2 . 0 : R E M M o n th ( 1 = J a n r 1 2 = D e c )

2 0 0 Y = 1 9 9 8 . 0 r R g M Y e a r

2 1 0 S N = l. 0 : R E !'t S n e lL e n R a t. io ( 2 O , / 2 0 s 1 . . 0 , g o o d l 2 0 / L O = z . O t

2 2 0 I N P U T "Z a i th d is ta n c e ( d e g . ) ! "r z

2 3 0 G O S U B 1 0 0 0 : R E M F x e in c tio n

2 4 0 G O S I T B 2 0 0 0 : R E M S k y

2 5 0 R E M visua l lin iting m gnl- tude

2 6 0 B L = B ( 3 ) / 1 . 1 1 8 - L 5 : R E lt in n e o la n ib e rts

2 7 0 rF B L > L 5 o O . O T H E N G O T O 3 0 0

2 8 0 C l - = 1 0 . 0 ^- 9 , 8 : C 2 = 1 0 . 0 ^- 1 . 9

2 9 0 c o T o 3 L 0

5 8 M a y 1 9 9 8 S k y & T e le s c o p e

fo u r"rd a tio n o f a ll m y v is ib ility p ro g ra m s .( R e a d c rs a re c a u tio n e d th a t th e p ro g ra mm a y not w ork w ith a ll B A S IC in te rpre te rs ,b e c a u s e s o m e v a r ia b le s m a y e x c e e d th era n g e o f v a lid v a lu e s . )

6 . u x l0 ' ' ' , 7 . 8 x l0 ' ' , a n d 2 . 5 x 1 0 ' r inu n i ts o f c rg s p c r s q u a re c e n t im e te r p e rs e c o n d p e r m ic ro n p e r s q u a re a rc s e c o n d .T h e v is u a l s k y b r ig h tn e s s is 6 l n a n o la m -b e rts , w h ic h c o rre s p o n d s to a n u n a id e d -e y e lim it in g m a g n itu d e o f 6 . 2 9 .

I t is v ita l tha t a ny such rnodc. l be e x-ha ustive ly te ste d

a g a in s t re a li-ty . T o th is

e n d , I

c o lle c te d n u m e ro u s a n d v a r ie d d a ta b a s e sfronr scie n tific pa pe rs a nd the n com pa re dthe m w ith m y m ode l p re d ictions. I a n . rg la d to find tha t the m ode l fa ith fu lly re -p ro d u c e s th e e x tir . rc t io n c o e ff ic ie n ts a n ds k y b r ig h tn c s s e s o v e r a n e x tre m e ly w id era nge o f cond itions w ith a typ ica l a ccura cyof 2 0 pe rce nt. 'Ihe d iffe re ntia l a ccura cy o fth is p ro g ra m is s u b s ta n tia lly b e tte r , l ik e lyon ly a fe w pe rce nt. T h is is re m a rka b le fo rsuch "s im ple " e clua tions w ith no a d justa b lep . rra m e te rs . N e ve rthe le ss, spe cia l cond i-t io n s ( s u c h a s lo c a l a ir a rrd lig h t p o llu t io n )m a y s ign ifica ntly a lte r the sky a s com pa re dto th e p ro g ra m . A n a rt ic le d e ta ilin g th e s ete sts ( a nd the m ode l itse lf) ha s be e n sub-

m itte d to the P ub lica tions o f the A stro -nom ica l S ocie ty o f the P a cific .

A s F a r a s a n E y e C a n S e eH o w fa r c a n y o u s e e o n a c le a r d a y ?T h e u s u a l a n s w e r is th e 1 5 0 m illio nk ilo m e te rs to th e S u n . B u t s p c c if ic

a p p lic a tio n o f th is p ro g ra m s h o w s th a tV e n u s c a n b e s e e n a t d is ta n c e s s u b s ta n -t ia l ly fa r th e r th a n o u r s ta r . N o rm a l o b -s e rv e rs c a n d is c e rn V e n u s a t o n ly a b o u tl0 ' f ro m th e S u n , w h ile k e c n - e y e d p e r -

3 0 0 C 1 = 1 0 . O ^- 8 . 3 5 0 0 0 1 : C 2 = 1 0 . 0 ^- 5 . 9

3 1 0 T H = C I * ( ( 1 . o + S Q R ( C 2 tB L ) ) ^2 . 0 ) r R E M in fo o t - c a d L e 6

3 2 0 M N = - 1 5 , 5 7 - 2 . 5 * ( rO G ( T H ) / r , o c ( 1 0 ) ) -

D M ( 3 ) + 5 . 0 * ( I J O G ( S N ) / to c ( 1 0 ) )

3 3 0 P R fN T : R gM w rite re a ults a d stop progril

3 4 0 P R M I U S I N G "V iE u a l s k y b r ig h tu e a s ( n t) : # * # # # # "; a L

3 5 0 P R I N T U S I N G "V is u a l l im it ia g m g n itu d e : # # # . * # "; lru

3 6 0 E !{D

1 0 0 0 R E M E xtinction subroutine

X 0 1 0 rO R I = 1 T O 5 : R E A D O Z ( I ) 1 I itE X T I

1 0 2 0 D A T A 0 . 0 0 0 , 0 . 0 0 0 , 0 . 0 3 1 , 0 . 0 0 8 , 0 . 0 0 0

1 0 3 0 F O R l= 1 T O 5 : R A A , D V {T ( I ) | N E X T I

L 0 4 0 D A T A 0 . 0 7 4 , 0 . 0 4 5 , 0 . 0 3 1 , 0 , 0 2 0 , 0 . 0 1 5

1 0 5 0 L T = L A * R D

1 0 6 0 R A = ( M - 3 ) + 3 0 . 0 * R D

1 0 7 0 s r . = rA lA a s ( r . A )

1 0 8 0 R E M A im ss for e a ch, com pone nt

1 0 9 0 Z Z = Z * N D

1 1 0 0 x c = x / ( c o s ( z z ) + . O 2 8 6 * E X P ( - 1 0 . 5 * c o s ( z z ) ) )

l . l , L 0 x A = 1 . / ( C o S ( z z ) + . O !2 3 * F , X P ( - 2 4 . 5 * c o s ( z z ) ) )

L 1 2 0 x o = 1 / S Q R ( 1 . o - ( s I N ( z z ) / Q . 0 + ( 2 o . o / 6 3 7 8 . 0 ) ) ) ^2 )

1 "1 3 0 R E U I ]B V R I e xtia ction for e a cb cdq)one nt

1 1 4 0 F O R I = L T O 5

1 1 5 0 X R = . 1 0 6 6 'E X p ( _ ! * N , / 8 2 0 0 ) * ( ( w A ( r ) / . 5 S 1 " - n '

1 1 5 0 ra = . 1 * 1 ( w A ( I ) / . 5 5 ) ^- 1 . 3 ) * E x P ( - l * A L l1 5 0 0 )

1 1 7 0 K A = K A * ( ( 1 - . 3 2 lL o G ( R H / 1 0 0 . 0 ) ) ̂ 1 . 3 3 ) * ( 1 + s l* s rN ( R A ) )

1 1 8 0 K O = O Z ( I ) * ( 3 . 0 + . 4 r { I rT * C O S ( ru | ) - C O S ( 3 * L T ) ) ) / 3 . 0

1 1 9 0 X W = W T ( I ) * . 9 4 * ( R g / 1 0 0 . 0 ) 'E X P ( T E / 1 5 ) * E J ( P ( - l* A L / 8 2 0 0 )

1 2 0 0 K ( I ) = K R + K A + K o + X W

1 2 1 0 D M ( 1 ) = K R *X G + (]|* , ( , !+ K O *X O + K !{*X G

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r d a y?rillio nre c ific,s th a tls ta n -ll o b -a b o u tI n e r -

\ ( ) l r \ C irn :e c i t to i tb o u t 5 o . V 'u m ig , h lw a n t to c a lc u la te rv h e th e r V e n u s c a n b es e e n a t c o n ju n c t io n , p e rh a p s ju s t a f te rs u n s e t f ro m h ig h lL r t i tu d e s .

V e tru s is c irs y in th e d a y t im e - i f y o ukn o w rvh crc to lo o k . N e ve rth e le ss , m o stp c o p le te n d n o t to lo o k u p , m u c h lc s ss c a n th e s k y c lo s e ly . ' l 'h u s , i t a lrv a y s c o n rc sa s a su rp rise to se e V e n u s c lu rin g c la y lig h t.' l 'h e C l. r in e s c c o n s ic le rc d th e v is ib i l i ty o lV e n u s in th e d a y t irn e to h c r ir ld a c h a n g ein th e d y n a s ty . A s ig h t in g in P a r is n ra r re da re c e p t io n fo r N a p o lc o n in 1 7 9 7 rv h e nth e 2 0 , 0 0 0 o n k ro k c rs p a id n o a t te n t io n toth e c o n c lu c ro r o f E g y p t b u t s ta re d a t th es k y in s tc a d . B y e a r ly 1 7 9 8 , th is p a r t ic u la rin c id e n t rva s th e n so rn ch u r,v co n vo lu te c lin to th e n o t io n th a t a c o m c t w o u lc l im -p a c t th c E a r th a n d c a u s e g re a t c lc s tru c -t io n . P a n ic e n s u e d o v e r a c o m c t th a tn c v c r a p p e a re c l.

T h e tlick to ca tc l- rin g V cn u s in d a y lig h tis kn o rv in g crn cfl1 r'vh crc to lo o k . 'l'h e

c , v c 's d a y v is io n is l0 to 2 0 t im c s n to res c n s it iv c in th e l ' a le a c e n tc re c l u n th efb ve a . T h u s , lo o k in g a rva y fro n r V e n u s b ye ve n !o co u lc l m a l< c th e c liffe re r- rce b e -t rv e e n c lc tc c t io n a n d in v is ib i l i tv . ' lb f in d i t ,

yo u co r- L lc l u se ' a tc lcsco p e w itlr se ttin g c ir-c le s , o r yo u co u lc l sc irn th e re g io n h o p in gto p a ss cxa ctly o ve r V e n u s. A lo w - te chrr . rc th o d fo r r ro rn in g a p p a r it io n s rv o u ldb e to firllo w V e n u s fio m tw ilig h t tod a y lig h t rv ith f re q u e n t o b s c rv a -t io n s . F o r e v e n in g i irp p a r it io n sn o te V e n u s 's p o s it io n w ith re -sp e ct to fb re g ro u n d la n c l-m a rk s ir t s u c c c s s iv e ly e a l l ie rt im e s o v e r a s c r ic s o f a f tc r -n o o n s .

V e n u s is n o t th e o n lyp la n c t th a t s h a rp - e 1 , e d o b -s c rv c rs c a n s e e d u r in g th ec liry . U n c le r g o o d co n ciitio n s ,m . rn y p g s p l( ' h . r r c : t ' t ' r r I u p i te r ,w h ile M a rs is p o s s ib lc to o . T h eB a b y lo n ia n s a ls o re p o r tc c l M c rc u ry ir . rd a y lig h t . S o o n a c le a r c la y u n d c r g o o dc o n d it io n s , w e c a n fa ir ly c a s i ly s e e ro u g h -ly f iv e t irn e s th c E a lth - S u n d is ta n c e .

I lu t w c ca n c lo rn r"rch b e tte r th a n th is .S ir i tL s ( 8 . 6 l ig h t - y e ir rs c l is ta n t ) is a ls o c le -te c ta b le . H o w e ve r, co n c litio n s h a ve to b eju s t r ig h t to s p o t i t - t l . re a tm o s p h c rem u s t b e v e ry c le a r ( w h ic h irn p lic s a h ig hir l t i tu c le ) , th e S u n m u s t b e a lm o s t to u c h -

in g th e h o r iz o rr , a n c l th c s ta r m u s t b en e a r th c z c n it l ' r .

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1 2 4 0 P R I N T : P R I N T u A ilm s s {g a s , a e ro s o l, o z o n e ) 3 , ' i

1 2 5 0 P R I N T U S I N G '# # # # . # # "; x c , x A , x o

1 2 5 0 P R I M ! , 'E x tin c tio n c o e ff ic ie n ts ( I T B I / R I ) : ";

1 2 7 0 P R I N T u s lN c "# # * # . * # ", K ( 1 . ) , K ( 2 ) , K ( 3 ) , K ( 4 ) , K ( 5 )

1 2 8 0 P R IN T I 'T ota l e xtinction (uB \ ,rR I ) : !' ;

1 2 9 0 P R I N T U s rN c "# # # # . # # ", D M ( 1 ) , D M ( 2 ) , D M t3 ) ,

D M ( 4 ) , D M ( 5 )

1 3 O O R E T T 'R N

2 0 0 0 R -S I S ky subroutine

2 0 1 0 F O R I = 1 rO 5 : R F "A D B O ( I ) : N E x t I

2 0 2 0 D A T A 8 . 0 E - 1 4 , 7 . O E - L 4 , 1 . 0 E - 1 3 , 1 . 0 8 - r . 3 , 3 . 0 E - 1 3

2 0 3 0 r 'O R I = 1 T O 5 3 R E A D C M ( I ) ! N E X T I

2 0 4 0 D A T A 1 ". 3 6 , O . 9 t , 0 . 0 0 , - 0 . 7 6 , - 1 . 1 7

2 0 5 0 I 'O R I = 1 T O 5 r R E A D M S ( I ) : N E X T I

2 0 6 0 D A T A - 2 5 . 9 6 , - 2 6 , 0 9 , - 2 6 . 7 4 , - 2 7 , 2 6 , - 2 7 . 5 5

2 0 7 0 x = 1 / ( c o s ( z z ) + , 0 2 5 * E x p ( - 1 1 * c o s ( z z ) ) ) : R E ! , t a i r m s s

2 0 8 0 :O , 1 = 1 / ( C O S { Z M * R D } + . 0 2 5 * E X P ( - L 1 * C O S ( Z I 4 * R D ) ) ) : R E M a ir

m s s M o o n

2 0 9 0 I F z M > 9 0 . 0 T H E N X M = a 1 0 . 0

2 1 0 0 x s = l / ( C O S ( z S rR D ) + . 0 2 5 * E X P ( - : . 1 * C O S ( Z S * R D ) ) ) : R E M a ir

m s s S u

2 1 1 0 I F Z S > 9 0 . 0 f I I E l i I x S = 4 0 . 0

2 1 2 0 F O R I = 1 T O 5

2 1 3 0 R E M D a rk night sky brightne ss

2 1 4 0 B N = B o ( I ) * ( 1 + . 3 * c o s ( 6 . 2 8 3 * ( Y - 1 9 9 2 ) / 1 1 ) )

2 1 5 0 B N = B N + ( . 4 + . 6 / S Q R ( 1 . 0 - . 9 6 * ( ( S rN ( Z Z ) ) ^2 ) ) )

2 1 6 0 B N = B N * ( 1 0 ^ { - . 4 * K ( r ) * x ) )

2 1 7 0 R E M M oonlight brightne ss

2 1 8 0 M M . - 1 2 . 7 3 + . 0 2 6 * A 8 5 ( A I ' t ) + 4 8 - 0 9 * ( A I ! l^4 ) ! R E M M a o n

m g in v

2 1 9 0 M M = II IM + C M (I) : R E la M oon m E

2 2 0 0 c 3 = 1 0 . 0 ^ ( - . 4 4 K ( I ) * ) c 4 )

2 2 L O F M = 6 . 2 E + 0 7 * ( R lr I ^- 2 ) + ( 1 0 ^ ( 6 . 1 5 - R 1 . 1 / 4 0 ) )

2 2 2 0 F l{ = r ! r+ ( 1 0 ^5 . 3 6 ) * ( 1 . 0 6 + ( ( C O S ( R M * R D ) ) ^2 ) )

2 2 3 0 A M = L 0 ^ ( - . 4 * ( M M - M O ( r l + 4 3 . 2 ' , 1 | |

2 2 4 0 B tv r= B ! , r * ( 1 - 1 0 ^ ( - . 4 * K ( r ) * x ) )

2 2 5 0 B !, r= B r, t* ( F 1 v 1 * C 3 + 4 4 0 0 0 0 . 0 * ( 1 - C 3 ) )

2 2 6 0 R S { T w ilig h t b r ig h tn e s s

2 2 7 0 H S = 9 0 . 0 - Z S : R E F I H e ig h t o f S u

2 2 8 0 B T = 1 0 ^ ( - . 4 * ( M S ( r ) - M O ( r ) + 3 2 . s - H S - ( z / { 3 5 0 * K ( r ) ) ) ) )

2 2 9 0 B T = B T * ( 1 0 0 / R s ) * ( 1 . 0 - 1 0 . 0 ^ ( - . 4 * K ( I ) ) )

2 1 0 0 R .B .t D a ylight brightne ss

2 3 1 0 c 4 = 1 0 . 0 ^ ( - . 4 * K ( I ) * x s )

2 3 2 0 F s * 6 . 2 E + 0 7 * ( R s ^- 2 ) + ( 1 . 0 ^ ( 6 . 1 5 - R s / 4 0 ) )

2 3 3 0 r , s = rs + ( 1 O e u . 3 5 I * ( 1 . 0 5 + ( ( c o s ( R s * R D ) ) ^2 ) )

2 3 4 0 B D = 1 0 ^ ( - . 4 * ( M S ( r ) - M O ( r ) + 4 3 . 2 7 ) )

2 3 5 0 B D * B D * ( 1 - 1 0 ^ ( - . 4 * K ( I ) * X ) )

2 3 6 0 B D = B D * ( F S * C 4 + 4 4 0 0 0 0 . 0 * ( 1 - c 4 ) )

2 3 7 0 R E M T o ta l s k y b r ig h tn e s s

2 3 8 0 I F B D > B T T H I N G O T O 2 4 1 0

2 3 9 0 B ( I ) = B N + B D

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2 4 2 0 Z t Z M < 9 0 . 0 T I I E N B ( I ) = B ( I ) + B M

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bottom of w e lls o r m ine sha fts . A la s ' nore lia b le firs t-ha nd re P orts e xist o f a nyonee ve r ha ving se e n sta rs in th is m a nne r. In -de e d , the re 's strong the ore tica l know le dgeind ica ting tha t v is ib ility a ctua lly w orse nsunde r such cond itions. M a ny m ode rn a t-te m pts to re produce the se cla im s ha ve onlyshown Aristotle to be wrong in ye t a nothe rw a y. S o th is o ld ca na rd m ust be re le ga te dto the sta tus o f "a ncie nt u rba n m yths."

W ith som e soph istica te d m odifica tionsthe progra m ca n a nsw e r the que stion o fw he the r using a co lor filte r o r po la riz e rsw ould incre a se succe ss. M y ca lcu la tionssugge st ye s; how e ve r, it's be e n m y e xpe ri-e nce tha t co lor filte rs don 't he lp w h ilepo la riz e rs on ly push the v isua l lim its bya sm a ll a m ount.

I e xpe ct the m ode rn d ista nce re cord islike ly fo r the sta r C a nopus a t a bout 3 1 0ligh t-ye a rs . I ha ve se e n C a nopus w hile theS un w a s a bove the horiz on from C hile 'sC e rro T o lo lo unde r optim um conditionsw ith m uch pre pa ra tion . H e re , I ha d thea dva nta ge o f a w orld -c la ss obse rving s ite ,the horiz on d ip a llow ing the S un to ge tlow e r a nd d im m e r, C a nopus ne a r z e n ith ,a long , ho llow s ighting tube coa ligne dw ith a scope tra cking the sta r, a nd a po-la riz a tion filte r.

N e ve rthe le ss, on occa sion , fo r una ide dv is u a l o b s e rv a tio n s , lh e c o rre c l a n s w e r isgre a tly fa rthe r tha n C a nopus. D uring asola r e clipse , fa inte r sta rs ca n be se e n, w ithD e ne b , a t a round 1 ,6 0 0 ligh t-ye a rs a w a y'a like ly m ost-d ista nt qua rry . Y e t e ve n th is

vis ion ca n look to m a gnitude 7 .9 ! W itha full M oon 4 5 " a wa y, a n a ve ra ge P e r-son ca n se e to on ly m a gnitude 4 .0 .

"W hy is the sky b lue ?" is the c la s-s ic que stion to stum P P a re nts . N ow ,the S ky subroutine a llow s Y ou toca lcu la te sky brightne ss for a va -rie ty o f cond itions ba se d on asim ple m ode l o f ligh t sca t-te r in g . T h e s k y b r ig h t-n e s s e s w ill b e e x p re s s e din e rg s p e r s q u a re c e n -tim e te r pe r se cond P e rm icron pe r squa re a rc-se cond, w h ich ca n the nbe in te rpo la te d in to theco lor ca lcu la tor o f m ygre e n- fla sh progra m (S & T :F e brua ry 1 9 9 2 , pa ge 2 0 0 ) . T heda ytim e sky is inde e d blue , whe the r ornot you include the R a yle igh sca tte ringcom pone nt. T he tw ilight sky sha de s fromblue ne a r the z e n ith to pa le ye llow s ne a rthe horiz on , just a s obse rve d . N ote tha tthe m ode l doe s not include the be a utifu lre ds a ris ing from illum ina te d c louds orvo lca n ic sunse ts .

A re S un-gra z ing com e ts v isua lly d is-ce rn ib le ? T he progra m show s tha t thelim it w ill be a round m a gnitude -8 fo r aso la r d ista nce o f 1 ", a nd so bright com e tslike lke ya -S e ki ca n be e a sily spotte d w ithno optica l a id . W ith a h igh ly m a gnifie dvie w , a n 8 - inch te le scope shou ld re a chz e ro m a gnitude , which is good e nough forthe a m a te ur to confirm the S un-gra z e rs

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the obse rve rs m usta vo id fa lse a la rm s by

w a tch ing long e nough to m e a sure a ne a r-ly s ide re a l ra te , by che cking for ghostsa nd p la ne ts , a nd by ge tting inde pe nde ntcon lirm a tion . I 'd like to he a r from a ny-one in te re ste d in pursu ing th is .

A d v e n tu ro u s a m a te u rs o r n e e d y p ro - (fe ssiona ls ca n use or m odifo the progra mfor m a ny purpose s. F or C C D fla t fie ldsin the u ltra vio le t, the tw iligh t sky is be st,a nd the progra m ca n provide sky bright-ne sse s for e stim a ting e xposure tim e s tow ith in a bout 2 0 pe rce nt. Inde e d , the e x-tinction a nd sky brightne sse s ca n be fe din to a ge ne ra l p rogra m to ca lcu la te thelim it in g m a g n itu d e fo r C C D c a m e ra s , a n dthis is e xa ctly wha t I provide in a com pa n-ion a rtic le on pa ge I 1 7 .

A nd w ha t a bout w ish ing upon the firststa r? H e re , the a nsw e r w ill de pe nd in de -ta il on spe cific c ircum sta nce s tha t youca n now ca lcu la te . A nd I pe rsona lly th inktha t it is pe rfe ctly fa ir to use a stronom i-ca l p re pa ra tion to ge t your w ish .

B nnorrv S cH . , ,e re n jour ne ye d to A ruba to w h-ne ss the F e brua ry tota l sola r e clipse , a nd he in'de e d sa w D e ne b during the da y. H e ca n be con-ta cte d a t P hysics D e pa rtm e nt, JW G 4 6 3 , Y a leU nive rsity, N e w H a ve n, C T 0 6 5 2 0 ; scha e fe r@grb 2 . phy sics. y a le . e du.

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is no t the a ll- tim e re cord , s ince va rioush istorica l supe rnova e ha ve be e n da y sta rsw ith d ista nce s on the orde r o f 1 0 ,0 0 0ligh t-ye a rs .

F u rth e r E x p lo ra tio n sT he progra m confirm s the w isdom tha tunde r da rk-sky cond itions typ ica l lim itsa re a round 6 th m a gnitude . T h is de pe ndson the a cu ity ( a nd e xpe rie nce ) o f the ob-se rve r, such tha t som e one w ith ve ry good

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T h is sugge sts tha t the ta b le s ca n beturne d a nd a m a te ur a stronom e rs cou ldd iscove r the se com e ts, pe rha ps se ve ra lpe r ye a r. S ta rting a surve y o f S un-gra z ingcom e ts w ould re qu ire good skill - tocove r the orb it tra ck w ith the sm a ll fie ld -o f-v ie w , to a llow the e ye to ge t in focus,a nd to a vo id a ny d ire ct v ie w o f the S un .A lso , s ince m a ny th ings m ight be in - http://www.skY P ub.com /