Visibility of Luna and Lunar Crescent

,.tdchltl = K, r ^ s + K,' x, + Ko' x o + X-' xs (4I 12)
lbe.qurioft (4.3.?) to (4-3.12) aE Pleed in a loop thal rum nv€ ddes oncc for €ach i
O. 1.2,I and 4. Aner$eexccution oflhb loop lhc rir m4ss al poin r, thc tosnion of
rhe M@nandfiarof theSunacc.lculal.dusinS:
rrr@/ = [cos{'drd'Jt )+o.o2s icxp(-II'co(z"dirt.)]
(4.l.ti)
il (nofu < 0) nnposl = 40
ar nnpoeJ -lcos(go - nul )+0025 r.xp(-ll
- . (4.1.14)
il (\ah <0) xn@ld =40
, , (4.l.tt
et:. snpoel = lcosleo - ett) + 0.025 'cxp( -l t
Th. masnitude olthe M@n is lhen @lculatd NinSl
mtut =
-.12.13 + 0.026.lt 80 -.to,@ | + a. ltso -.tons )a' r 0 t (a3.16)
+ c'.rrt4
FoUo$rd by nid -am. bnghrncs. honlidl biehh.ss. twilishr bnghl.s and $c
ctree - n
4 1. Lkhlil' nq6tl
(4.3.r7)
kn = rc15t5 ftmp" | 40) +6.2.107 t(leto,stunf ,+
tot36 .(r 06 +cos'(/.io'sui )J
$hm /elo,At, is $c clonsrtion ofF fon $. ccnft oflhc luE di$
(4.r.r8)
noohh =rc o!'lo,htus D6c'il4+.r:7) '(l - ro-0 4'ri.,l'l'"*/ )' 1t3.rot
(tuh . ahree + aaoo@ . lt - c!tuae )i)
^filb = t0-0at(,*.r,14 nschlil ttz 5 -s.t' -!'dt' t(t@ I llchlnl '
i_ roo l, (r _ r o
-0r.,,.,r,r"*./ )
(4.120)
ctort = rc4 a' t'chlt l' |rydql
/g-, - ro(6 r5:/./d,N* i a0)
+6.2'to1 tlfetoresn)z +
ro$6 .(.oe *.o.'?(tt,,r* ))
.tqh - |o ort'l' ;i,l't'n6chlil'ar'').t -I0 03rrs/'I4\fuir' )'
V"' , "fat *aaoooo'(t -
"hn))
(4.1.21)
(4.1.22)
(4.12l)
150