Visibility of Luna and Lunar Crescent

forg nodf6c(160.?lo8+390.67050284rtoy'0.00161I81rcc're'
0.00000227'powtle .3)-0.00000001 l'por(1e. 4)):
omes=modtun(124.??46_
I 56175588'kav'000206?2'l.e'tc. 0 000002I5'po$(tee3)l:
eFl.0-0.002516're-o.00000?414nei
msur<PV180.0);moon.-(Ptl80-olr!re'1Pvl8o.0);ones'1PU180 0);
oe--0.,r0?2.sin(mmoo.)+0. t724l.selsi!(ns!i)+o.016061sin(2.0'ndoo.)r
perF(o.ol039rsin(2.0rfaq)+o oo739tceersin(nnoon-nsui)'
o.005l4,eee,sin(msu+moon));
p€r+=(0.0020S'po{€ce,2 0)'sin(2-o'Et!.}o 0o l I t'si'(mmn'2 0'taq)
0.00057.sin(mnoon+2.01raq))i
@r+=(0.000561ee'sin(2.0xmmoon+nsun}
0.00042{sin(3.0*hm@n)+o 00042'ee\in(nsu!+2 0*fdd)r
pe*=(0.00038'e*;sin(hsun-2.orfds)_0 00024teee'sin{2 0hmoon_nsui)-
0.0001?'sin{omes));
Fr+1'0.00007'sin(mmoon+2 o'msd)+{ 00004'sin{2 o'mhon-
2.0.fa€)+0.00004.si.(3.0'osun))i
'
De.F(o.00003'si.(omoon+nsun_
20.Lre)+0.00001+!n(2.0'mmoon+20'fare))
eeft I-O.O0OO3!n nmoon-nsu 2 0'fargh0 00001"in(mmoon_
msun+2 o.fes))i
'
Fr+=Co.00002'sin(nmoon_msun 2 0rlarg)_
000002'\i l.o'mmoonrsun,'O00002'sn 40'mdoon)):
ol=(299.77+O lO?408{kay_O 009l?3rteettee);al *=(PI/1 80 0ll
a2=(25 1.88+0,016321'kay)ra2'=(PI/180.0)l
a11251.83+26.6t1336rkay)i.lr=lPul80 0):
a41140.42+16.4 I 2478'kayl.a4'1PUl 80 0)
a5{84.66+1E.206239ik.y)ra5'1Pvl 80 0)i
16=1 141.74+5l.lOl7?l rkav):a6r=lPl/180 0)l
a7=i207 l4+2 4tlTl2tkayl:r7+1Pl/180 0):
a8-l I54.84+?.106860'kov),i8'=(PUl80 0):
r9=i14.52+27 26l2torkayr.Jq.=tPVl 80.0),
slo=l207 l9+0.121824'lavl:alo'=(PUl80 0),
rl l=(291,14+l 84a379'tot) tl l'=tPl/180 0)l
al2=i16r.72+24 laSl54rkry),a12'=(PVl80 0l
,ll={219.56+25 tllo99ikav) allr=(PVl800):
ar4il3l.55+l 592518'kav);al4'=(Pl/I80 0):
addcrj Oo0l25.s,n(al ,, addq+{ 0001 65 | sin(t2)i
addc*=O.O00r64tsrn(.1), addfr=o.000126'sin(aali
iddcr+=o.oool ro'sinl15J; addc+=0.000062tsin(46)
d&cr-0000060'sin(a7)i iddcne0000056'sin(aEI
addcir=0.0OOO47rsin(ag): .ddcr=0.000042rsin(al0):
addr-0.000040'sn(.1 l)i addc*=0.000017'5in(al2)i
addcP -O oOOOJt'siral3\: addcrjo 000021'sin(514)i
mjdanjd+pe*addcr z-rdoubldlongrMjd+osDr:
2t9