Visibility of Luna and Lunar Crescent

d[dl! of pdallq. Using lhe local siddnat timc tb. @rdina€s e then trdsfomcd inlo
Ioc.i hori@ntd @ordinalcs dr. ahitud. ud &imuth,
Once $e tine of leal sunsct (T) and th.t of Moon sr (I.) d obt in.d lhe
o@ctcr LAG = Tn - Tr is elculat€d. Unlc$ lh. LAC is posnive for the New Moon
dd ncSrdv. for old Mmn th€ cFsent cd ncv.. b€ sen.
Suppoe (..,,r.,r.)ed t,.j,,r.) d ftc p@ie dislanes, aliflic lo!8it!d.
sd th. lalirudc of rhe M@n and 6c Su, Esp.ctivcly. af@d ro the ft4 .qtinox of
rhc dD. or sunst at any lMtio. on $c Elnh with tftstiat coordinaies(1.r) on rh.
day, or day aftcr. lhe binh ofNew Msn (al$ oll.d the Csenlric Coijliction oi th.
Moon).Thefi'slsteDinthedelemimtionofih.visibililyoflh€nevlunarcresce,on
thc day of conjuncrion or the day affer, is io dcternihe lh€ actual dy.anical ihe (TD o!
TT) T", oflhc coojuction. Ncxl one requires considcrins the local rines ofsening ofth.
Sun &d tb. Moon. Le! Tt dd Tn (Coordimi.d Univdsal Tine TUC) b€ th. tihes of lh.
l@.1 sunsel dd the nooi.eq vi|h Tj < T..
Using rnc .cliptic @rdimLs oa lh. $n ad rh. Men E alculared for th. T6 thc
egutodal @rdimrs of rhe two bodics (d.,4) dd (d,,t,) e c.lolat d usins
(Me$,1998):
s t h\^ )c os\r ) - Tdnl P)sth(E)
cas6)
(2.8 )
st(d) = si,,(l)co(.J + codB)st(€)st(r)
o.8.3)
wl@d, fi. nd emid is in 0r s. qudtul6 t, ed ',
the obliquily orrh.
dlipri. is d$ adjug€d for lh. d, . ed thc b.9 rine Th. tsal Hou Atgl. H is th.n
oblaincd tion rhc difreren@ ofth. l@l Sidftal Tiru (Zsl) 4d th. rishl 6c.nsion
Tnis finally gjves lhe l@d nonzontal c@dinal6 amulh (,1) $d the allilud. (ir) bv:
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