Visibility of Luna and Lunar Crescent

Tn€ v.lu. of F s, !,'3 md G's Bd in lh. qp63iont ahovc tt! gt!€n in
thc T$1. 9 in Chlprcnr-Tooze 6d Chlpotrt (Ch.pre -louz; &d Ch.pon!
l99l,pp.l9):
Oft. rh. @retion dE to .ubrion is dre onc my so ro 6trd da Eq@tori.l
c@dihal.s, the Rjght Asnsion d dd thc dcclin tion 6:
St.p6:
EQUATOI.ULCOORDIANIES
"=r-'(
c6(tpriio")Si4v)C6(U) -.t4 Eps i t d) Si dlu
'l
(2.5.r0)
6 = sn't l3ih(Epsitm)Si"(v)cos(UJ + cB(Eptiron)sinei (2.5. I I )
Thc* re rh. nle cqubri.l c@'dinar6 of lh. Men wnh EfcEn.. b th. toe
L
cqulor of $e dare ahd the trua dyunical equioox of the dar€_ Th€$ m stiu lhe
s.oqtic c@diMl* md lhc afr.cr of lhc D6nion of lh€ ob*rcr on rh. glob. is ycr ro
b. lalfl ifto @ounr so tb.t rhc ..iopoccnt.ic" c@rdid., (coordin t€s relariw lo thc
posnion ofth. ob*fr.r) nay be obl.iied_ In odd rcd5 rh€ !ffftrj oftE ..paraltd" arc
to be t t.n inlo &count. Th€ Pdttd r i! givcn by:
12.s.tz)
wh@ 4 ir rhe g€catdc dist4. of dE Mer HowEr rhis q@nry paml* d.Fnds
on rhe Hoq Ancle (ihe since ibe object cosad thc l@al n.ridim) tor whicn w. ncd
thc lad sidc@l tin. LST.
St FTl
Fqhtlate tiw dgM't tlor t UTlq !h. dat. ,tdet cwidqatio,.
5l