Visibility of Luna and Lunar Crescent

lf thc hviligh briebhes rv/, doninats ovc. tne day lieh briehhcs dat, rhc. thc sud
.i r,grrb and .' ,1, are slored in ,r.r/t otncffi$ rhe sun of ,'s&r, md etb rR noE'd
in L.r/t Morcover. ifrhe Moon is.bov. horizln thm de,, C lho addcd to bs.r/t/.
l-iially, fic brighbes ,.\rrlt is @neened inlo .m-tanb.6. fon cquaon (4l.16)
till rhis point all conpulalion is done id a looP that €recutes Ilve timcs again, once for
sch wavel€rylh bdd *l4td fnc €aicula$on ol 6e limitins naghitudc /€, is donc .s
la (tel < l5o0) ic,,e=loat..eo lo-re)
Els { co,a - I o ! rr . .n o " I 0 r ' }
kh = tum'\t + Jctu" tb.t r
(4.1.24)
(4.3.25)
(4.1.26)
t.. = t6 i1 -2 t,IVD) d.".htzl
\ In(I0) l
(4.) 21)
Schaelcr (Scha.fer. 1988) in his drtshold co.tdsl nodel calculates /i as rhe log
of $c ratio of rhe acrual tohl brigltoBs of th. M@n ad $e tolal biSlttnss oi $c Moon
neded for visibiht fo. rhc givcn obsping condiions ln this rc|k we considr rhc
mlg.itude oflhe Moon and $e lisual limiliog naennude slculatcd frcm thc alsoinhm
givcn abovc- The diftcmc. of Moo.s naenitude z"d!A and lhc visutl limitins
nalnitude le- is consideted .s nugnitude .onxas de"or.d 4 zDzq A plol (Iig 4l I
bclow) sbows dirercncc ofscbacfcls thEshold cohtrasl I and $c nasnnudo contasl
/r43 Scries I sho*s ,1aas lor crcsmls $ wca not $cn and erics 2 shows ,'lu zg ror
crusoent ihrl \vcre sccn Sdies I and series 4 sbow ,4 cot.spondins lo dcsccnc $al
wce not sen d lhal scte sen Esp.clively.lheda1a lor this fig is talcn lrom Sch.cfc!
(1988). P$nive vales ol cont6$ fo. crcscns $al wrc nol *o ad lhc nesrtilc
vrlues lor conlrdt lhal *erc sccn snoN lhc inconsistcncics ol thc modcLs qirh lhc
ob*ndion. Th6e inconsisteoci.s may E$ll fDn .stiDatcd lalues of t€npcaorc a.d
Elative hlmidill adopt€d for lhe calcllalions.
l5r