Visibility of Luna and Lunar Crescent

dau ofnininum aE ofvision for difcrc el.tiv. uinurhs- tlowrcr. all th.* modcls
isDrc the ridrh of fi. n.w lba cas4.d ftar vdie SMrly with thc Eanh-M@n
diskrcc for rhc saec elongllion. Thk c.!s!s vdiatioB in thc elully bdshh.s or th€
.Eeent of emc donsdion. Cons.qEntly, ft. s. pln of ARCV ad DAZ $c
t'i8hh.s of casnt v&i6 for dif.rcnt Eanh-M@n disranc.s. Th€ lsk of this
considdrion is rh. Fain caus. of l.ss.r succ.ss pec a8. of $.* n.thods N
conDlEd to the later ftod.ls foi posnilc ob*nations.
Th. Glliaion of vdyiiS bid nas of crc$crl si$ fic widrh or cE*.nt ro!
se €lonSa on (and $m. pih ofARCV-DAZ €luct thc phriical d.$nPlion otth.
poblcm by Bruin lead Yallop ro dcduce bdic dala €lating widtu ol cErent to $c arc
ol visioi. Yallop d.dwed this dll! fod $c minima of lhe linning visibihy .ur$ of
Inuin. Cons.qu.ndy. Ydlop @s su.cc$ful in dcducins hh3inel. p.6nttc' r.sr. rhc 4_
ulue ciledon. This crir.ion Produed bdler Gsuhs i. compari$n to atl th. ptcvious
mdhod!. Th. dcdudion ofvadous visibiliry condirionson lh. bsis otdircBnt dngcs o!
.r.valu.s $d rh2t ol rhc besr rimc of visibility' of .een frem rh. limitins risibilirv
cunes of ENin !'e thc motr markable of Yallop\ contibution l-hc \isibili'!
condirions pro\ idc ruidclinca lbour uds *h.t condnioos rlt co*cnr \ould hL casilv
risibl€. $hcn n $ill b. visiblc undo P.rfcd st.rhct condnions whc. Ue opricrl \o(ld
b< Eqlircd .d when fte cB$ent $ould bc sinPlv nor visible $ith ot Nnhout atrv
opti.al aid. rfu* condilio* har. poKd ro b. noN and morc Eli.blc $i$ incBtsnB
Thc najor co bution ol or e
is rhc comp.ri$tr ol .ll fi. htljcls
@rclically, frathcm.ricElly, phytictlly.nd in vi.w of$eir success p.rcentagcs
s.r of ob*wations colled.d tom d. l.t. l9ri c.ntorv till dcntlv. Anorhcr 3isnillcst
contribudon ol lhh wott is lo convcn aU th. mo<l€ls ino si.8l. Padm.tcr crn€ria 1 h.*
arc listcd bclo{ in th. inccsing order ofsucc€ss pcE.nlagc:
'or
a
vp = (ARcv -
( 12.'o-0'.00s(D,{z)'z rYlo
200