Visibility of Luna and Lunar Crescent

l.nglh of new lum ccscenl (Qucshi and Khrh, 2007). In the fouowins we reprcduce
this cflorr wilh slighr nodiilcation md a codection,
Schrrer cjecred McNall! s expldaion on $e bais or his Yiw thar rhc
shonening oflhe cr{ent length is situply b.ca6c oflh€ sharP d*line offie brigntn€ss
of rhe cr€scenr clo* ro rhe cusps ( SchaelTer, 199 ! ). Usins rh. dcudte dodel of Hatl@
(llapk , 1984) for calcularing rhc surface brighhcs ollhe cesnt Scbaetrer claims that
Daljon\ collected obse aions anJ his own n€* dara fic tbe nodel Howewr, nenhet
Danjon nor Schaefer have sneecsred a ddhod lor calculaling cacehl ldg$ Hapk€t
rDdcl nat be accurat for $eoreical setling rclatcd lo thc clongalion ofrhe M@n bul as
frr as the obscryed cresc€nls are conconcd dEre oughl lo be a depanur€ frod snooth
relarion berween elongation and lhe crescenl lcngth. Thc tason we co.sider n baFd on
obsenarions ofsone norning and {enihs cesccDh.
ltosl of the edly desfiption of the phononen, concenuated on rclatine it to the
plEs (or dongation) of the Moon ihal is gcnet lly th€ !e6on b.hind the Phenonenon
As rhc clongalion increass rne lengrh of rhe cesccnl fronr cusp to cusP k€eps ioc€Ning
Nhich a connon obseryalion. The nathemalicd dc*riprion ol lhe phenomenon lems 'n
ufdeficicncy arc. br Daijon Nd !ho\t to bc incoftd bv McNallv Hosev€r. e or€r
esrimrrcd limil oo rh€ ninimu \idlh of visibl. cEse (2 to 6 arc seconds) bv
VcNJlly le ro ren .mdll "dlu*
lbr DJnjotr Liilil lhe d*np'ion due lo McNallv i:
logicall, souDd so is $at of Suh dd bolh rcsulkd in$ tcchniques for calculatng
hDglh of se$oa. HoNerer bolh llcNally dnd Sullan hrve nol reponed lhe aptlicalion
of rlEn desription o. lh€ Ecorded hisloricll dria found in lii€iatuE (Yallop 1998.
Schaeffer l99l elc ). Accordinglo Danjon, d desctibed by F.l@hiet al
si,(a) = st(.) cot(@) (5'l l)
Wh.c $e @ PQ = o is fie deli.icncy at in fiS l (Fatoobi e|' Al" 198) a is rhe
elongltion dd o i5 half the cccenl l€nElh tr apP€6 rhal Dojon tr*d lhe Sine
t14