Visibility of Luna and Lunar Crescent

l2t +w \
{5.1.5)
wirh w is the dim€ter of e snallsr visible .quivalent Bl&kqcll dnc and l/ h cental
widtholrhecre$e.t. (5.1 5) is$ecorsted fomof (1.5)inQureshi a Knan(Qutshi &
Kian, 2007). Sultd.onside6 minimum diameter of Blacliwell dGc lo bc 0.14 alc
minucs Nho the Moon b near peris€e md 0.16 m ninul€s wh€n the Mmn is n.or
The presenl $ork is based on rhe obseNalion or the last (old) rcsceit oD
February 26,2006. Duling this obsenation rhat sGned from lhc bcginhing ofnorning
oviliglr rill \ell past sutrie, il was noriced rhar for rhis 48 holrs Mon. noE tlrn 2?
dcFcs aMy ton lhe sun ftc ce$ent l€n8fi srancd ro derede \rith lhe rising suD
simihr obsnalion on Mdch 28'' shen lhe aee of Moon wds dound 3l tous !.d
arolnd 18.5 degrees asay lron rhe sun. rhe cdscenr leneth d*leased nrorc npidly qi(h
d(E6ing co.ra$, The l.n rine thb ciescent wJs $en lvilhou optical aid well at$
sunriF s?s less lhd 90 dege* in l€ngh. Tso dtys later n€w cc$enl with agc 27 6
hols ar 15 degees a\ey fom lhe sun Nas olsned till setling Close lo lhe lDtiab
though rhick humid a(mosphde the crcs€nt lenglh Ms aganr obscrved to bed4rcsnrg
Thee obsFations cleaily demonslrare thai lheF isnuch notc 1o b€ expload abolr lhe
phcnohenon ol shonening of cc$ent lcngth apan fom tlapke s .c€urate model thrl
shows detendoce ofcB*cnt lcnsth on clongalion tlone.
TherefoE, inrhis qorl,lo besin si$ qecoisidera simPl. seodeuical
model ior
rhe ce$e.r. fu model dFsibes the phenoncnon of shortnine of lcn8lh that depends
on th. aclual seniSiaocLr of lh. Moon d *ll a the rclaliv. alliiude (ARCV) of th€
csc.nl o\fr tftal sky. This is denved fro,n thc sinste pmnct.t (q-vatue or !!al!c)
crilerion of edlie$ visibiliry or cre$ent (chapler 4) fld is bascd on th€ facl thai
whe.cve! rhe widlh (o' btigb$e$) of cF*c clos to cusp is below lhe mininuto
vhiblc c€nrnl widrh (or b ghtn6, or rh. dcscent the vhol€ l.hsth or ccscent wirh
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