Visibility of Luna and Lunar Crescent

For thimer c6c.nr rh€ ,r + s aSaitur r plots Sive thc b.st time of vhibility 6 the
poinr whi.h is the midhum of rhe cwe, h rlso 3ueSens a tug. of tim. for *hich Oe
crc*dt my Ehajn visibl€- Th* de excellent id6 rhar @uld help cre$ent-hunre6
bul untdtunably Btuin has nol pesenl€d a clear cul ompuratond lrchriqu€. Brs.d on
sihil& ided Schaefer ha worled out Enorher schehe of computario. lo b€ discu$.d
latcr. The schcnc for computrtiohs is d€duccd frch the visibility cuNes olBruin sd is
bsed on ll)e dinimum point of rbe r + It plor againn s. A relarion belken rhe cE$.nl
vidth cor.sponding to d€ r + , cwe sd rhe valu. of , + r ar rhe minimum oi lh.
cufl. nay be d.duced fron abularing rheF ratucs. For lhis purpo* rhc data deducrd
fiom 6g 9 b, YaUop (Yallop,1998) is d follows:
Table 4. L2
2 3
The valu€s of ARCV ore the valucs of , + r picked fbo rh. ninimln of rhe, + r cufl es
asaisl r whi.h coqespon.ls to the b.sl -tine ofvisibihy ofcresent. Tlh dar! 6 edto
a dird degd polynonial usinS lean sq@. apptuximrion lqdr lo the follovine r.larion
ARCV =12.4023 9.487arv +3.9512W' O.5632tr'
(4rr)
Tnis ( an be tEnslomed ro lh. \ Fibitrly oaEmero . r, lunc,ion as to'toq:
v), =(ARCV -(12.4021 9.481W +3.95t2t/) _0.5632W)Dtrc
(4.1.2)
Tnis crn be le$6d on rhc obscnarional dara with the visibitiry condilio thal a cssce.l
should be visible if,, > 0 olheNi* it should E@in invhible. Using condiion (a.1.2) on
lhe data *t ed ro evatuar. n rhods in ch.prr 3 dlc plor w obhined is shoM in ligu.
no. 4.1 ,2. ln this fig@ lhe cue nmed ..Boin\ Limit,, is the plol of $e equrion 4. t .2.
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