Visibility of Luna and Lunar Crescent

Moon. wlee6, oncc rhc hinimm &stc of sepaDrion !s (.quivd.nt ro LAc) fo, $e
visibility of @w l@d ct€.st is tnoM for thc day the @rcspondine agle HS sinS
(1.1.9) cs als b. .vatua&d. Horev.r, rhc ue of (j,j.6) is ind.p.nd.nt ofany visibility
condition ed is fixcd for rhe day ir d.pcnds only on rhe posirions oflhe Sun and lhe
M@n for fie rim. ofobsenato. &d the locaiio. ofrhe obF ei. On the o$( hahd rhe
u$ or (3.1.9) dep.nds on trE vjsibifty @ndiiioG, @cly lhe mininu del. of
s@ml'on tu, thar.& b. kmh only on lb. bdis ofa t gc nunbd of obo€Mrions tor
At rhe rim€ of Muslih Gtrononcts rhe .phener€des of $€ Moo. oay nol hale
ben so aeudely tnown s ir is today, but rhe Eligiou tecnn.ss oflhe seing $e new
lund cr€s@t nusr hlve tcad ro moc rcchre valu6 or,s. Bruin (t9?7) hs i.dicared
that Muslim arbnoheG rveE welt awe of rbe f&! lhar d8Lnce oalhe Eanh ild rh€
Moon and hence rhe width ofcrescent for sde uc oflighr varies. Though exploiations
ofdr ancienr considcred lhis variarion ro behdve tibearly we now know thal it inlolves
lne lflgononefic func on.
In lnis worL $is prcbleb is h&dlcd by considering rne actual eni_d.in€ler of
th. Mooh dd lhc fer $at MnslinvABbs ob*tued thal ar shone r .lisrances the crcscenr
wasseenwhehtheLACo!arcofseparationaswaslOd€elccsor40minulesoftimcand
al la€e! dishcca thc cErcent ks seen Nhen rhe m ot seplFrion dJ B t2 d€8res or
48 ninules of timc. -r1li5 teads b a siople Eladon b€lwn /s md lhe aduat semi-
^-- D 22
ol r0)
Using rhis etalioo thc @ of *pdlion necded for ce$enr
*p@tion felor is .alcutated in ihe sonwar. Hilalol.
9l