Visibility of Luna and Lunar Crescent

allow visibilil, ofthe cltsm wilnoul oprical aid bu rhe magnitude conkasr is in f.vour
ofvisibility. This happens s aemi€npirical modcl dcs nor bl. i.to considcnrion lhc
elsvation of lhc sne of obseoation abole sed levsl md dr wcarher conditions t-he
maSn'lud. contBl model consided all lhese facto6.
Dcyond $eorctical considerarions a na$ematical model should possess poucr oa
appliabilily. The prine applidion of rhc mathemaical nodels cxplo&{. anatysed an,l
develoFd in this $ork is lo dermin€ rhc €adiesr visibihy ota ncN lunn cft*cniar 8J
location oflhc {orld and lo lerify a chim ofcre$on lhibiliry. Ap.n froh $is prirlc
applietion in the fiih chafler rhc sedi+mpi.ical modch arc applicd b devetop a
hchnique for cilculdring the leneti oan$v obsc(€d lun cascent. The phenom..on of
shonentu! otcrcscent lengrh is lino"n for centuries ond drrinS 20ri cenl!try a nrnrbc! of
4!$ns hale b(tn suSgcscd lor $e eme. Ilo\€rer. our sugg.srd rNhnique is rhc tld
ofilsn rc ihr pdvid. a simplc com brionili@lforcrlculatirglensrholob*ncd
.Nsccnl. Mooover. lhc *-nlichpincdl nlodch are nlso rfplicd r. lcril} thc act(dl
p@ti$'l obsen.t,onal lun.r cdendar i,r Paki$an for lhe lasr sc\cn )c s. rhc nDdcls
and thc tnctis.d
calcndar aN found to bc in asEemcnr in 95% oi$e ncs mooff duling
thc pciod of srudy. Morivaled by rhis hish rare of consh(cncl rve hrvc pNscntc(t a
''PEdicted Obscn arioml Lunar C.leod.i forPakisan.
A sumntr' ofrhis Nhole.flon h preseired in lhe lasr ch.prcr. v.nols ihpoarrr
issues aE hiehliSlt d $nh a di$ussion on rh. aurur. scope of Esearch nr the arcd