Visibility of Luna and Lunar Crescent

criterion or our s-value (or Q&K) cnterion. The disagr.ededt ls lhe resull ot eilher
the bad weather du.lo whlch the.ew lonarcr6cent could not be slghted 6nd th.
lunar nonlh b68an one day lare, or too opilmjsrlc clalms ol obse atloh and tho
Lunarmonthbeganonedayearllerthanpredlcted.
Funher, In ihls work another aoollcarlon ol these models is consldered. Tnls
is lhe use ot lhese modelsto dwelop a compui.tional roolro detemlnethe lenglh
of cesce.t from cusp to cus!. flie n€w lun.. c.scent as well as crescent on next
few evenan$ b obsened io bs shorter tha. its rheoreli.ar length Le. 180 degree
IromonecusDlotheother.Anumberoialrho6haved€scribedthereasonsforthe
shortenln€ of the obsenBd crescent (Danlon, 1932, Schaefer, 1991, McNally,
1943). However, Jew have atlempted devislng a mathemallcal technlque lo
delenino the exrenr of rhis shorrening ol rength ot crescent. On the basis ol one
pafamelef dlleia ee have used cresent ot minimum visible widlh as limil on lhe
le.$h or .re$enr and devrs6d a simple rechnlque to calculate lr. The chapter
beginswilh a desc ption ofthesme.
5.1 LINCTH OF LUNAR CRESCENT
Ihe hct,lld rltc nc\v luhlrclesor appcds stroncr llEn 180. terA r.islnorn
ldt cenlrics. Il wns Denj.h wlD fi^r savc rn exptturarnr for the pbenoneion (Dor.ru_
lt32&1936)andalributcdi(o$etunarteniincloseto$ecuspsMcN! yanribuluda
dillerenl reNon snh tis pbenom€ion disadine Danjon\ hlpo$esis (McNa y, 198:t).
McNall) proved rhar lh€ tcngrh ofrhc shadoss ctose to $€ hrnar cNp ond fic d.panolc
oflunar suiface IoD beins pertecr spherc coutdnl,jimiiish rtre brignllrss oflhe regions
ofcresent close ro cusps lo bc rhe caNc ol rhe phenomenon. IIe arribured ttrc tength
shorlcdng ofcNscent to lbe,.seing afeca,due lo $e turbrlcDe of lne ,rhosplrere.
McNally has also developed a limula for calcutalnlg te knBh of rhc desceDl, Larcly
Sull (Sulta., 2005) has anribured 0E shortening of lengtn of crcscenr duc to the
Blackwell Conr.st Threshold (Btackwclt, 1946) and has d€leloped I forhula lo
c.lcurale ciesenfs lcngrh. W. have aho devctopcd a sinpte &chniqne tor catcul.ring
173