Visibility of Luna and Lunar Crescent

Tne nodel dcvcloped in lhis e for borh Ih€ brigh$6s ad th. lenglt of
cmce.i is nainly geomerric, suppl€n .led by rhc single pmercr crilcrjon for $e
earlien visibility of ncq lunar cFsc€n1, Thc model prcvid6 a simpte method of
cdculaling lenglh of lunar ce$eot and tak€s inlo accounl lhe atnospheric afects
indiicclly through singlc pdaneler crit ria for th. vnibility of new llnar cressenr only.
whenerer t/. < n/- fi€ €r€$ent l6grh is nor cakulaled dd rh€
according lo eordcd obsedation (lable 5.1,1), TL nodel hd been Gn.d in nw $ays
I:i6r. ior so6e of $e rcccnt obeflarions whose phologlaphic Ecoids arc available $e
cilculated dd obscrvcd cescenr le.erhs tre compared and shown in jablc 5.1 2 and nr
lig 5.1 7. The cFscent l.nerhs calculared ushg ou! lornula (5.1.13) arc SEaler thm lhc
obseoed values dd rhose due ro Sultan srechnique arc genedllt closer to the obefled
!alu6. In calcul{ions using th. fomnla of McNrlly A-t = ,r- dd X = seni'diafreter ol
The colu$ns nr rable 5.12 show rhe dalc ofobseruation lhc coor\iiMlcs ol rhc
locatior ofthe obseNer (lalirode md longitudes ii degr€e resp*li!ely),lhe elongation o1'
rhe Moon fod rhe sun in d€8rees, the seni-diamcrer oflhe Moon. thc c.nlral rvidt[ ol
lh cEsce.l. ninioum visible width of cre*.nl (all in dc minul6). lollosed bv lhe
crescenl length crlculated by our nodel ,id $e obsded crc*chl l€nglh. lhc .a'nc ordrc
obseNer Th€ l.( No colunns contain cGsce|n lcngtlrs as calculaled usirr8 rlE nrodek
rlu" ro sutron onj Uctlutty .,p.ctvely. Thc du(a in rhh ubl€ has bccnlnlnucd iD ordcr
oiincre.sine elongalion ot ARCL.
To d€Gmine rh. l€ngh ol! crcsenl fom picroial record the dieital phoroemph
is opened in any sraphic $nw l@l- SeleclinS coordinales of lhe oa the poin6 (*o
ofr&n do*roeachoftu cusp md on€ closc ro supposed cenftof$ccrc*enoon the
vhible oute! liob ot lhe oe$eol an equation of circlo h developed $at leads to dre
coordinales of lhe centre of the luft disc, toining lhe cenlre of the lund disc with lh€
two yisible cusps of thc crsce.l tbe dsle made al fie centre bv thc tso cnspc is
mc6u€d. Tn€ picue of one of tlE cre$ent m.$u.d in this Mv is shoM in Fi8 5 l ?
185