Visibility of Luna and Lunar Crescent

depends on ils width dd oi iis dltilude .bov. hori@n d th. rioc of su.sd accodi.g lo
Bruin (Bruin, l9??) dd Yallop (Y.llop, 1998) a @nsht q'valu. describes a cufre on
th. globe i.di@lin8 sinile visibiliiy @nditio.s along all poinc of$e curye' Such a
clne is a psldcr@bolic cwe wi$ v€icx on the 6l-dost loisitude Thc
lonpludi.al p6nion of lbis ven x vei* nonih 1o nonlh 6nd th' hnude of |he vqar
d.Fn& on lhe d.cliMtion of th. Moon ed lhe Sun on the ccle$itl sphere Duing
sumheG in nonhem henisph€lc lhe sun\ declimtion h extren€ nodh dd if ihe
d.climtion of ths Moon is norrh of $c su lhis ledex no!.s to exlEne nonb and lhe
c6@ visibilily is edier i. rhc nonn hitudes Duing summer of the nodnem
ladud.s if lhe Mmn is eufi of lhe s6 then ftis v.nex d@s not @ch irs
'xcm€
nonnern posilion dd still tne .e{ cE*mt vhibilitv is better in 1ne norlhen laitudcs
Thc situaion h revese for lhe $liheal henisph€te Tne palabolu opens westMd above
(nonhwardt and below Goutbwrdt fion th€ vcnex The CuR' A is rhe collection of
points on rhe 8tob. fot which rhe q_value is 0.216 All rc8io's $ithin lhc lwo b6nches ot
$. p&abola wesl of rhc vertcx e the EgioB wh.e |h. q_vdhe is s@ler
lhm 0-216 md
the cle$ent h ea3ily visible to ln. Mlcd eve in lhis rcgion' Csc B is the colleclion or
ed B lhe
all points where the q-value is -0014. In all tbe Eeions be$€e! cuftes
cicsc.nl is lisible to thc nai.d ete onlv undet pcrfed visibililv condnions
The Fgions b.(wen cuN. B and C (q_value _0-16) de $e tgio's io wbich d
obsen.r suld Gquire opdcal did 10 locatc ihe cr*c'nl dd th€n it mav be visible lo
naked cye. For reSio.s wi$ q-vdlue I€$ t\ai _0 16 rhe cresenl wolld not be visible to
the .akcd eye For a comnon. untaincd obsePer it h highl) unlikelv thal ihe cFscem
*ould bc seen in rgions ed oflhe aNe A Thc scienificallt ecoded obsaliom (oh
ehich all $c sludy of the rwnli€th cdturv i3 bNd) do oot Pohibil obedalion of
.r.sc.nl wiln mkcd €ye in region belwn cwet A 6d C In sucn t'gioN' in facr' lhc
probabilily of obsenation incFdes whh the nlmbef of keen tdined od expenenced
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