Visibility of Luna and Lunar Crescent

4,4 A NEW CRITERION TOR NEW CRtrSCENT IISIBILITY
while d€vcloping rhe "vbibilitv cudcs" (it againsl 5) $d the limi$n8 visibilitv
c!ru€J (, + r against r) for.onstad brightn.ss Bruin @nsidcrcd the avedgc brightnes
of w$m horian duiog rwiligh od fi. ldistion of lh. bdgltN of lh' full M@n
with tlE alitude above hotian c me ion d @lier' Instcad of @cid'dtrg av'ase
brightness oi sky we hav€ coNideEd dual blighrnds of skv and fte cr'scent calculakd
sing the techniques developcd by S€hefet sd olh'6 (Schmier' 1988b, l99l) i' lhe
$nw@ Hilalol. W. $lslcd c@ent vi.ibilitv circUmtarcls of ldious rcw Mm6
css wh€n lhe crcscenl Ms rponed b hav. beo sn For cFs415 ofa pan'culd
width we found lhe altiludes I oi skv points with btighhess equivalent lo that ol tho
particlle crc$. at dill€tnt $l& depEsio.s r' Th. ovcdgd of the
'ltiludes
of skv
Doinrs for difl'rnl $ln dctr.$ions for plirhuld sidlh d Lbllat€d in T'blc no 4 4 l
The left most column of lhe lablc contains ihc solar dept€ssions r and ihe toP rov grv€s
rh€ {idrhs r oflhe crcsenrs sclaled ed thc n xl one giv.s its na8lnude Thc enties of
$e 6r of rhe €blc ue lhc aldtu&s , shcE lhe stv hs rh' sm€ brighhAt 4 lhc
briehtness of tnc cresknl ofthc width al th. top of lh€ @luon.
It should b. nol€d thal duins ihe twilighl 1ne widrh of the crc*dt vd'es up b a
dc seconds for very wide d.sc.nls. Se6on to eason ed for dif|ere'r lalitldes the skv
bddrlnes fot th. sdde altitu.l€ cl6e lo th. poid ldee ihe sun sts also vdi's lor qch
column of th. lable 4.4.1 a numbq of c!*s of alnosl eme cE$enl widtb wE
@nsidered md each ahitudc is aveEg€ of lh.se cdes Thc dtla of lhe tabl' 4 4 1 is $e'
plott€d on a sraph shown i. fsw 4 4 1.lb lhis figure n as a fuhclion ofr (i' =/6,) @d r
+ ,' = s 6 a fuclion ofr (rl = sat) aG bofi ploned /ft represnl the "visibilitv
cwea &d the s(, rc9dnc the liniting visibilitv cudcs" sinild lo wh'l Btuin
(Bruin. 1977) developed.
159