Visibility of Luna and Lunar Crescent

siglling of such a youg ed rhin cesc.nr wb n€vd rcpon.d- In lhe norlel $ar is
developed in this sork thc losct limil ofihe *idth ofvisibl. ctsent is considered ro be
o.l8 aE minut€. However this ninimum is not th€ abelule ninimm for all c6@nls for
all posible el ile altitudes (ARcv). I. fiis work *e consider rhh ninimun of 0. 1 8
. arc-ninutcs of crcscenl width shen fic Elaliw dinulh. DAZ of $c M@n is ao md
rlr r.larir. alliiudc ARcv gives lhe q-lalueof_0.22. Y.llop s ditedon (4 2 3) for $n q-
,1R(y =9 6311-6J226W +0 7319 t'i2 ol0ls,t/3 6'18)
Thc values of ARCV according lo lhis *iteion giving $e q_rdlue equal to '0 22
Nould ield ! difcre lotr€rlihiion lhc visiblc width olthe crescenr' Tbis is causcd bv
dilTriem relarivc dzinulhs DAZ FoT lh. lasl posibl' ARCV (4o) th€ *id(h ol lbe
iNisibk ae$erl Nould bearcund 108 alc{cconds $at occur dl a large valucofDAZ ln
\i.\r ol diis $ilcrion ihi nininud {idth of lisible cr€$eol for @v ARcv is Gm'd trand
s te *esent isjusi invisible for$is{idth:
(tIa)
Whqrc l'l. is tlE tlmrclical enlEl sidlh of he ces'enr and 4costl
is $e r€duced
rvidth al aogte V Irom lhe center of $e de$ent
'/-
n dre sidth r€duced bv the chnve
ahnude ARCV li ordcr thal soEe pan ol dsenl is visibl€ 4(!'rvl
> l'l' ar sonc
\alue V = Vn 'llrus thc eftstive visibte widlh of$e ce$cnl tor v nnsing fon 0" ro
(5.1.r0)
Th. brishlness of crescenl falls sha4lv s 0 approaches 900 - t th' aclul visible reidrh
of cE$.nt at any val!. of V m6r tE less tbd d€ e'onetic valu€ of vidh eiven bv
equatioh (5.1.8) Therefore rhc etr6tiv' v6ible width siven bv (5 1 10) is justiced
178