Visibility of Luna and Lunar Crescent

4.1 BRUIN'S PHYSICAL MODEL
Atuin bsed his wolk (BNin, 1977) on 1he obseded avedge brigbh.ss of sky
agaiBl rhe posirion of th. sun b.los ho,iD, ,ner ssel (0ut natched tnc resuls ol
K@h{ et. al. 0 952)) and &e bdshrB of rh. M@n s a tu&tio. of ddud., b6ed or
lhe 1h6ry ote inclion dw B€npoFd (Benpomd, l9O4). The fi8ures gi!e, by him, Fie.
? $d 3 (Bruin. 1977, pp.339) arc r.poduced here in Fi8 No.4.t,1. On rh. b6h ofthcse
sludies Aruin developed the Lund visibilily cuFes (relarin8 atdtude, , of qeeenr
plottcd asainst s, lhe els depE$ion b€low hoizon) 6d fie Lioiring Visibitiry curyes
{Elatine, + r,gai6r r) ed pEenled in fis. no. 9 (in€tude<t in rh. eme Fig No.4.Ll)
(Bruin., 1977pp.339).
Fis ? shows how $e .!e,a8e brighhss of the sLy ,s diminishes afre! suist s a
Iunclion oI the allitude of dE sun, lhe elar dcpG$ion or orp r, s !n. su g06 b€tow
hodrcn. Fig 8 (Btuin, I977) shos ihe @iarion of rhe av€ragc brightne$ offu M@D
ar s a fnncrion of the alritude ofthe M@n n above honzon .r h. Lnnar Visibility odes
dev€loped by Btuin shown in ng 9 @ruin, r97?) are d€vetop€d using the two functioB
Asum. a panicular brignness ofsky after rh. sunse! ey lU_ stitb, ead our lbc
corespondhg sotar deprh below horizon fbn nC 7, r = 4,a degEes m rhis casc. In o!de!
lhat lhe @en is visibh in such a bright sky lhe ctscenr should also be at lsr a
bighl (lor s!ilb). Then ftod fig 8 Ead onl rhc alftud. of ihe M@r wirh Ih.
coftrpo.ding bnghh€s rhar @Des our to be, = 1.9 d€gr*s. This pmduccs a poi on
!h. visibility curye jn Iig 9 1hal shows a rcta onb€rwentheahruderofth.cresc.nted
ne &ld dip r below hdjrcn foi a panicultu brighrness of cre*enl and oa sky. Thus a
visibilitycure isa coltectionofpoinbG,i =//r), shere oe bnenbes of cr*.nt ad
thal.of sky mrh for cooshfl widrh of cE*nl. The qucslion is rhar fig 8 giv6 rhe
brishl.ess of&c tull M@n (dound 30 d hiiur.s Mdc) and rh€ cGcenr is eeneo y
less rhan t alc minule in width. Bruin Galias this probteh bul t.av$ i! s ir is by shrinS
Oat any dikrcpalcies shau b€ accounrd for by soh. rtnd of .Gcsbh,, taclor As
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