Visibility of Luna and Lunar Crescent

rr' = ls<t - c.{A RCv).os(D,4z))
(4.2.D
a$uming ih€ seFi-dim€ld of tne M@n to be 5 con$lnt 15 dc ninutes. This basic Daia
cs b. t@sfomed inlo .Lt! rclating the width of the cesenl ed @ of lhion ARCV
likc thlt in table 4.1.2 ofYallop bed on Btui.. Yallop tr4Iomed ihal d4ta fittine it lo
r cubic polynomial6ing 16l sq(@ appoximdion 6d ohainqlIh. following eladoni
ARCy = ll -aJ7l - 6.3226u/ +0.7119tf1 -0.10)8w'
(4.2.)
While applying Brui!'s melhod (€qu.tion 4.1.2) or lhe Indim method (4 2 2) $e actual
vidrh t/ sbould be consid@d (nol a @nstonl l5 e minulet. The method says lhat if
,4,RC,/ for lhe place of obseruation is norc than $e value of lhe right nmd side oa (4 2,2)
the .Escent sholld be visible. Thus a visibilitt pameler may be dein€d s:
V| -\ARCV (rr.8J7r - 63226W +073r9w'-0tntw')Jtto
(4.2_3)
Yallop €alls lhG ,/p 6 4-value. In g€n€tal if the visibilily pemetei /p n Positivc lh.
crcsce.l.may b€ s*n. Applyins this lisibility condnio. on rhe dala et of chaPtct 3 ii is
found rhot 16 positive sighi.Ss out 196 deliate fom this lndian visibililv condilion
Thcse d.viating cases ae shoM i. 6guft 4 2 1 as vhible ciescenls below the lndian
"Limit' ed re rabulated in rable 4.2.2 .nd ihe r€sults for cosPlele dao set ats prescnled
in rpp€ndixlll io the s4ond colmn und.t lhc heading "Models" l. view of lb'sc
eluhs w find rhar rhe Bruin's Mo&l is ndgiMlly better ihm Yallop's crnction fo! this
Yallop ds @nvert d Maundd's condilion tom DAz-based lo lhe width-bsd
and oblaircd lh€ foUoving cubic reladon b.tw.et ARCV ed W:
ARC|/ lJt78) e.Olt2w - 2.O1OaW1 -Ot16OW' 142.4)
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