Visibility of Luna and Lunar Crescent

the lonsirnde orthe sd, Arc{f-*pdtion fa.tor, Sitd by (3.3.10), Esdnat d Ripencss
Iuclion, ,{.r olcularcd eqution (3.4.2), Ar6of-epdalion ractor, Aversge Ripen.ss
Fwrion X., calcllared Ning avcds. tu = 10.5 d.gEs dd lh€ €quarion (1.4.2), Aclul
RiDene$ Fucrio. ,Rdy calculated sins equtioh (3.4.I ), AP-" the difie€ncc of AveEge
RiFn s Fwrion & th. Acrul one. Th. ribL l.l. I des nor show thc visibility @luons
s tbis table @mprises of css wher ihe cesftnt Ms r€Podedly seen withont oflical
The lsbl€ is soned on the values ofd&y. On the basis of a clo* dalrsn of the
results of conparing ARNi ihe dilleences of Av.lage Ripeness Funclion valu€s End lhe
Actual Ri!..ess Fuclion v.lucs we ob*de dEt:
The Tablc shows ft.t lh.E are only 14 pGitive sidrrines out ofa rolal nmber of
196 positive siShlings that are nor according lo lhe Lunar Ripe.ess t { (ARo, = Rn",
The€ a!. no posilire siSndne wirh A&q < -1.58 wirh or wirhour oprical aid the
Ens€ in wnich l8 aft.npb have ben nention.d in the lne6ud. We consid€r it as
Coup-A for thc Modificd Muslin Lund Ripencas Las lhal we slal. ih ihis erlq 6:
''tt th. tlill..e,ce ofAv.rase Np.ts Fanctior R-, omt the Actuot Rip.h6s
Fu"cion Rro F /Re) is l.ss nnh -J.6 it is ihDossibl. to see nE n.N luat .rcsc.nl
tor att ldtitula uith or Nilhott optical aid'.
The ncxl I27 c6es dc grcuprd 6 coup-B. Therc de la (llolo) mked cye
viibility cdes, 25 (19.?%)binoculd visibihy cesdd l6 ( 12.6%) r€lesopic visibiliry
cses for values of AFw lying betwen -1.58 dd 0.0. Oul oflhe 14 natred cye lisibiliry
ca* in thn range, threc lery low AR{yfvalue cdcs have comon chancterisdcs. Th.*
e No. 286. 2 dd 2?2 witb AR.!i valu. -3-5, -3.4? md -2.88 All lh* c4s m ner
autumnal.equiiox (Sepr.20. Oct.2l &d Ocl. t epecdvety), €r€$enl hs oldc. age
(39.1 l, 39.24 dd 4l .91 hous Elpectiv.ly) md hav€ consqueitly larger phe.
l0t