Visibility of Luna and Lunar Crescent

As mc ioned abov. dE Mulin sao&Ders have alaldy d€duad from
obrpatios lhar for very thin but visibl. cE$ent mirimm ss @ 12 lime degds (48
minureO dd for d {ider but bmly vbible cresent mininm as w6 only l0line
degl6 (40 minulcr. This nininm as ie acturlly dep.ndcnr on the width of $e crc*ent
rhar @ be dedvcd 6ins (2.E.E) dd (2.8.9).nd rhe Elarive atitud. (ARc9 thar cd be
obtained using (2.8.5) for th. sun ed the Moon. Th. issue shall b. dieussed in noe
d.tail larer. Usins 0.3.10) rh.t shows 6s beins dependent o. the lisull dimers (in arc
minulet of lh. M@n in our sky one ce compute lhc Lun Rip€i.s Fudio. A(,i9)
as henrioned by Btuin (Brui., 197?) or tha! is siven by (3.3.6). Aaodihslo Bruin rhe
rul. d€dr€d by M6lims w6 thal if thc lalue of HS calculat€d using (3.1.9) equals or
exccds lhar @lcolared by (1.!.6) rhe c..s would be visibl. orhcNi* nor. In thn
work this rule has ben named M6lin Lunar tup€ness Law or sifrply Lumr Ripen€ss
According ro Bruin (19?7) $e valu6 ol HS de.ored a R()., 9) obkin.d fron
(3 3.6) seE pGsenled in rhc $+ lled Lunat Ripenss Tables sDd fisr visibility ofne!
Lunr cmcent ws walulcd by Mulin BltonomcB usiog rne sboE rul€. In lhis work
HS a3 deived tom (3.3.6) h d€nokds,l4 and:
^d.,
- sin r[sin/, r.nre+^t+lM ts (l.r.r l)
Fo, a fixed pl&e (e constal0 it is noted lhat forsDallvalues ofl,, sin ly
is also smatl
&d lko n ahosl sme as rv ,j. Bui when the *liplic is wll inclihel io$&ds lhe
hoien (q + A is large bu lcas rhan 9oo) 1r'4, nay becode noE rhan 1! ri(iflv > 0
snd ecliptic is roweds nonh) or renain le$ rh& 1, - .ls (ir pr, < 0 and etipric is
iowdds nonh). Ho@er,{da is endely independenl of Oe se@. aod dep€nds only on
rhc rcladve coordinates of rhc sun md rhc Mood. As rhe major componen in (3.1.t l) is
lhc diferenc. ol longnudes of rhe su and lhc Mooh ,taa h closely linked to ihc ACE of