Visibility of Luna and Lunar Crescent

ine argunent md the explicii tin€ eries fomulas of the ELP ed lbe VSOP th.
c@rdicrcs of lhe M@n ad rhe Sun m calcrl.t d for fte s.me i6i'nl of rhe day or th.
-
d.y aAq @njudion- In s. @ spheric.l pol& @ordimtes a th€ gtucsrdc disr.nce, X"
th. ecliptic longitud. and 9. the dcliplic ladtude, refeftd b as th. Ediprh Coordimles.
Tn* c@rdinals i. lh ft sqt dsirely ro obrain rh. im€s of th. Su$.i &d dE
Mooisr (or rhos of $e sun.ie ad noosi*) for 1hc day in qu6rion.
TIE lune ca* (or rhc cE*enrs of M€rcury &d venls) k fomcd by $e
region of $e lbn suface tow,rds fie Sun tnar fa.lls belwn rhe two plancs rhrcu8} the
e E of rh. Moon, one perp.nd'.ulr ro rhe tine ol vi.w of fie obFn.. dd thc o$.r
FrrEtrdicule to rhe di@rjotr of rhe Sun. Thc nrio of rh. ea of lhis crcw md lhc
total dea of th€ Lund disc is called lhe.phs.. ofihc Moon, The phse ot th€ Moon is
di@tty r€laLd ro rh. seperion bcrwen rne Sun and rhe M@n or .lorgation.
The Astronohical Alm$ac pubtished amually shtes lhar $e dew luna! cr€scenr
is sencElly nor visibtc who irs phe is te$ lhan t% (Askomniqt Almde, 2007).
- This ha prcv.d ro b. nisl@dine in vicw ofihe fac| rhar the brightn€$ oflhe csenr
can sr.auy vary rbr the ehe vatue ofthe phas owins lo the varyin8 dislanc. ofrhe
Mmr froh $. Eanh. The Elrri-Mmn disunft Eics foo t5O $o@d kitomcrrs lo
400 lholsdd tilomer$. Tnus when dosl lo ihe Earlh the luntr 6cshl hay be
vGibl. wilh ns pnsc much l€s lhan r % and in cae of fanhd ir nsy not b€ vkible evdn
wilh ph& g@ler thd l%. D@ ro rhis varying disr.rce rh. siz of rhe tuu dis i. fer
cha.ges. Closer the Moon ih€ disc dppees larger. Th. Muslims had nodccd rhh vdhdon
ii th€ sizc of rhe luie disc hund I OOO ye6 aeo. tn rbe Modm rimes il was nol before
Bruin lhar lhc imporrace of 1he actul visibt. widrh of lh. lutu cllsqr M @liz4
Uhinately n w6 yaltop who ued the widlh of luo{ cr*cent in his ohe_psmei€r
nodel of tu4 cre$.nr vjsibitity etadng n b the ahnnd. of rh€ c@.nr on rh. local
orce rh€ sc@orric c@rdinar6 of thc sd md thc M@n e catcutar.d lh.
.fieIs oi Refracrion, Abcration hd fic pddta @ @lculat.d for llc.@odinaies of
2a