Visibility of Luna and Lunar Crescent

Solsr Cal.nd6 m b4d on the ulrl motion of lhe F-!nh @und the Su..
''ycai in such calendds h ihc "Trcpial Yee, defined abolc. Thon the lcng$ ota
'tropical y€&" (Dogger, 1992) b givcn by:
365.2421396698-0,0000061s359r-7,29xr0_r0Ir +2,64x10'07r (1,4,1)
7 s $e tinc in Julian cenruics sincc fic epoch J2000.0 gilcn by:
T-(JD-245rt4t0!t6525 (1.4.2)
vherc JD is rhe Julid Dat€ which is th. dm€ in .mber ofdavs ctaD*d sine heo n@n
at Genwich on Janua.y l. 4712 in Julid Cal6d{. Cwnlly thc loglh of t@pi€l ycar
n 165.2421898 days or 365 days.5 hos.48 ninurcs ed 45.2 sends. As it is nor a whote
number on yer of a eld calodar @rsists of cirher_ 365 days ot t66. tn old Jution
crlendr cvery fourih yc& @.lained 166 days (i.e_ a teap yed) a otbq yff conhincd
165 days In lnc cuftntly us.d Cregoiian calendr! the leap ycd rutc is nodificd. A
century ycd y 0ike 1700, 1800 elc) whict is a lop yer i. Juli& calmdtr bur is nol
complerely divisible by 400 is nor a tep ycar in OEsorian mtcndar. Thus in crer,400
yeas theE ae I 00 l@p y€6 in Jnlitu Cal€rdff wiced in cESori& calqda, rb@ are
only 97. The s€etu od nfuy o1her natMl pbsomcna toltov lnis sotar cyclc. sp.cialty
haBcsing rides, lhe length ofdays,lbc dmes of imir, suser, sunds. etc. I$e JLrtian
calendar B insrilured on Jdu.ry l. 45 Bc by Juli$ caM. wirh rhc h€lp of
Alciandlie stronon€r Sosigm6 &d w r nodificadon ofdc Roman Republidn and
the ancicnr Egyptian calendaB (Michels, 196?). WtEcd lhe crcso.ian catendar was
n(csibrcd du. to rhc facl ln.r dqinS oe od . lDlf nil.mia lhe Julim otcndar w6
displaed from the ssonal vsiatioos by s much s l0 days. Thus pope Crcsory X t
corclnukd a conmission in l6rt €qrury AD for lh. csl€ndar Efoms. The dain anrhor da
dE nN sysrem w6 slononer Aloysiu Litju of Naplcs (Coync el ,t_ 1981. Dull4
1988, Moyer. 1982 ed Micb.k 196?). When it ws implcn.nted ofljcialy. rhe ddre
October 4, I t82 (Thuday) in tne Jllie cal.ndar 6 fouosEd by rhc dale Ocrcb$ I 5.