Visibility of Luna and Lunar Crescent

A I 2= 1 6t. 7 2+24. I 98 I 54.k
A I 3= 2 39. 5 6 + 2 t. 5 t t099.t
at 1:33 t. t5+ 2.7925 I E.*
(2.3.22)
(2.3.23)
(2.3.24)
Tlus $c ,ulid Dlle of lh. Na M@n ie giv.n by
JD=JDE+X+Y
(2 r.2t
Thc dm€ deeribcd by this dat is lhe DlaMnical Timc and lhc coretions for Al mcr be
mad€ lo get $e Universal Time (discu*d in 0Encxtarticle). For anr l@al coopuralion,
th. Ld.l Zonc lide and d!i. n6r b. calculated ftom |he UniveMl Tim. and dale
ohaincd abovc on rhe bdis oatbe lonsirudc ofany place on rhe Eanh. Thc darc h $en
de day of conjuncrion fo! the place and rho rime of conjuncdon (he bnrh orNcw M@n)
can b€ dy rinc fom 0- 10 23r" 59'" t9h on thd dav.
2.4 THE TIME ARGUMEI{T
ft w6 mentiohed earlicr thal rhedynahicsofatl soltr systcnr objec$ isdescibed
by lomula b6cd on 6adcs of Cl6sic.l Mcchdics and lhe Relarivisric Dyneics in
t.m3 or rid€ serics. In order b ersriv.ly ue rhcsc fomulas an apprcpriate ?rrs
argMerr cotrcsponding to rhe honeht of obseiving the lunar crescenr at my place on
lhe surface of the E rth h6 io be €valualcd. Such a lime a.sudent h6 ro b€ co.inuou
and mui halc a clearly dcUncd point of i's beeimine (|he aro rine). called .p€h.
various theorics and problems uF difercnr .pochs depending on rhs co.rext for a
geneEl consideFtion in pls.lary ad luE dynmics thft ,re lwo ihporlanl epochs.
Th€ nr$ of lhese epochs is a oonefl in edote pdsl coftsponding to rhe Noon al
G@nwich on Janlary l. 4? l2 B.C.E. on th. Julid c{l.ndar (or Nolember 24, 4? I I on
Cdgode cal.ndtu) (R€ingold & D.Rhowila ?001), Fren $is pojnt of timc rh. rine
elapsed tiu my laler point oflime in number of days md a possiblc fierion ofa day h
4l