Visibility of Luna and Lunar Crescent

An |pDDxiE.r. valu. of "'*" wirh e G@ of f.e d.,s m*! wll. If UE "yd" it r
vholc nmba $c algoriihn si!4 lhc ,!lie D.rG to! $. Nd Men th.t @6 cl@n
ro thc b.gimine ofthc !d".
otuc rhc ,ulid D.rc of$c binl ofrlE Nq M@n cl@n b lh. .xpdrcd d.y ha
b..i found tb. m. b inni.lly conwn.d lo lhc UniEEal rift dd darc ed
coneqE ly rhc le.l lih. and ddc. For ln.s convffirioE ftom Julis Dat. to rh.
le.l rim. ed drlc th. tehniqu6 of rhc .rricl. 2.4 6 u$d, Bcfoc thb im. lh. Ew
'lun.rion" h6 nor b.!un s no qNnid ofrlr visibiliry ofrhc Bw l|!w cEghl on rh.
A6ins bcfoE this rin . B.foE this tin. only th.'bld cG*dl" ce b. lat wn b.foa
rh. sutuie on rhc dry of onjudion or a dly o! tvo b.foa-
Ar dr rimc ot@dudion dc M@n n.y b. &rwhcrc wi$in . strip ot widd loo
18 eud dG elipric, i-.. wirhin 50 9 of rhc Sun. ap.n fom |h. ecume of . slar
dlips $G "@.nl'cxisl5 bul dE lo irs.xlrEh. clo*ncs ro lh. slai!8 su ir co nor
b. s..n ed ha ndcr ben sn,
Thc ndr inpondr p.md4 is $c l@.1 lim. of suel ed th. M@n $t Th.*
can be conput d for ey day of lhc yd Bins th€ r.chniq!.! of $c anicl. 2.7. Howvr
$ce rehniqEs 'lquiE
th. dctmin ion of th. c@diEtcs of both lh. Sln &d th.
M@n for D dFckd rihe of lrsi! dsing dd s.ltinS of dh of thd. Thc c@diDL3
of th. su !rc obl.incd usi.s dE VSOPE? fi6ry of Brdagnon ad fEncou {or a
sihplificd v6ion sivcn by MeE) &d bricfly prc*ntcd in aniclc 2.2 Dd 2.6. Sihildly
rh. D@iF @rdidtcs of thc M@n c oh.in d aing th. ELP2000 of ChrFo -Tot
ed Ch.pont pr*nrcd in dticL 2.2 and 2.5. Th. .oddinal6 ofrh. Sun &d lh. M@n
lhis wr e th. SMtric sph.dcd pold c@dinrl.s (dis1@ P. alatial lonsilud. r
dd d€ c.l.nial l! rud. n. And @n cdon for .bdnlion thc sc e lMtfomd lo
th. g.on.rric .q@torial @tdidlcs, dght s.cioi o &d &cliDlion 6. Firlly th.
roFcc'tric dSlu e.sion ed d.cliMdon !r! oh.incd itld.s irto cosi&tstion thc