Visibility of Luna and Lunar Crescent

SuDpoe ('-.r",/.)!d (.,,r",t) E thc p6isc dist nc6, etipri. tonSnld.
..d Oc hnud. of lhc Moon .nd rt Sltr Bperiv.ty, Ff.Gd ro fi. nsr cquircx ol
rh. d.y of @njucrion. For .ny t@tor on th. Esnh wnh Gcri.l eotdimrcs. I rh.
rcGrdal lonsiud. ot rh. d@ .d t is rh. Lcid.l tlrirud., thc ti6t scD i. de
d.rcmimtion of dc visibihy ot ft. nd t!@ cE$.ni is ro d.r.diF rh. aclut
dyMicrl tin (TD oi rD T., of rlE @njwtion. N.xt, om Eqdc coBidcrine rh.
la.!l tima ofslrdns ofrt. Su {d rlE M@n. IfT, lrd Tm (CoordiDr.d Urivcdt Tin.
TUC) bc lhe rinB of rh. lcat sunsa ud rhc hooEt, ihcn d. i* G$cnr h.y b.
visiblc only ilT, < To, This La4 to lh. p.md.r LAG - Tr - Tr.
Using th. cclipric c@rdiNl6 ot |he sun 6d thc Mon drt.ut.l.d for rh. 1.. o,
dy orho noD.ni of tiD., Oc cqq|oi.t @rdin c! of rh. |m bodiB (a.,4)!nd
(a..t,) cd bc oh.ircd. Vhcdd. rhc nght aeBion k $c djspt@mcnr of$. objer
fbm wdal .qdnox .long lh. cctcsli.t cqu|or (in $. q. qudtut s I ). md d js $c
delin.rion or rhe displ.ccftnl of$. obj.cl fbm dc pt.E or ue.qullor t c.l lour
Aigl. tf is rh.i oblaircd fon Oc dilT.Ene of thc leEt Sid.c.t Tin. (r_SD and rh€
ishr e.6iotr. This liMuy gies ihc leat horianr.t c@diiat s, dimuft (,r). rhc
displ&.md ol rhe objer fbi rhc diEcdon of lh. Nonh rowrds E 5r ,tong $.
hodenlal in l@l sty .nd rlE ald|ud. (r), rh. hciehr or rh. objer lbov€ hori&o. Aftcr
.djustus for $. cf@rioi ed $. h.ishr of rh. obencr's to..rion .bovc s.. trycl rhc
ropo..nric c@rdiiaks (,4., rr ).nd (,{, .}. ) of lhe M@n and de sun, 6!..riv€ty aE
lo almosr all rhc nod.ls fo..&lid hoo!-nddng, rh. mj.nt s rcll .s lh.
mod.m, th. difieE@ ofeinurlrs (D,,tz = l!r. - /r.l. can.d rlodvc szimurh) .id thrt ot
rltiluda (ARcv - ,- -/'., c.llcd e of vision) $ rhoM in rhc fig 1t.2, at th. rin. of
lc.l su@t T, Th. e of vkion is ale l.m.d s F of d.fft$ion. TIF tig, |.t.2 de
show rhc *pa{ion bctwn ln. Sun lnd rh. M@ that is tsM !s 0E .rc of tilnl
abbrtviacd s ARCL .rd is .ls tioM $ .tong$ion.