Visibility of Luna and Lunar Crescent

Onc. lhe lincs of fting edor selting ofbodr fie Sun 6d rh€ Moon are oblained
on€ d work our att th. p.mete6 of fic import,nce for lhc atrsl (ot la0 visibilitv ot
rhe n€v (or old) lutr crc$.nr.
2.2 DYNAMICS OF THE MOON AND THE EARTH
T!. dcv€lopn€nt of nodem dy.di4l lhoics for $e sole sv$em beg& wnn
$e discov€ry of Laws of Pleel,rf Motion by Jobannes Kepler in the 16('centurv At
aboul rhe sm.lin€ haac N€Mo. cme !p wilh his tt$ of Motion dd the Univeisal
Law of Cdvi|llion. Whar fouowd is a long histo.y ol developool ol nathemtiql
techniques lead i ng 10 the fo m! latioi o f Cd 6tial Dynam ics The e llois w.rc d ir4t€d to
describcrh€dorionofplanctsandlheirsal.lliles,dteroidsand@nebinordcrtopledicl
then positions in tuturc with accey of SEater 4d g@l€r d€sG Conuibntio.s of
Eul€r, Laplace, Poison. Gauss, Olber, Cowll. Encke, Claittul. Hesn. D.launav. Hill
and Brown. besides daoy olher nahemalici.ns and astdnoneb. bare ben oi grat
si8nificancc. A nunbei ofcldsical md nodcn books de now available thal d.scribe thc
d€rails ofd.F conuibutions (Sna41953. Deby, 1992, Plunmer, 1966. Pollard 1966.
Woolard and Cl€nene 1966. Bouvct lnd Cl€mence, 196l elc.). Contibutions ae oho
availabl€ rhat give delails ofthe lund dynamics (chaplont_Touze dd Chapront. l98l'
1991. 1988. Chaproni er. al. I998, Srandish I981. 1998 etc) Einsrein's theolv of
rldrivu suc(aded in dc$nbrns the molion olthe penhelion
The satllite to planet nss !.tio in case of lhe Moon_E nll svst€n s larg€sl
( 1.23 x l0-r ) in compdi$n ro ey o1h€r saEllite-ple.t pait (lh. nexr ldecar beins lhar of
Triton-N.Drune l6s ntio = 2 i lO I ). Thccforc rhe Eanh do.s not prclid. lhe dominmt
efecrive fore aclins oh lhc Mooh.It is not only lhe Sun bul all msjo!pltnels and la€€r
of lh€ dtdoids lhat @nkibute 10 th. cffcctiv€ force ,cting on the Moon Thus d
cph€ncredF prcpded *ilhout tdtinS into eout all lh.e contibudons b boud to be
emn@u' Mey of the epheheedes of $. Moon of.dlv dsvs, both b.lor' md aliet $e
lomJlauon of $e Neqonie ndhtuics. weE bded on obieBed sd lompukd
averages of various Lnds r.laled 10 lhe dyndics of lhc Moon
30