Visibility of Luna and Lunar Crescent

BdicaUy a nhcory of pldelary ed lund motion involvd inies ionolasysrcm
of di0eGnial eqladoi dat constin&s th. major pad of th. sfudy of elcstial n46mic'
Therc & i. gddt t$o.ppoachcs for slving such dyndical systctu, ealytol ud
nusical, Anallri€l nerhods m b6ed on solutio. by Iouder sen€s ed thc Poiso.\
S€lies. Thc ELP-2000-85 (Chdprcnl€r,al, 1988) is semidalttic sd has be€n obla'ncd
frod a fil o f ELP-2000-82 (Cn!po!i cr. al. I 983) to th. nlncrical inrcer.tion of lhe .lei
Propulsion Labomrory DE200/LE200 (Slstrdish l98l). P@$ion in this o@ry ha b€en
$keh iion Lasrar Gsklr, 1986).
For te an lylic par! ELP-2000 Fpet€s th€ nain lEblm fbm th.
penurbarions. Th. 6ain problem tak s into accout thc &tio. of thc E nn's ce E of
m6s aid lhe acion ofrhe Sun's orbir aound lhe Eorlh-Moon baycentr. such lhat Ihe
Sun\ odit is asuned to be Kepl€rid cllipse. This rcrulls inlo Fouri.r series w'lh
numdical c@fiicie s snd ar$mdb th.t m suns ol mulripls of fou fundade.tal
paBmeted D (diffeence of ihe ned longitudcs of the Sun ed $e M@n). / (mean
monaly of rh€ Moon), l(hem anohaly of $e Sun) lnd a (M@n s argumen( ol
h ude). Tlis main problem 6uhs inlo dne *.ies fomnld for Mmn\ longitudc.
ladtude and gocenrric disrscc @daining 2645 rcos in all. Apan flofr lh* *rics
acrons of all rh€ other significant objects in solar sysren dt consideed N
'Fnurbadons lo ihc mdin pbblen lhol include:
L tndiKr pl&c(ary perturbarions rbar re induced by lne diff.tsoc.s b€lwecn
the lrue orbit of the Sun aound lhe Eanh-Moo. bdycenue and tssuned
Kepbnm Elliplhal orbil oflhc Sun *uned in the min Pmblem.
2. Dir€ct planerary penub.tioN due lo etions of othr plan$ on ibe M@n
lor borh the direct ad rhc indt€ct planetlry penubalions lhe ELP-2000
co6id6 th€ orbib ofthe pldct giv€n by BGlagnon\ VSOP82 rh@.y.
L P.rurbations du. ln€ figues of $e Edh md thc Mon (Moons, 1982).
34