Visibility of Luna and Lunar Crescent

a - sdimjor uis of th. dbil
l, = m@ ld8itlrL ordF ddt
l= ?,@$
p= sincr,i Dsino
c= si(Xi)coso
whec. is thc.@eotriciry ofthe orbn, r is ln. bngnud. ofp.dhelion, i ir th. incliodon
oflh. orbit fmm rh. plD. ofeliptic dd O is the logilud. oflh€ e.lding nod. oa th.
olbit. €.cholth. rcctarsul$c@rdioat (X L a or &c aph.ic.l polar coordimt€s (2. I
t) is u.xplicir tunctionofiime ed is inlhe forn of p.dodic eds md Poison $ies.
Every lcd ot Ues $.i6 is in fic tod of:
I"(ssii9+ I:cosp) or 1"..i€os(, +c?)
(2.2.t6J
$,lEE a - 0, l, 2, l, 4, 5. I is tn. tire in lhoFnds of.,ulie )€s fod J2000.0, i.€.
f=
165250
e=ia,1,, i
= I to 8, ! reprsent rh. m.m longnud.s of the plancc Mercury lo
= 9, l0 6d I Lc rcpllsfl th. Dclawy sgmen& of lh. Men D, F md
The hsl of I is the na longiMe of U. Mon Bivd $nh 6p€t to lh.
tlay. In thc ah@te €xpcsion,
B= Za,^," + P
c=>d,N, 12.2.11,
S - -,asinp,
(2.2.r8)
l8