Visibility of Luna and Lunar Crescent

t236.42664
(2 t.2)
An approximarc valu€ ofth.Iulid Dale ofthe Ncw M@n ir $cn giv€n by:
JDE - 2451550.09166 +29.5JO58886t.t+0.00015437..r -0.OOO00Ol5
j.r
+ 0.000000000?3' r!
(2.3.3)
$herc t i. d inteSer Thus @ording ro this fomula rhe for t = O |h€ Jutiil Dar. of$c
lid ces.nr ofycar 2OOO is 2451550.09766 lhar is J&ury 6.2000 ar I8n r4m, md
4l *!. I of dynlmical lime. For a horc accmle valu€ oa ihe Julia D.te of thc New Moon
lhe p€dlrbation tchs due lo lhe Sun md rhc planer ar€ added, Thc pertuibafions tenrs
due to thc sun d€ given byl
x= -0 t07 2.SlN(M )+ 0 I72J t
T
EISIN(M) +O.0l60A.SINOr M )+0 0lAj91stNe,F)
+0.007i9.E"'lN(M -M)-O 0O5 1.t.ErSINtM + V +a 0a208'E^2istN Q,M)
0 00| t t 'SlN(M -2.F)-0.000t7.StN(M + 2*F)+O OOO|6.E.SI^-(2+M, + M)
-0 000J2.slN(3.M )+ A OOO.| 2+E.StN(M+ 2tF)+0,aoB8*E.SIN(M_2.F)
-a 00021'E.stN(2. M'-!r' o 0u | 7,stN4.] 0.00007.stN(M'+ 2.io
+0 0a0u.slN(2.M -2. F) +O.00001'S!N(1.M)+0 \oaol.stNi,,t-+ M-2+F)
+0 0040j.SIN(2'M + 2.FrO 00O03.S|N(M +M.2.F)
+0. 0000J.StN (M -M + 2.D -0. @OO2.S|N(M. -M). D -O.O0OO2.StN(r. M, + M)
+0.00002.s1N(1'M)
Q).4)
wherc ,r,1 = rb. mce &omaly ofth. Sd al ihc JDE
= 2. I SiJ +29 I A5 3567.k-0 ,OOO0 t I t -0 oaoooo I I I
(2.3.5)
M = thc mee anomly of de Moon d lhe JDE
= 2A 1.5613+ J85 8 1693528'k+O.Ot 07j82N I +0 OAOA I :38. I
-0 0A0A0A0,8. 11
4l