Visibility of Luna and Lunar Crescent

,is = I +l8O! Fs= -e 12.2.2t)
ond the hcli@entric dislanft ofthe E.nI is smc as th. s€@edtic
distanc' oflh€ S!n'
2.3 BIRTH OF NEW MOON
A3 menioned earlier the Moon in ilsjounev dound the Eanh llavels arcund 12
dcgrees cvery doy in our sky and $l.s ovcr tic Su in lround €vcry 29 5 davs whc' rhe
Ccoc€ntnc Lonsnude of the Sun e.l lhe M@n N se rhe nonent is tnoM s tnc
Tine ol Bidh of Ncs Moon Tbe dudion berve€n two succe$ive Binhs of Nev M@ns
is called lhc Lun.lion Period Ho$ever dE Llnal'on petiod is n
from 29.2 days lo 29 8 davs This is rh. cMn b€hind
'ons
irt tu'd mon$s of 29
d.ys €ach or lhe con*culive luor monlh of lO davs cacn For fi€ tine ofBinh ofNew
Moon one requiEs to find lhe noment when rhe seocentric lonsilud's olilt Moon and
rhc sun coiNide Thus one needs to lracl lhc lo'Siludcs of eeh of thcn rinc
Coisidcrins $e najor rcms oa lhe line scrics fomulac fo' lhe lonsiodes of the Sun md
$c M@tr in th€ planeurv rhcorv VSOP'2000-8? and lhc l(nw th@rv ELP-2000'8? $e
noment when thc rwo lonsiludes aG sMc can be evaluatd An alsori$m due b Meeus
(Mceus, l99E) for $e dclemiiation or $e rin' or Binh of Ns Mmn is as rollos:
On a!c€8. lhe tnpic.l Y€d (dudiion betw'en t*o conseculive
passages ol lhe
Sun lhroush equ ox) iscudcnrlv 16524219 davs (from (l I l)) Thc avedge svnodrc
Monrh (trre intedal bclwccn r$o cons{u'r\c t\e* Moonsr toten o\er a rcn'ur} ii
29.530589dar(fon (1.3.3)). 'Ixus in oft topical vear rh're aG otr a\€Esc 12 1682664
Synodic mo h5 Thqeloe since lhe $ad of lhe vcd 2O0O i e J2O0O O the nunbei of
synodic monlhs elapsd oregrveh bvl
t = (f,' - 2000) x l2 3682664
(2.1 l)
and lhc time in lropical ceoruries el.Psed since J2000 0 is Siven bti