Visibility of Luna and Lunar Crescent

Seid.lm@, 1988). The TT is d.fined in FlatioD witb the "lnt matioDl Alonic Tine"
T"I=TAI+]2F.IE4
c.l.t)
Btce TAI it dgul.t€d &cording ro atomic rimc, In TAI $c b6ic uoir of rime is thc SI
sond {defined by Bueu Inremarional des Poids.l M.su6, BIPM, in t96?, a
dudlion of9,192,611,770 periods of rodiarions cooesponding ro lh. tmsition b€rween
uo htFrfinc levcls ofd.gbund slat oflneCesinm lll abm G.t tenerat.,2OOt)).
A day on rhk scale is 86400 SI seonds long {Astonomicat Atndrc, 200?). On rbe
other hand rhe clet dm." is thc Univ.Ml Tin€ (Ul denned wirb rcf.r.nc€ ro nem
sun and Nocialed vi1h thc Crccnwicn Md Sid@t Tim. (GMST). UT is detircd as
$e hour angle ofrhe Med Sun ar cEenwicb ptus 12i6. Due ro rhe in€euta ries in the
rctations of th€ Eanh ihcr N di$repancies b.reen the lwo rimes. rhe TT and rhc UT.
This dillcrcrce is ruferred ro as $c delht (At):
AI=TT-UT
(2.t.2)
Th.rcaore wh.nevcr w wanl b dd@irc th€ position of $. SM and lhe M@.
lbr a panicular lime on ou! clocks w€ have to fomutate rhe rine argudenr using rhese
cons'dcEiions othcnvi* fie clock dn. of the phcnomena shaU nor be appropriat€.
Finally. rhc lime arSunenl in drc rhcorics requi,es lhe delemimtioh otrh€ Jutim Dare of
the UT in question. TIE Julim Dale is th. sys!€h ofconrinuols limc sle lhar begins o.
Noon or crcen*i.h Jduary t, y6 -4?t2 (cdlcd lhc cpoch oftne..r!lian dde,) ln rhis
r,m€ scare tlre moment described by a date (CEeorie or Julie) ond rine (UT) is
considercd as rhe "nmb.r of dayJ,, d.nor.<t 6 JD, (consisting of a whole number
indicali.g rhc nuober of days .tapsed sj.ce tbe ep@h of Juli& Dar€ dd a filclion
d.sribine the flacrio.s ofa day after lhe whole number of dayt since the ep@h of
Julie Daie. Using rhjs JD for &y Domol lh. 1 is tten .ddcd lo .c@unr fo, th.
icguldnies in the oradon of thc Edrrb. The theories use tinc arghehl I lhat is on lhe
$al. of".umber ofJulio centudcj ehps€d rinc rh. epoch r2OOO.O. Thus usine tbn
21