Visibility of Luna and Lunar Crescent

L
2.
L
Pl&erary otbiB d. clliptic with lhe Sun a1 one ol lh€ foci.
R.di6 vdtor of ! pldel (V@lor dnM liom the sun lo rhe Pld€D
sw*ps equal &.a5 in equl lihe jorensls.
Th. sqlle of rhe Friod of rcvolulion of a Plder eund rhe Su is
proponionalto lhe cube ofils dea. dblance ftom die Sun.
N€fion nol only prcent€d his Law ofUnive6al Gralilaion but verified KePleas
of Pleetary Motion usi.8 lh. tnw ol G6vilation. According to N€Mon s Larv rhe
of atmcion beM.en two bodi6 wilh nas*s 2' ed ,, pl@d 6t a dista.ce /
F =c!+i
(2.2.r')
The force is aflnclive and G is the PmPonio.ahy constant dllcd Univ.dl Cavilalioml
Consranr (6.6?2x 10 'r-)*s rrr). i is enhs dit€ctcd ircn ,L to -r or rron ',rou|
Frem rhe ddc of publicalion ot tte'Priripi.l bv NeMon in 1687 a nudbet o'
astlononeB, physicisrs and na$cnalicians conribulcd sisnilicontlv in $e dcvclophenr
of th. lndesl..dins of Lud sd Plm€hry dy.amra.
Howele. at lh€ time of NeMon (and p€ftap3 lill lodav) the dvnanics of lhe Moon
pa*nred sear dilficuhy rhar forced Ne\\'lon lo darc thal ",',e Ltmr theo'v nale his
he.l ache dtut kept hih aeake so olen thut he vorld think o! it no norc " lDanbv 1992)
He had tlitficulry in describing lh. modon of Fnge (the poill in lod orbil cloesr ro
the &nh) and could explain it ro only withi. m accurev ot 8 percenl Clanaut (1749)
appli.d ml)lical merhods ad succeded in explainilg d€ molion of p€ngee bv 6'ng
seohd o.der approximation. He published his lraorP de Ia /,,e md a se! ofnumencal
tablcs ih 1752 ior computation of lhe posnion of fie Moon. the Eost sisnificmr
contribudon frcm Euler appered in l 7?2 shcn he tublish€d his srcond lL@ lh'ory
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