bill@utastro.UUCP (William H. Jefferys) (11/04/83)
I thought that it would be useful to give the locations
of the L1, L2 and L3 Lagrangian libration points for mass ratios mu
close to the Earth-Moon mass ratio. The coordinates rotate with the
origin at the barycenter (center-of-mass) of the Earth and Moon; Earth
is at +mu on the x-axis; the Moon is at mu-1 on the x-axis , so that
the unit of distance is the distance from the Earth to the Moon; the
mass ratio mu is defined by
mu = M/(M+E),
where M is the mass of the Moon and E is the mass of the Earth.
For the nominal value E/M of 81.3, mu = 0.01215067.
This table is taken from V. G. Szebehely and C. A. Williams'
article "Collinear Libration Points", which appeared in
*The Astronomical Journal*, Vol. 69, pp. 460-470 (1964).
Please note that *none* of the libration points is at the
barycenter! Szebehely and Williams' data show (in other
tables) that L2 --> 0.5 as mu --> 0.5; this is the
equal mass case, the only one for which the barycenter coincides
with the libration point L2.
mu L1 L2 L3
--------------------------------------------------------
0.0110 -1.151081 -0.842735 1.004583
0.0111 -1.151496 -0.842216 1.004625
0.0112 -1.151907 -0.841699 1.004666
0.0113 -1.152316 -0.841186 1.004708
0.0114 -1.152722 -0.840674 1.004750
0.0115 -1.153125 -0.840166 1.004792
0.0116 -1.153525 -0.839659 1.004833
0.0117 -1.153923 -0.839156 1.004875
0.0118 -1.154318 -0.838654 1.004916
0.0119 -1.154710 -0.838155 1.004958
0.0120 -1.155100 -0.837659 1.005000
0.0121 -1.155487 -0.837164 1.005041
0.0122 -1.155872 -0.836672 1.005083
0.0123 -1.156254 -0.836182 1.005125
0.0124 -1.156634 -0.835695 1.005166
0.0125 -1.157011 -0.835209 1.005208
0.0126 -1.157386 -0.834726 1.005250
0.0127 -1.157758 -0.834245 1.005291
0.0128 -1.158128 -0.833766 1.005333
0.0129 -1.158496 -0.833289 1.005375
0.0130 -1.158862 -0.832814 1.005416
Trying to shed more light than heat, and publicly apologizing
to Roger Noe for offending him, however unintentionally.
Bill Jefferys 8-%
Astronomy Dept, University of Texas, Austin TX 78712 (Snail)
{ihnp4,kpno,ctvax}!ut-sally!utastro!bill (uucp)
utastro!bill@utexas-20 (ARPANET)