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Position of Earth and Moon
Tab.5 gives also ecliptic positions of Earth and Moon.
DE200 and VSOP87 give only the heliocentric position
of the EMB. DE200 gives in addition
the geocentric position
of the Moon. If both values are given the position of the
Earth can be calculated exactly (within the IAU1976 system) using
the mass ratio Moon/Earth of
[A. K6] (or its respective value used for the ephemeris) by:

(31) 
The velocity vector has the same transformation. For the VSOP87 system we
apply following formula by J.L.Simon [personal communication] describing
the rotation of the Earth around the EMB:

(32) 
where is the Delauney argument from eqn.3.5 in Simon et al. (1994):

(33) 
where the rotation period is
.
The Earth velocity vector can be calculated
by

(34) 
where
and the ecliptic angular velocity vector is given by
.
If only
and are given the ecliptic position and
velocity of the Moon can then be calculated by

(35) 
But the precision of the resulting lunar velocity is rather low (190 m/s).
Neglecting the difference between
and
increases the total error in the Earth position to (EarthEMB in Tab.5).
For slightly lower precision without solving the Kepler equation (26) the
geometric ecliptic longitude of the Earth
can be calculated by the approximation given for the Solar longitude in [A. C24]:

(36) 
where
and the mean anomaly
for the EMB
can be taken from Tab.4. This approximation has also been used
by Hapgood (1992). The respective precision is (Earth in Tab.5).
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Markus Fraenz
20170313