The theory parameters which result from the analysis of these data are listed
in Table 6 (click here), which will produce coordinates in the B1950 frame
when used with the galsat software.
A future paper will document how they, and any other set of galsat parameters,
can be transformed to the J2000 system in a manner such that the galsat
software will directly produce J2000 coordinates. In Table 6 (click here), the uncertainties listed for the 
and 
parameters are the
formal errors obtained in the estimation process. By comparing the coordinates
of ephemerides E3 with those of E5 and interpreting those differences to
represent a 1-
error, we obtain a scale factor which should be applied
for the formal uncertainties listed in the table. That scale factor ranges
between 2.5 and 3, so we recommend that the formal errors be multiplied by 3.
The derived values of the angular variables for E5 are given in
Table 7 (click here). The series coefficients for satellite
coordinates 
and 
are
summarized in Table 8 (click here) for the E5 ephemerides.
Representing the Jupiter-equatorial projection of the orbital radius by 
,
and the true and mean longitudes by 
and 
, respectively, then
the equatorial radial component
consists of cosine terms
while the longitude component 
consists of sine terms
and the latitude component 
consists of sine terms
As developed by Sampson (1921, pp. 229-230), the "time-completed'' 
may be defined as
where t is "ephemeris time'' (TDB).
One can employ the time-completed to compute the latitude quantity
from the shorter series for 
via the relationship
It effectively amounts to calculating the latitude perturbations
as a function of true longitude rather than as a function of mean
longitude.
The Jupiter equatorial coordinates
are computed
from the orbital components 
using the equations
The Earth-equatorial coordinates 
are then
computed from the Jupiter-equatorial coordinates via the rotation
matrices
It is these Earth-equatorial coordinates 
that are provided by the
galsat software.
As described
in Theory, the
Earth-equatorial coordinates are constructed from the series for and by the relationship
where the right-hand sides are the result of computing the series given
in Table 8 (click here). The third equation for s(t) employs the
time-completed 
to evaluate the series for
and thus to obtain s(t).
The adjustable parameters and for ephemerides E5
in the B1950 frame are given in Table 6 (click here). The derived values of the angular variables for E5 are given in
Table 7 (click here).
Acknowledgements
This paper represents the results of one phase of research conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The CCD observations were made by D. and A. Monet of the USNO Flagstaff Station and were processed into right-ascension and declination normal-point residuals on a fixed ephemeris by W.M. Owen Jr at JPL.
and
for E5 in B1950 frame [see also Tables 2 and 3]
Table 8: Series coefficients for E5
Table 8: continued
