A variety of different observational data types were employed in developing ephemerides E5. A new and very powerful data type of CCD observations from the U.S. Naval Observatory Flagstaff Station was used for the first time, together with very accurate Voyager optical navigation data from 1979 and the mutual event observations 1973-1991, photographic observations of D. Pascu from 1967-1993 and Jovian eclipse timings from 1652-1983. Doppler observations from 1987-1991 were employed to assess the value of the Doppler data and evaluate the ephemerides.
| Data span | observable type | observ. | % chg |
| 1992-1994 | CCD data, Flagstaff ra & dec | 870 | -52.6 |
| 1979 | Voyager opnav ra & dec | 366 | -19.0 |
| 1973-1991 | mutual events ra & dec | 860 | -55.5 |
| 1967-1993 | photographic ra & dec | 8462 | -3.2 |
| 1652-1983 | eclipse timings | 15711 | +2.7 |
| 1994 | CCD data, Table Mountain | 72 | +68.3 |
| 1987-1991 | Doppler | 50 | -55.6 |
By intercomparing various data types one learns of the strengths and weaknesses of each individual type of data and discovers inconsistencies among the data types. The data are described in Table 4 (click here), which also gives the percentage change in weighted sum-of-squares for ephemeris E5 relative to ephemeris E3. A plus sign indicates an increase and a minus sign indicates a decrease in the weighted residuals. The various data types were combined by weighting each observation by the reciprocal of its squared a priori standard deviation. A common data set (including weights) was employed to evaluate all ephemerides so that one can compare the relative merits of a given ephemeris to a common data set. Thus, although no CCD observations were employed in the development of ephemeris E3, the residuals of the CCD data employed in this paper are also given for ephemeris E3 so that the reader can make meaningful comparisons.
In order to more closely compare the various ephemerides with
the different data types, we present in Table 5 (click here) the residuals of unit weight
for each data type for the different ephemerides E2 through E5 by Lieske, as well
as for the Bureau des Longitudes' ephemeris G5 (Arlot 1982). In comparing
Table 4 (click here) with Table 5 (click here) it should be remembered that Table 4 is related to the
square of the residuals while Table 5 (click here) employs the square root of the sum-of-squares.
The comparison for Flagstaff CCD data, for example, for Table 5 (click here) would indicate
that the Table 4 (click here) entry should be about 
for the E5 vs E3 comparison.
| Observable type | E2 | G5 | E3 | E4 | E5 |
| CCD Flagstaff, mas | 43 | 40 | 43 | 32 | 29 |
| Voyager opnav, mas | 1309 | 1334 | 929 | 904 | 820 |
| mutual events, mas | 62 | 53 | 62 | 47 | 46 |
| photographic, mas | 107 | 106 | 106 | 104 | 104 |
| eclipse timings, sec | 55.5 | 74.5 | 53.2 | 53.9 | 53.9 |
| CCD Table Mtn, mas | 43 | 73 | 41 | 52 | 53 |
| Doppler, Hz | 15.3 | 18.4 | 13.7 | 11.7 | 11.9 |
The new CCD observations were made at the U.S. Naval Observatory Flagstaff
Station (A. Monet et al. 1994) during the years 1993-1995, employing techniques
developed by D. Monet and described in Monet et al. (1992) and in Monet &
Monet (1992). The Flagstaff data were processed at JPL by W. Owen who produced
normal-point residuals, typically from 30-50 CCD "exposures'', for the author
using ephemeris E3. Those residuals were then employed by the author to generate
pseudo-observable "normal-point observations'' by adding the residual to an
artificially-constructed computed position at the mean time of the CCD exposures
using the same ephemeris which was employed in computing the CCD residuals. Such
a "normal point observation'' could be employed with other astrometric data in
an analysis of the observations, and should represent a valid description of the actual
CCD observations. Additionally, the pseudo-observations will serve the purpose
of archiving the CCD observations in convenient form. In processing the CCD data
Owen would estimate the pointing and orientation parameters and employ a single
telescope scale factor (modified for refraction and atmospheric effects) for
all the Flagstaff data and he would use a single ephemeris (viz. E3)
which was not adjusted in the reduction process. If that procedure is valid,
then the pseudo-observables generated should behave like valid observational
data, viz. the residuals should decrease if one employs a better
ephemeris with the original pseudo-observables. It was for this reason that
ephemeris E3 was intentionally employed - it was known to need some correction
and we desired to explore the validity of the process of constructing normal
point pseudo-observables. If the normal points were constructed instead on a
different ephemeris, then the pseudo-observables differed by less than 15 km
(
) from those generated via ephemeris E3, even though the residuals
might actually be significantly different using the two ephemerides. That 15-km
reproducibility of the normal points is a good indication of the intrinsic
accuracy of the CCD data.
Some less-accurate CCD data from the JPL Table Mountain Facility (Owen 1995) were also employed, although with hindsight they probably should not have been included in developing E5. They did not exhibit the reduction of residuals with a better ephemeris, and that is believed to be due to the fact that there were too few Table Mountain data to adequately separate the orbital effects from the telescope effects.
The CCD data were processed using Lambert scattering to compute the offset between the center of light and center of figure (Lindegren 1977) and it is believed that the dominant remaining unmodeled error source in these data is due to albedo variations across the disk of the satellites. Recent estimates of the albedo variations by several scientists (Goguen 1994; Mallama 1993; Riedel 1994; Gaskell 1995) are not entirely consistent and for the Galileo-mission ephemerides it was decided to limit the processing to computation of the difference between center of light and center of figure due to Lambert scattering only, since it represents a reasonable first approximation to the scattering properties of the satellites if one excludes albedo variations (viz., effects which depend upon features on the satellites and which vary with planetocentric longitude of the central disc). The extrapolation of Voyager-derived scattering properties (which occurred at high phase angle) to the scattering properties of the satellites at low phase angle as observed from the Earth is not entirely satisfactory and the several efforts done to date are not entirely consistent with one another. It is hoped that some series of observations made from the Hubble Space Telescope will resolve the problems. Employment of Lambert scattering is a useful first-approximation. The differences between Lambert, Minnaert or Hapke scattering laws is minor compared to the albedo variations introduced by physical features on the satellites, which may introduce center-of-light relative to center-of-figure variations on the order of 75-100 km.
The Flagstaff CCD data were weighted using a standard deviation of 003,
which corresponds to about 90 km for these earth-based observations. The Table
Mountain data were weighted using a standard deviation of 
corresponding to about 150 km.
During the Voyager mission in 1979, some optical navigation images of the
Jovian satellites were taken from the spacecraft for use in navigating the
spacecraft to the Jovian encounter. We have 183 observations
of the Jovian satellites in right ascension and in declination, made during the
Voyager I and Voyager II encounters (Synnott et al. 1982). The optical
navigation images are analogous to earth-based astrometric observations of the
satellites except that the "opnav'' images are taken by an "observer'' much
closer to the Jovian system (typically 13-95 light seconds from the
satellites). At 5 106 km from Jupiter, one arcsec corresponds
approximately to 25 km. Additionally, the spacecraft-based observations are the
result of analyzing extended satellite images. By inferring the center of
the satellite from observations of the limb, the Voyager data do not have the
center-of-light vs center-of-figure problems which are common to disk-integrated
images such as those contained in CCD observations and photographic plates and
mutual events. The Voyager data were weighted using a standard deviation of
(as seen at the spacecraft's distance from Jupiter).
For spacecraft-to-satellite distances of 13-95 light seconds, the
corresponds to 19 and 140 km respectively for these spacecraft-based
observations. The Voyager optical navigation residuals on ephemeris E5
are depicted for right ascension and declination in Fig. 2 (click here).
Figure 1:
Residuals in right ascension (left) and declination (right)
for Flagstaff CCD observations relative to Satellite 1 using ephemeris E5.
The observations of Europa relative to Io are indicated by a 
,
those of Ganymede by a 
, and those of Callisto by a 
Figure 2:
Residuals in right ascension (left) and declination (right)
for the Voyager optical navigation observations using ephemeris E5.
The ordinate is in arcsec with an approximate corresponding
linear distance scale
on the right. Jupiter-relative observations of Io are indicated by ,
Europa by , Ganymede by 
, and Callisto by
Since 1973 there have been successful campaigns to observe the mutual event seasons every six years, when the Jovian satellites eclipse and occult one another as the Sun and the Earth pass through the plane of the Jovian equator, in which the satellite orbits lie. Aksnes and colleagues (Aksnes 1974, 1984; Aksnes & Franklin 1978, 1990), along with Arlot and colleagues (Arlot 1978, 1984, 1990, 1996), have made predictions of such mutual events available to scientists throughout the world and have organized scientific programs to observe the mutual events. Aksnes' team has produced astrometric separations of the satellites, at times near the mid-event times, which are very useful for ephemeris development purposes.
The early
Galilean satellite ephemerides E1 and E2 (Lieske 1980) employed the Aksnes data
from 1973 (Aksnes & Franklin 1976) and 1979 (Aksnes et al. 1984) and were
affected by the phase offsets between eclipses and occultations which led
Aksnes
et al. (1986) to recommend that 
be added to the published observation
times for the 1973 and 1979 data. The ephemerides E3 were generated using the
recommended additions of to the observation times
in processing the 1973 and 1979 mutual
events astrometric data.
Figure 3:
Residuals in right ascension (left) and declination (right)
for astrometric mutual event observations using ephemeris E5.
The ordinate is in arcsec with an approximate corresponding
linear distance scale on the right
In the processing of mutual event observations by the
Aksnes team in 1985 (Franklin et al. 1991) and 1991 (Kaas et al. 1997), it was
intended that no value of would be required but that instead the
authors would incorporate the phase effects into their published times and
separations. However, the effects were added in the incorrect direction for the
published data and hence it is recommended (Aksnes 1993; Franklin 1993; Lieske
1995) that the 1985 and 1991 Aksnes data be employed by adding twice the
published values of the phase corrections to the observation times.
Essentially the first addition of removes the erroneous application
of the phase effects with the incorrect sign
and the second application of actually corrects for the phase problem. Additionally, some infra-red
astrometric mutual event separations were obtained from Goguen et al. (1988) in
1985 as well as in 1991 (Goguen 1994). Astrometric separations from the 1991
mutual event season which were employed in the development of E5 were also
published by Mallama (1992a), Spencer (1993) and by Descamps (1994).
The
mutual event data were weighted using standard deviations of 
to
, which corresponds to 60 km and 140 respectively for these
earth-based observations. The typical weight corresponds to a standard
deviation of 
or 90 km.
The obvious offset in right ascension residuals for the 1991 mutual event season depicted in Fig. 3 (click here) is believed not to be due to ephemeris errors, but rather is due to albedo effects since almost all of the 1991 mutual event observations involved Io and were made at comparable longitudes on the satellite disk. The CCD and photographic data, for example, show no such offset and those data were sampled at various longitudes.
The long and valuable series of photographic observations made by D. Pascu of
the U.S. Naval Observatory have been an essential ingredient of the Galilean
satellite ephemerides since the first development of the Galsat software. In an
extended series of observations 1967-1993, Pascu (1977, 1979, 1993,
1994) provided astrometric observations of the satellites.
He pioneered the development of
neutral density filters to enable the accurate observation of the Galilean
satellites on a regular basis. The Pascu data were reduced using a single
scale factor (modified by adjustments for refraction for each observation) for
the ensemble of observations, as determined by Pascu. Additionally, a
correction to the Pascu scale was applied for a refraction-related effect,
amounting to a relative change in scale of 
, which probably
resulted from the manner in which the plate scale was originally determined.
The photographic data from 1967 through 1975 were weighted using a standard
deviation of 
per exposure, while those from 1976 onwards were weighted
using a standard deviation of 
per exposure, corresponding to position
uncertainties of 400 km and 275 km, respectively, for each exposure. A
photographic plate typically consisted of 4 exposures of each satellite.
The residuals on E5 for photographic observations are plotted in Fig. 4 (click here). In the figure, normal-point residuals are presented for each photographic plate, in order to make the comparison with the normal-point CCD observations more feasible. In the plots, the residuals for all exposures of a given satellite on a single plate are averaged into a single normal-point residual.
Figure 4:
Residuals in right ascension (left) and declination (right)
for photographic observations relative to Io using ephemeris E5.
The residuals for exposures of a given satellite on each plate
have been combined to produce a normal point for each plate. Observations
of Europa relative to Io are indicated by a , those of Ganymede
by a and those of Callisto by a
The Jovian eclipse timings, representing the classical observations of the Galilean satellites back to the 17th century, were discussed in Lieske (1986a,b). The early data are from the Pingré 17th century collection later published by Bigourdan (1901), and from the Delisle collection (Bigourdan 1897). The book on 17th century astronomy by Pingré published by Bigourdan was originally scheduled for publication 100 years earlier by Pingré. But Pingré's death and the French revolution intervened, and the printer's proof copies were destroyed as scrap paper. It was only 100 years later that a copy of the proofs was found and ultimately published by the Paris Academy. The manuscript collection of J.-N. Delisle contains a wealth of historically and scientifically interesting observations of Galilean satellite eclipses. These two collections effectively re-construct the "lost'' Delambre collection.
We employed satellite radii of 1815, 1569, 2631 and 2400 km for Io through Callisto, respectively (Davies et al. 1985), in reducing the eclipse timings.
Additionally, the series of eclipse observations by Pickering from 1878-1903 (Pickering 1907) and those accumulated by Pierce (1974), together with those of many amateur astronomers, especially those coordinated by B. Loader and J. Westfall, were employed. Finally, a few eclipse timings by Mallama (1992b) taken in 1990-91 were analyzed.
The eclipse timing data were employed with average standard deviations between 44 s for Io and 150 s for Callisto with a mean of 63 s, which correspond to position uncertainties of 775 km for Io, 1225 km for Callisto, and 800 km on the average for all satellites. The residuals appear visually similar to those depicted in Lieske (1986a) and therefore they are not presented here again.
The Doppler observations discussed by Ostro et al. (1992) were employed to evaluate the ephemerides and explore the potential of Doppler data, but they were not included in analysis and the development of E5. The data are consistent with the observations which were analyzed, but they were not included in the analysis because of possible uncertainty in the radar scattering properties of the satellites similar to albedo effects which depend upon the planetocentric longitude. The 50 Doppler observations of the outer three Galilean satellites were made between 1987 and 1991.
The Doppler data were weighted using standard deviations of 19 Hz for Europa, 12 Hz for Ganymede and 10 Hz for Callisto for the Arecibo 13-cm S-band system data.