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\title{A European campaign of observation of the phenomena of the first eight 
Saturnian satellites in 1995}
\author{Pascal Descamps, Jean-Eudes Arlot, William Thuillot \\
 Bureau des Longitudes, URA 707 du CNRS, Paris \\
 e-mail: DESCAMPS@bdl.fr} 
\date{}


\begin{document}
\bibliographystyle{alpha}


\maketitle



{\it 
Starting from July 1992, the apparent inclination of the orbital plane
of the satellites of Saturn has begun to be small enough to induce
phenomena. This configuration occurs every 15 years and gives opportunity
to observe eclipses and occultations of the first eight Saturnian satellites
by the planet. Moreover, 
in 1995 and 1996 the Earth and Sun will pass through the plane of the
rings and we will observe mutual events of the Saturnian satellites;
the satellites will eclipse and occult one another. We have computed the
whole set of these phenomena. The observation of this type of event
gives the opportunity to get astrometric measurements with a very high
precision and will permit us to improve our knowledge of the dynamical
motion of these satellites. Furthermore these observations are an
interesting method for physical investigations concerning the
atmosphere of Titan, and they can be used for a photometric study of
the surface properties. An international campaign of observation will be
organized by the Bureau des Longitudes for that goal.
}
 
\section{Introduction}

Powerful groundbased technique for exploring different problems related
to their dynamics and physics. Every 15 years the Saturnian satellites
presents a particular configuration which gives the opportunity to
observe mutual events. They occur when the planetocentric declinations
of the Earth and the Sun become zero. Since Iapetus has an inclination
on the Saturnian equator very different from the other satellites, this
satellite is not implied in the mutual events. Table 1 shows the main photometric 
data
concerning the seven first Saturnian satellites and the number of phenomena
where each satellite is eclipsed or occulted by another and for light flux drop
greater than 0.1. The calculations of the
predictions of these events were made using Dourneau's ephemerides
(Dourneau 1987). The results previously obtained by analyzing similar phenomena
involving the Galilean satellites of Jupiter show the interest of such
observations. Campaigns of observation of the mutual events of the Galilean
satellites , which occur every six years, have been
recently organized (Arlot et al. 1990, Arlot et al. 1992, Franklin et al. 1991). The results
obtained have shown that, with the help of a photometric-astrometric model,
measurements of the surface characteristics and very accurate astrometric data
can be  deduced from them (Mallama 1991, Mallama 1992, Descamps et al. 1992) 
works may be carried out for studying the Saturnian satellites and they can
lead to a better knowledge of these satellites. They will be also be useful for
preparing the next space projects to the Saturnian system, particularly the
Cassini mission.


The Bureau des Longitudes will organize a campaign to observe the Saturnian phenomena and
the mutual events and we call for observers. A listing of predicted
eclipses and occultations by Saturn and mutual events has been published by  Arlot and Thuillot
(1993).
 An international workshop will held at Bucharest, Romania, on September 
19, 20 and 21, 1994. The installation of an anonymous ftp site is in
progress for further workshop information. Ephemeris of the Solar
System bodies will be also available into ftp.bdl.fr. 

\begin{table}
\caption{
Data concerning the Saturnian system and number of 
phenomena where the satellite is eclipsed or occulted  
}
\begin{center}
\begin{tabular}{|lrcccc|}
\hline
&&&&&\\
\bf Satellite & \bf Eclipsed & \bf Occulted & \bf Magnitude & \bf Geometric & \bf Limb \\
 &  & & \bf  $V_{0}$   &  \bf albedo    &  \bf darkening  \\
	        &          &  & (mag) & p$^a$  &  k$^b$    \\
&&&&&\\
\hline
&&&&&\\
1 Mimas         &   64            &   11     &  12.5  & 0.77  &
0.65 \\
2 Enceladus     &   23            &   21     &  11.7  & 1.04  &
0.78 \\
3 Tethys        &   13            &   12     &  10.2  & 0.80  &
0.63 \\  
4 Dione         &   7            &   12     &  10.4  & 0.55  &
0.54 \\
5 Rhea          &   6            &   6     &   9.7  & 0.65  &
0.53 \\  
6 Titan         &  6            & 2     &   8.3  & 0.20  & - \\
&&&&&\\
\hline
\end{tabular}
\end{center}

$^a$ From Voyager clear filter data ($\lambda \sim 0.47 \mu $) (Buratti et al. 1982
, Buratti 1983) \\
$^b$ From Buratti 1984 
\end{table}
\section{Issues in the dynamical study of the Saturnian satellites}

The system of the first eight satellites of Saturn has been the subject
of recent astrometric and dynamical works. Since the works of Struve
and Woltjer, different theories have been developped to model the
motion of these satellites and to study the resonances (Sinclair 1977,
Taylor 1984, Rapaport 1978, Harper et al. 1988). Analysis of
adjustements of theory to old and modern observations led to new
orbital elements and ephemerides (Dourneau 1987 , Taylor and Shen 1988 ).
Recent works gave an estimate of the precision of the moderne
ephemerides. In his analysis of 21,794 observations spanning 1886-1985,
Dourneau (1993)  gives a RMS (root-mean-square) of the residuals close
to 0.20 arcsec. (about 1200 km at Saturn's mean opposition distance)
for the first six Saturnian satellites, 0.55 arcsec. (3300km) for
Hyperion, and 0.25 arcsec. (1500km) for Iapetus. By comparing with the
0.05 arcsec. accurac (about 200km) of the ephemerides of the Galilean
satellites of Jupiter (Arlot 1982, Lieske 1980), we see that the
dynamical model of the Saturnian satellites needs improvements. A
theoretical effort has been recently made with a new approach to the
dynamical prolem: by means  of the development of a general theory of
the motion of the Saturnian system (Duriez and Vienne 1991, Vienne and
Duriez 1991, 1992). New periodic terms appeared and important results
could be next obtained by the analysis of new accurate observations.

Observation of mutual phenomena will be an opportunity to get very accurate measurements
of positions of the Saturnian satellites. Similar observations of the Galilean satellites
led to an accuracy better than 100 km on the position measurement. Contrarily to the
photographic observations, the accuracy derived from the timming of a photometric 
observation does not depend on the distance from the observer to the system of satellites.
Therefore an accuracy close to the high accuracy of the observations of the Galilean
satellites can be obtained for the Saturnian system. The timing of a closest approach
during a mutual event may usually be made with an accuracy of 10 to 30 sec of time
depending on the photometric accuracy of the lightcurve. The maximum relative velocity
between two satellites may reach 15 km/sec for inner satellites and 5 km/sec for the
others. Therefore, the astrometric accuracy of the measurement of the relative positions
deduced from a mutual event is most of time of 200 km (0".03).




\section{Planetologic interest of observing mutual events}
 
In order to reduce the observations of mutual events, we have recently
developped a photometric -astrometric model based upon the behavior of
the solar light scattered by surfaces. This model was successfully
applied to a set of observations of mutual phenomena of Galilean
satellites (Descamps 1992, Descamps 1994, Descamps et al.
1992). Light scattering by atmosphereless bodies is well represented by
laws such as the Hapke law (Hapke 1986) or the Minnaert law. 
The optical properties contain information on chemical composition and
surface microstructure. A lunar-like law of surface optical scattering
were found for Dione and Rhea but others are somewhat more complex,
involving a significant component of Lambert-like scattering (Buratti
et al. 1982). 

 The major drawback for ground-based observations is due to the
scattered light from the rings and plane in the case of the closer
satellites such as Mimas, Dione, Tethys and Enceladus which induces a
serious hindrance to accurate photometry.  Another limitation results
from the coverage in phase angle which is always limited to a little
more than $6^\circ $. Thus, up to the Voyager imaging observations in 
1980-1981, it was difficult enough to measure the surge in
brightness near the opposition or surface roughness of Saturnian 
satellites.  
For instance, Franz et al. (1975)
found a significant opposition surge for Dione and Tethys whereas
Verbiscer and Veverka (1989), from Voyager observations of Rhea, have
derived only a slight opposition surge.

However, several
extensive photometric studies of Saturn's satellites have been
published since 1971 and global photometric data of the Saturnian satellites are presently
available and well known. They are reported in the Table 1. 
The limb darkening parameter of the Minnaert's law, k, would approach 0.5
for a dark surface in which single scattering dominates and for an ideal Lambert
surface, k=1 at all phase angles.
The determinations of k were made
from disk-resolved scans of Voyager images at relatively high phase angles for
Mimas, Enceladus and Tethys,
respectively at $16.8^\circ $,
 $13.4^\circ $ and $9.9^\circ $ .
 These results may not be considered as 
entirely reliable estimates because according to the laboratory and theoretical
works of Goguen (1981), Minnaert's function is regarded
as inadequate except when the phase angle is near $0^\circ$. 


 Although Minnaert's model is useful in 
understanding differences at low phase angles among the satellites in their scattering
properties, they cannot be directly related to the physical properties
of the surfaces. 



The characterization of satellite's light scattering properties in terms of
Hapke parameters makes it possible to discuss these properties in the
context of the satellite's geology and surficial microstructure. So far only a few Saturnian satellites
have been studied with the help of the Hapke model.
Classical methods of study require disk-resolved or/and disk-integrated
observations such as those obtained from spacecraft like Voyager. Unfortunately,
the Voyager data sets are most complete for only Enceladus, Mimas and Rhea. In
general phase angle coverage extends to $30-40^\circ$, with a few points at 
higher phase angles ($\sim 100^\circ $). For example, observations of 
Enceladus extend only to $\alpha \simeq 40^\circ $, they are not suited to
detect the possible influence of large-scale roughness. The situation is 
better for Mimas and Rhea ($\alpha = 1.8^\circ - 135^\circ $). 
 Hapke model results
for Mimas, Enceladus and Rhea are summarized in Table 2. The discrepancy 
between results on Mimas may arise
from the assumption made by Verbiscer and Veverka (1992) on the Mimas' opposition
surge considered as identical to that of Rhea due to lack of data at low phase
angles. 

\begin{table} 
\caption{
Hapke photometric parameters
}
\begin{center}
\begin{tabular}{|lcccl|}
\hline
&&&&\\
\bf Satellite & \bf Single scattering & \bf Asymmetry & \bf Macroscopic    &  \bf Source      \\
              & \bf  albedo           & \bf factor    & \bf roughness      &                  \\
	      & $\tilde{\omega _{0}}$ &  g            & $\bar{\theta} (^\circ )$ &            \\
&&&&\\
\hline
&&&&\\
 Mimas         &   0.93            &   -0.30     &  30    & Buratti  1985 \\
 		     &   0.95            &   -0.21     &  30    & Verbiscer and  Veverka
1992\\ 
 Enceladus     &   0.99            &   -0.35     &  30    & Buratti 1985 \\ 
 Rhea$^a$    &   0.86            &   -0.29     &  13    & Verbiscer and Veverka 1989\\ 
Rhea$^b$	   &   0.89   &  -0.32  & 13  & Verbiscer and  Veverka 
1989\\
&&&&\\
\hline
\end{tabular}
\end{center}
 $^a$ Disk-integrated data 

 $^b$ Disk-resolved data 
\end{table}

Accordingly,
since estimations of macroscopic roughness become trustworthy when data are
available at $\alpha \geq 40^\circ $, these results need at least to be
confirmed by other observations. 

From this point of view, mutual phenomena observations are particurlarly
interesting. Indeed, our approach succeeds in estimating not only macroscopic
roughness and single-scattering albedo but also opposition surge parameters 
in the  context of the Hapke model. During a phenomenon the photometric effect
of the macroscopic roughness dominates especially at the beginning and at the
end, that is, where shadows are prominent in areas near the limb or the
terminator. This effect induces an asymmetry in the shape of the light curve and
provides therefore constraints on the determination of the macroscopic roughness.



 Thus the upcomming mutual events will
provide an ideal opportunity to obtain near-opposition data with minimal
scattered light from the broad ring system wich will appear edge-on in 1995. They 
are also an excellent Earthbased approach for measuring limb darkening on objects
that are too distant for Earthbased disk-resolved study. 
Moreover, mutual
events observation allow a regional analysis namely leading side/trailing side 
differences by acting as a disk-resolved scan.. 



  


Finally, a lot of information relating to the surface properties in
terms of Hapke parameters and limb darkening of
 the major Saturnian satellites might
result from their mutual phenomena observation. These determinations would allow
to discuss or comment precedently published results not confirmed yet.

\section{Observation of the phenomena}

In the past, several campaigns of observation of mutual events  of the
Galilean satellites took place and succeeded in obtaining a large
amount of useful data. However, the Galilean satellites have a
magnitude of about 5 and are easy to observe, even with a small
telescope. The Saturnian satellites are much more difficult to
observe because of their magnitudes, which are given in Table 1. The
main difficulty arises from the proximity of the planetary disk because
of the brightness of the rings,except during the transit of the Earth
in their plane. This will lead us to select instruments and sites
particularly adapted to these observations. We have also to note that
some events are very difficult to observe because the magnitude
difference between some satellites is too large (events involving Titan
and Hyperion for instance imply a light flux drop never larger than
0.001). Events occurring near Saturn will be observed only with very
good seeing. Photoelectric photometers as well as CCD could be used but
preliminary tests have to be made by observing the Saturnian satellites
before the date of the events in order to estimate the 
Signal/noise ratio. Antiblooming CCD will be preferable for the
observations of satellites near the planet but one has to be careful to
avoid a saturated image of the observed satellite in order to have a
good photometric measurement. Tests have also to be made to know
exactly the time resolution of the photometric measurements. One
measure per second of time  is at least  necessary. If possible light
flux measurements of each separated satellite before and after the
phenomena are necessary for the calibration of the lightcurves.




\section{Conclusion}

New data of high accuracy are expected from the next series of
phenomena, eclipses by Saturn and its rings and especially mutual events 
of the Saturnian satellites in order to improve the dynamical
model of the motions as well as our knowledge of the photometric
characteristics. These data would also be helpful to the preparation
of the next spacecraft missions to the Saturnian system. Further 
details on these events or on their topocentric conditions of
observation can be obtained on request from the authors.
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\end{thebibliography}
\end{document}
