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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Natural satellites dynamics from observations
N. V. Emelianov
Sternberg Astronomical Institute, Moscow, Russia
Dynamics of the natural satellites has to be studied with the most accuracy
for several reasons. First, it is necessary to prepare the missions of the space
probes exploring the system of the satellites. For example, with the coming of
the Cassini mission, the dynamics predictions of Saturn's satellites are becoming
very important. Second, the researches of the recent state of the Solar system lead
to the discoveries of its new members and new properties of the known planets
and satellites. Third, the mass distribution in the Solar system and its motion
properties serve as a source of great information for the reconstruction of the past
and for the prediction of the future of the Solar system.
The motion of the natural satellites is affected by numerous perturbations.
This motion is one of the most complex in celestial mechanics. There are theo­
retical problems related to the satellite motion which are not solved. There are
some systematic discrepancies between the parameters obtained from different
observational sources and by different authors. For example, let us look through
the values of planet parameters obtained from the observations of the satellites
of Mars.
Authors fm J2 J3 J4
km 3 s \Gamma2 10 \Gamma6 10 \Gamma6 10 \Gamma6
Christensen and Balmino, 1979 42828:4 1959:2 +29:6 \Gamma10:2
Sinclair, 1989 42839:5 1951:7 \Gamma26:4 \Gamma33:1
Emelyanov et al., 1993 42837:6 1950:4 +13:5 \Gamma35:2
In this table f --- the constant of gravity, m --- the mass of Mars, J2, J3, J4 ---
the coefficients of planet gravity potential expansion.
The properties of satellite motion raise some particularities in the stu2dy of
natural satellite dynamics. Let a satellite be observed in the time interval from
t 1 to t 2 with a precision of satellite position that is of oe in the orbital longitude.
The precision oe e
of the ephemeris in the longitude in the time moment t e
will be
evaluated by
oe e
= oe
t 2 \Gamma t 1
(t e \Gamma t 2
):
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This leads to important conclusions. The advantages of one data set with respect
to another one depend not only on the precision of observations but implicitly
on the time interval of observations. To build an adequate model of satellite
motion one must use the most large data base of observations. Continuation of
observations with the former precision remains to be useful. Any new observations
even more precise ones are used as the supplement to the previous data base.
The use of more precise observations made once does not lead always to the more
precise ephemerides. For example, the set of observations of the satellites of Mars
made by the spacecraft Mariner 9 in 1971--1972, Viking 1, 2 in 1976--1980, and
Phobos 2 in 1989 with the real precision of 20 km leads to the same precision of
ephemerides as the ground--based observations made from 1877 to 1988 with the
modest precision of 0:4 00 in the apparent coordinates.
This particularity implies the composition of a data base of all observations
made in the world. It is reasonable to make some unique data base accessible to all
researchers. The Institut de M'ecanique C'eleste et de Calcul des Eph'em'erides in
Paris is in charge of support of the Natural Satellites Data Base (NSDB) with the
help of some members of the IAU Working Group on Natural Satellites mainly
from Sternberg Astronomical Institute in Moscow and CNPq Rio de Janeiro
Observatory in Brasil. The problem is to suggest all observers to send their results
to this data base in real time or after the publication.
In other circumstances we deal with the ephemerides of natural satellites. The
creation of the ephemerides is a very complicated process. It includes various
theories of the satellite motion and a lot of methods of the data processing. To
make the satellite motion prediction more reliable it is reasonable to develop
several independent sources of the natural satellites ephemerides in the world.
To provide the process of natural satellites observations with an independent
and suitable service of the ephemerides a special software was developed in Stern­
berg Astronomical Institute in Moscow and proposed to be transferred over the
observatories [1].
Very accurate astrometric data can be get from the photometry of the mutual
events in the natural satellites. Light curves have to be processed to obtain an as­
trometric result of such observations. In contrast to the usually accepted method
of deduction of the apparent topocentric relative coordinates of satellites an orig­
inal approach was proposed and developed in our paper [2]. To facilitate the use
of the photometric data we reduced them to the planetocentric rectangular coor­
dinate differences of satellite pairs for one instant of time from each observed light
curve. The advantages of this approach consist in the fact that after processing
the photometric data one will have to deal only with the planetocentric satellite
motion to fit the satellite orbit to observations.
The most exact data are received from measurements of coordinates of one
satellite relative to other. The accuracy of determination of mutual coordinates
of satellites is improved with decrease of their apparent angular distance. The
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apparent encounters of outer satellite of Jupiter are very rare. We have pre--
calculated these events to profit by this circumstance [3].
Saturn's inner satellites have poorly determined ephemerides because they
have rarely been observed only during the ring plane crossings (``RPXs'' for short)
when the usually bright rings become faint. The epochs of these events are sep­
arated in time by 14 years. All small satellites were discovered either during the
RPXs in 1966 and 1980 or during the Voyager spacecraft encounters in November
1980 and August 1981.
The August 1995 HST images revealed at least 19 unidentified moving objects.
Most of these images were linked with three different objects.
Saturn co­orbital satellites Janus and Epimetheus have very interesting dy­
namics. The satellites move on horseshoe­shaped orbits when viewed in a reference
frame rotating at the average mean motion of two satellites. The time period for a
complete libration around the horseshoe is 8.01 years. The values of the libration
period and the distance of mutual approach are very sensitive to the masses of the
satellites. In other way new observations of the satellites lead to a more precise
determination of the mass. Unfortunately satellites Janus and Epimetheus are
difficult to be observed being very faint objects and moving very closely to the
bright A ring of Saturn. The only favorable opportunities to obtain the positions
of the satellites occur during the RPXs.
The solution find by Nicholson et al. [4] was to exploit the strong planetary
methane and hydrogen absorption at – 2:0 \Gamma 2:4 ¯m. Thus using the infrared
camera, the light of the bright planet may be eliminated. Saturn's rings, however,
remain bright in this spectral region. It was a good idea to use the disk of Saturn
to occult or to eclipse the bright ring and to observe the satellites as they passed
through superior conjunction. The relative positions of the Earth, Saturn, and the
Sun restrict the useful windows. Such a situation occurs only on four occasions
during Saturn's 29­year orbital period. Nevertheless this offers additional points
for the 8­years period of libration. We have published [5] the predictions and
circumstances of these events observable from August 20, 2004 to June 1, 2005.
One of the most surprising results from the 1995 Saturn RPX campaign of
observations was enigmatic peregrinations of Prometheus. From the satellite dy­
namics it was discovered that Prometheus lagged some 19 ffi behind its predicted
position based on the ephemerides derived from Voyager 1 and Voyager 2 ob­
servations. The simplest scenario consistent with the observed lags involves a
horseshoe encounter with an unknown small co­orbital satellite.
An exciting enigma arises from the motion of the Galilean satellites of Jupiter
as the famous acceleration of Io. The Jupiter--Io problem is very complicated for
two reasons: the motions of the three inner satellites (Io, Europa, and Ganymede)
are interlocked through strong mutual perturbations, and the tidal response of
Jupiter is totally unknown. In apparent contradiction to the lunar tidal theory,
which predicts decreasing mean motion it was found through comparisons with
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observations that the mean motions of these three satellites are increasing very
slowly with time. This result implies that Io is now spiralling slowly inward,
losing more orbital energy from internal dissipation than it gains from Jupiter
tidal torque.
We expect new exciting and useful results from further developing the mod­
els of natural satellites motion. New methods of observations as well as more
sophisticated theories are wanted.
References
1. Emel'yanov N. V. A new tool for providing observations of planetary satel­
lites with ephemerides. Astronomy Letters, 1996, 22, 135--137.
2. Emelianov N. V. et al. Mutual positions of the Galilean satellites of Jupiter
from photometrc observations durung their mutual occultations and eclipses
in 1997. Astron. Astrophys. Suppl. Ser., 2000, 141, 433--447.
3. Emelianov N. V. et al. Visible encounters of the outermost satellites of
Jupiter. Solar System Research, 2001, 35, 209--211.
4. Nicholson P. D., Hamilton D. P., Matthews K., Yoder C. F. New observations
of Saturn's coorbital satellites. Icarus, 1992, 100, 464--484.
5. Emelianov N. Observing rare events of natural satellites. In: Astronomy
and Geodesy in new millenium. Proceedings of International Conference
``AstroKazan--2001'', September 24--29, 2001, Kazan State University: Pub­
lisher `DAS', 2001, 111--113.
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