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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Estimate of P/Shoemaker--Levy nucleus size
M. D. Zamarashkina, Yu. D. Medvedev
Institute of Applied Astronomy, St. Petersburg, Russia
The problem of disintegration of the cometary nuclei due to the tides produced
by the major planets is considered. The dynamics of the comet Shoemaker--Levy
9 (SL9) is studied in details in this connection. 13 fragments of SL9 having 50
and more positional observations have been selected. We computed orbital so
lution for this fragments with impact times, based on the timing of observed
impact phenomena in July,1994 [1,2]. Using this solution the estimates of orbital
parameters and nucleus dimensions before the disintegration of the comet have
been obtained. The motion of the nucleus fragments has been traced numerically
taking into account perturbations due to the gravitation of the Sun, major plan
ets, Galilean satellites, and the second zonal harmonic of the Jovian gravitational
field. The mutual gravitation between the separated fragments is investigated.
This effect involves the changes of the size of the parent body by only 1 %.
Therefore, the mutual gravitation interaction has been neglected when integrat
ing the equations of motion. The orbit of this fragment H is considered as that
of the maternal body. We have supposed that all fragments were formed due to
the tidal breakup of a parent object. Accepting such a supposition the size of the
parent body has been evaluated using the observations of the separate fragments.
It was addmitted all fragments had the same velocities but they were arranged
at different distances from each other at the breakup instant. We have estimated
the diameters of the maternal body for the different moments of disintegration.
The results of calculations are given in Table 1.
Table 1. The diameters (D) of the maternal body for the different moments of
disintegration (t).
t t 0 \Gamma 2 h t 0 \Gamma 1 h t 0 t 0
+ 1 h t 0
+ 2 h
D (km) 9:73 3:50 1:24 3:73 8:67
Here t=2448811.34 JD is the time of the perijove passage of the fragment H.
The errors of diameter values represented in the table are about 1 meter. The
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computations show that the maternal body of the nucleus was of 1.24 km in
diameter, if its disintegration happened at the closest approach of the comet to
Jupiter, and of 9.73 km, if the nucleus had been disintegrated two hours before
the moment of approach. The possibility of disintegration of the maternal body
by stages is investigated. For this aim the positions of other fragments on the
phase portrait of H are considered. Estimates of positions of each fragments in
radial (r) and normal (n) components with respect to the fragment H are shown
in Figure 1. The results of our investigation allows to assume that fragments
A and B have been separated about one hour before the moment of approach.
Therefore the diameter of maternal body can be estimated about 3.50 km.
Fig. 1
The positions of fragments on the phase portrait of H.
This research has been supported by the RFFI grant 010217078 of Russian
Academy of Sciences.
References
1. Chodas P. W., Yeomans D. K. In: The Collision of Comet Shoemaker--Levy
9 and Jupiter, ed. by K. S. Noll, Cambridge University Press, 1996.
2. Meadows V. et al., Icarus, 2001, 152, 366--383.
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