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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
On non--gravitational acceleration in
Harrington--Abell comet motion due to Jupiter
O. F. Grigoryan 1 , Yu. D. Medvedev 2
1 Vologda State Pedagogical Unyversity, Vologda, Russia
2 Institute of Applied Astronomy, St. Petersburg, Russia
The problem of the tidal forces influence on the cometary nucleus in vicinity
of Jupiter is considered. Two effects of particular interest are as follows:
i) The additional warming of the nucleus and, as a consequence, the ap­
pearance of the new non--gravitational accelerations in addition to the known
Sun--generated effects of this kind;
ii) Partial disintegration of the nucleus and, as a consequence, the instant
displacing of the centre of inertia of the latter.
The comet Harrington--Abell is chosen as an object of study. It had the close
approach to Jupiter in 1974 and was observed during 3 apparitions before this ap­
proach and 4 apparitions after that. The perturbations from eight major planets,
the Sun, the second zonal harmonic of the Jovian gravitational field, and from
Gallilean satellites of Jupiter when the comet approached Jupiter were taken into
account. When numerically integrating the comet equations of motion, the Ever­
hart 11th--order procedure was used. We employed the Encke's transformation. It
has been supposed that there exists some additional non--gravitational accelera­
tion in the cometary motion inversely proportional to the squared Jupiter--comet
distance:
a i = A J
i \Delta 1=r 2
J ; i = 1; 2:
A linkage of the five apparitions within 1968--1999 has been performed. The
results of computations are presented in the Table. Here the components of po­
sition X, Y, Z (in a.u.), the velocity components V x ; V y ; V z (in a:u:=day), and
non--gravitational parameters of Style II in Marsden's model [1], A 1 ; A 2
(in
10 8 a:u:=day 2 ), the coefficients of proportionality of the additional acceleration
A J
1
, A J
2
(in 10 8 a:u:=day 2 ) are given. The epoch for these parameters is 1.0 Decem­
ber 1978 TDT. The set of parameters obtained allows to represent the positional
observations for 5 apparitions with the mean unit weight errors oe = 0:84 00 .
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Orbital parameters Values Errors
X; a:u: 0:507251454 .669E­05
Y \Gamma4:638083407 .131E­05
Z \Gamma2:953283821 .149E­05
V x ; a:u:=day 0:005306157 .245E­08
V y \Gamma0:001485409 .426E­08
V z \Gamma0:000530134 .299E­08
A 1 \Delta 10 8 a:u:=day 2 0:1240 .940E­02
A 2 0:05324 .286E­02
A J
1
0:04567 .458E­02
A J
2 \Gamma0:07204 .419E­02
Correlation coefficients:
X Y Z V x V y V z A 1 A 2 A J
1 A J
2
1:00
\Gamma0:75 1:00
\Gamma0:67 0:58 1:00
\Gamma0:74 0:86 0:88 1:00
0:98 \Gamma0:78 \Gamma0:56 \Gamma0:67 1:00
0:96 \Gamma0:77 \Gamma0:79 \Gamma0:81 0:92 1:00
\Gamma0:26 0:11 \Gamma0:20 \Gamma0:23 \Gamma0:39 \Gamma0:25 1:00
0:62 \Gamma0:48 \Gamma0:78 \Gamma0:75 0:45 0:72 0:27 1:00
0:77 \Gamma0:66 \Gamma0:87 \Gamma0:90 0:63 0:84 0:26 0:94 1:00
\Gamma0:63 0:51 0:79 0:76 \Gamma0:47 \Gamma0:74 \Gamma0:19 \Gamma0:99 \Gamma0:93 1:00
The coefficients of proportionality as obtained from observations are
(4:75 \Sigma 0:46)\Delta10 \Gamma10 au/day 2 for the Jupiter--centre radial component of the accel­
eration and (\Gamma7:20 \Sigma 0:42)\Delta10 \Gamma10 au/day 2 for the transversal one.
The hypothesis of the partial disintegration of the cometary nucleus at the
approach to Jupiter had resulted in displacing the nucleus centre of inertia in
the direction of Jupiter at \Gamma1:83 \Sigma 0:75 km. It means that the exterior part of
cometary nucleus has been broken during approach and went off the nucleus.
This research has been supported by the RFFI grant 01­02­17078 of Russian
Academy of Sciences.
References
1. Marsden B. Comet and nongravitational forces. II. Astron. J., 1969, 74, 720.
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