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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Estimation of masses of some minor planets from
observations of perturbed bodies
O. M. Kochetova
Institute of Applied Astronomy, St. Petersburg, Russia
The most straightforward method of mass determination of minor planets
is the dynamical one which uses the gravitational perturbations produced by
minor planet in the motion of other bodies. Its disadvantage consists in large
relative errors of mass determination which are common for this method. They
arise from insufficient accuracy of observations of `test bodies' (minor planets)
and deficient number of close approaches resulted in perceptible perturbations
in the motion of small bodies. The merit of this method is its independence
of any a priori suppositions concerning internal structure of a minor planet, its
mineralogical composition and correspondingly assigned mean density what is
essential for determining value of the `photometric mass'.
As was shown in [1], the number of perturbed minor planets used as ''test par­
ticles'' can be substantially enlarged by considering bodies moving in the vicinity
of commensurability of mean motions with a chosen minor planet. In the present
paper one more attempt has been made to estimate masses of some minor planets
with as high precision as possible.
The work was done in several steps. At first, the perturbed minor planets
having a single close approach to the perturbing planet up to 0.05 a.u. or less
as well as perturbed minor planets close to the commensurability with the per­
turbing planet and having several approaches to it up to 0.1 a.u. or less have
been selected. Then, several determinations of the perturbing mass have been
fulfilled using observations of each perturbed body separately. The results were
separated by the value of the error of mass determination. Those bodies with a
single approach that gave error greater than 0:5 \Delta 10 \Gamma10 M Sun as well as those with
several approaches that gave error greater than 1 \Delta 10 \Gamma10 M Sun were eliminated
from the subsequent consideration.
After that, the general solution was found for each perturbing planet. This
solution provides the best fit to observed positions of all perturbed minor plan­
ets used in solution and of the perturbing mass. When finding general solution
the positions of perturbed minor planets were determined with accounting for
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perturbations from nine major planets in correspondence with DE403. Besides,
the perturbations from 300 minor planets (including the minor planet with the
mass to be improved) were taken into account. Masses of these 300 minor plan­
ets were taken in conformity with DE403, but their coordinates were obtained
by numerical integration starting from the osculating elements published in [3].
The relativistic terms due to the Sun were included in the equations of motion.
The observations were corrected for gravitational deflection of light and for phase
effect by Lommel--Zeeliger law of scattering.
Some results of the work are presented in the table. The values of the masses
of corresponding planets, found in [2] from their IRAS diameters and the mean
densities assigned in conformity with their conventional taxonomic classes, are
given for comparison.
The values of the masses of minor planets (15), (29) and (65) appear to be
rather close in both papers. In contrast to it, there is still a difference in values
for planet (7) obtained in various ways.
Perturbing Number of perturbed Mass in Mass from [2]
minor planet minor planets 10 \Gamma11 M Sun in 10 \Gamma11 M Sun
(7) Iris 4 (1:1) 1:5 \Sigma 0.6
26 (close approaches) 1:4 \Sigma 0.2
30 (total) 1:4 \Sigma 0.1 0.6 \Sigma 0.1
(15) Eunomia 14 (total) 1:2 \Sigma 0.2 1.4 \Sigma 0.2
(29) Amphitrite 15 (total) 0.77 \Sigma 0.12 0.74 \Sigma 0.1
(65) Cybele 25 (total) 0.58 \Sigma 0.15 0.52 \Sigma 0.03
The author would like to thank Yu. A. Chernetenko and V. A. Shor for their
assistance and valuable advices.
References
1. Kochetova O., Chernetenko Yu. Determination of mass of Jupiter and that
of some minor planets from observations of minor planets moving in 2:1 com­
mensurability with Jupiter. In: Dynamics of Natural and Artificial Celestial
Bodies. Eds. H. Pretka--Ziomek, E. Wnuk, P. K. Seidelmann, P. Richardson,
2001, 333--334.
2. Krasinsky G. A., Pitjeva E. V., Vasilyev M. V., Yagudina E. I. Estimating
masses of asteroids, Communications of IAA, 2001, No. 139.
3. Shor V. A. (ed.) Ephemerides of Minor Planets for 2003, IAA RAS, 2002.
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