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(2) DUNCAN STEEL ON ASTEROIDS, BUFFON & COMETS

D.I. Steel: The ABC of ACM: asteroids, Buffon and comets. PLANETARY AND 
SPACE SCIENCE, 1997, Vol.45, No.12, pp.1501-1503

SPACEGUARD AUSTRALIA, POB 3303, RUNDLE MALL, ADELAIDE, SA 5000, 
AUSTRALIA

Most of the participants in the ACM 96 conference would have made use 
of the facilities in a building named for Georges-Louis Leclerc, the 
Compte de Buffon (1707-1799). Buffon made many major contributions to 
the natural sciences, and may be considered to be one of the founders 
of planetary science. He proposed a theory for the origin of the 
planets which involved a massive comet having an oblique impact upon 
the Sun, the ejected material condensing so as to form a regular system 
of planets. Amongst his mathematical contributions is what is known as 
Buffon's Needle, whereby experimental evaluations of may be made by 
randomly dropping a needle onto a length, and accumulation the fraction 
of times that the needle cuts one of the lines. Near-Earth asteroid 
(NEA) trails imaged onto a CCD chip provide a two-dimensional analogue 
of this, and where the pixel size is very large (this having some 
advantages for NEA searching) an analysis based on Buffon's Needle 
provides probabilities of the NEA trail lying within one, two or three 
pixels, such probabilities affecting the chances of detection. It is 
therefore appropriate that Buffon and his contributions to studies of 
comets and asteroids be remembered in these conference proceedings. (C) 
1998 Published by Elsevier Science Ltd. All rights reserved.

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(3) ROSETTA AHOY: HOW TO ANCHOR A SPACECRAFT ON A COMET 

N.I. Komle*) , A.J. Ball, G. Kargl, J. Stocker, M. Thiel, H.S. 
Jolly, M. Dziruni, J.C. Zarnecki: Using the anchoring device of a comet 
lander to determine surface mechanical properties. PLANETARY AND SPACE 
SCIENCE, 1997, Vol.45, No.12, p.1515

*) AUSTRIAN ACADEMY OF SCIENCE, INSTITUT FUER WELTRAUMFORSCHUNG, 
   ELISABETHSTR 20, A-8010 GRAZ 

Owning to the low surface gravity of the Rosetta target comet 
46P/Wirtanen, a means of anchoring the Rosetta Lander to the cometary 
surface will be necessary. This task can be accomplished by firing an 
anchor into the cometary soil immediately after touchdown to prevent a 
rebound of the spacecraft from the surface or subsequent ejection by 
other forces, and to allow for mechanical activities (drilling, etc.)
at the landing site.. The rational for anchoring is examined, based on 
estimates of the main forces likely to act on the spacecraft after 
landing. We report on the development of an anchoring device using a 
pyrotechnic gas generator as a power source and an instrumented anchor. 
In addition to the anchoring function, which is the primary purpose of 
this system, the integration of acceleration and temperature sensors 
into the tip offers the possibility to determine some important 
material properties of the cometary surface layer. The accelerometer is 
designed to measure the deceleration history of the projectile and is 
thus expected to give information on how the material properties (in 
particular strength) change within the penetrated layer(s), while the 
temperature sensor will measure temperature variations at the depth at 
which the anchor finally comes to rest. As the mechanical properties of 
the material are not known, it is difficult to predict the final depth 
of the anchor with any great certainty, but it may well be greater than 
that reached by any other of the lander's instruments. The instrumented 
anchor will be part of the MUPUS experiment, selected to form part of 
the Rosetta Lander payload. We report on results of laboratory 
simulations of anchor penetration performed at the Institut fur 
Weltraumforschung, Graz, and compare these with models of projectile 
penetration. The value of the results expected from the penetrometry 
experiment in the context of an improved understanding of cometary 
processes is discussed. (C) 1998 Elsevier Science Ltd. All rights 
reserved.

==========================
(4) COMPOSITION OF COMETARY DUST 

L. Kolokolova & K. Jockers: Composition of cometary dust from 
polarization spectra. PLANETARY AND SPACE SCIENCE, 1997, Vol.45, No.12, 
pp.1543-1550

MAX PLANCK INSTITUT FUER AERONAUTIC, KATLENBURG DUHM, GERMANY

The wavelength dependence of the polarization ('polarization spectra') 
of cometary dust is discussed. It is shown that, in the case of large 
phase angles, the wavelength dependence of the polarization is mainly 
controlled by the complex refractive index of the particle material, 
whereas the spectral dependence of the intensity is also sensitive to 
the size of the particles. This suggests that observations of 
'polarization spectra' may determine the composition of cometary dust. 
An attempt is made to find the composition of the cometary dust 
material by comparing the observed polarimetric data with laboratory 
measurements of complex refractive indices of possible cometary 
constituents. Silicates, graphite, metals, organics, water ice and 
their mixtures are considered. It is shown that astronomical silicate 
must be the most abundant constituent of cometary dust in the range of 
heliocentric distances from 0.8 to 1.8 AU, whereas the volume fraction 
of pure graphite or pure metals is less then 1%. A substance similar to 
that of F-type asteroids may be present in comets. There is evidence 
for an organic material that is being destroyed between heliocentric 
distances of 0.8-1.8 AU. (C) 1998 Elsevier Science Ltd. All rights 
reserved.

====================
(5) THE LAPLACIAN ORBIT DETERMINATION OF ASTEROIDS
 
M.J. Sokolskaya: On the Laplacian orbit determination of asteroids. 
PLANETARY AND SPACE SCIENCE, 1997, Vol.45, No.12, pp.1575-1580

RUSSIAN ACADEMY OF SCIENCE, INSTITUTE OF THEORETICAL ASTRONOMY, 
10 NABEREZHNAYA, RUSSIA 

A modified Laplacian technique is described for initial orbit 
determination of asteroids from CCD observations and its applications 
for orbit determination of the main belt asteroids and near Earth 
asteroids. The proposed modification is based on a simultaneous 
improvement of both the orbital elements the derivatives of spherical 
coordinates in frames of Laplace's method. It provides an orbit which 
represents the used observations with the residuals comparable with 
errors of these observations. The improved values of the derivatives 
might be used as ephemeris parameters for identification of newly 
discovered objects. (C) 1998 Elsevier Science Ltd. All rights 
reserved

=======================
(6) THE DANGEROUS BORDER OF THE 5:2 MEAN MOTION RESONANCE

Z. Knezevic*), A. Milani & P. Farinella: The dangerous border of the 
5:2 mean motion resonance. PLANETARY AND SPACE SCIENCE, 1997, Vol.45, 
No.12, pp.1581-1585

*) ASTRONOMICAL OBSERVATORY, VOLGINA 7, YU-11050 BELGRADE, YUGOSLAVIA

After discovering that asteroid (2953) Vysheslavia, a Koronis family 
member, has a typical dynamical lifetime of the order of 10 Myr only 
against 'falling' into the 5:2 Kirkwood gap and ending up in a 
hyperbolic orbit (Milani and Farinella, 1995. Icarus 114, 209-212), we 
decided to repeat the same study for two other asteroids: 1991 UA(2) 
and 1993 FR58, lying also very close to the outer edge of the same 
resonance. The orbital elements of these bodies were not yet accurate 
enough and we appealed to observers, both professional and amateur, to 
obtain more astrometric data. Eight groups in three different countries 
carried out observations, and as a result the Minor Planet Center could 
derive updated, accurate orbits for both objects. Here we report on the 
preliminary results of our study. Whereas the long-term behavior of 
1991 UA(2) looks fairly regular and stable, 1993 FR58 exhibits a 
typical 'stable chaos' behavior; nevertheless, it does not end up in 
the resonance within a time span of 50 Myr. On the other hand, its 
fictitious clones, placed just 3-4 x 10(-3) AU closer to the resonance, 
undergo large irregular semimajor axis changes, fall into the resonance 
and escape on a timescale <1 Myr. (C) 1998 Elsevier Science Ltd. All 
rights reserved.

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(7) ESCAPE OF ASTEROIDS FROM THE HECUBA GAP

T. Michtchenko, S. Ferraz Mello: Escape of asteroids from the Hecuba 
gap. PLANETARY AND SPACE SCIENCE, 1997, Vol.45, No.12, pp.1587-1593

UNIVERSITY OF SAO PAULO, INSTITUE OF ASTRONOMY & GEOPHYSICS, CAIXA 
POSTAL 3386, BR-01060 SAO PAULO, SP, BRAZIL

The dynamics of the 2/1 mean-motion asteroidal resonance with Jupiter 
is studied by numerical integration of the equations of motion of the 
Sun-Jupiter-Saturn asteroid system. The measurement of the fundamental 
asteroidal frequencies by means of Fourier and wavelet analyses allows 
us to construct the web of the secular, secondary and Kozai resonances 
inside the 2/1-resonance boundaries. The structure of the phase space 
of the 2/1 resonance is discussed with emphasis on the acting 
depletion mechanisms due to presence of these inner resonances. Special 
attention is paid to the study of the middle-eccentricity depleted 
region. The importance of the great inequality of the Jupiter-Saturn 
system in the acceleration of the diffusion processes in this region is 
pointed out. The existence of a group of asteroids like (3789) 
Zhongguo, inside the 2/1 resonance, is also discussed. (C) 1998 
Elsevier Science Ltd. All rights reserved.

=========================
(8) REQUIRED ACCURACY OF THE MOTION THEORIES OF PERTURBING BODIES

E.D. Kuznetsov: The celestial bodies motion theories: on the required 
accuracy of the motion theories of the perturbing bodies. PLANETARY AND 
SPACE SCIENCE, 1997, Vol.45, No.12, pp.1595-1606

URAL STATE UNIVERSITY, DEPARTMENT OF ASTRONOMY, LENIN AVE 51, 
EKATERINBURG 620083, RUSSIA

The equation for calculation of the required accuracy of the perturbing 
bodies motion theories is obtained. The equation relates the accuracy 
required to take into account perturbing acceleration, acting on the 
perturbed body, with the accuracy of the motion theory of the 
perturbing body. The solutions for estimation of the required accuracy 
both for the inner and external cases in the spherical coordinates are 
coincided. The solution for the calculation of the required accuracy 
for the general case (combining the inner and the external cases) in 
Cartesian coordinates is obtained. The special cases for the solution 
in Cartesian are studied. As an example, the estimations of the 
required accuracy of the motion theories of the solar system planets 
for some perturbed bodies (the near-Earth asteroid 4179 Toutatis, the 
main belt asteroid 208 Larcimosa, the trojan asteroid 588 Achilles, the 
centaur asteroid 5145 Pholus, the Kuiper belt asteroid 1995 QZ9, the 
comet Halley) are obtained. The conditions of the use of the obtained 
results are discussed. (C) 1998 Elsevier Science Ltd. All rights 
reserved.

============================
(9) MONITORING CHIRON'S BRIGHTNESS

D. Lazzaro*), M.A. Florczak, C.A. Angeli, J.M. Carvano, A.S. 
Betzler, A.A. Casati, M.A. Barucci, A. Doressoundiram, M. Lazzarin:
Photometric monitoring of 2060 Chiron's brightness at perihelion. 
PLANETARY AND SPACE SCIENCE, 1997, Vol.45, No.12, pp.1607-1614

*) ON CNPQ, DEPARTMENT OF ASTROPHYSICS, BR-20921 RIO JANEIRO, BRAZIL

The results of photometric and spectroscopic observations of 
comet/asteroid 2060 Chiron carried on at the Observatorio do 
Pico-dos-Dias (Brazil) at the European Southern Observatory (Chile) and 
at the Mauna Kea Observatory (Hawaii) during 1996 are presented. The 
analysis of the photometric data shows that even at a minimum of 
brightness 2060 Chiron presents some activity. The absolute magnitude, 
H-v, varied from 6.79 in February to 6.22 in March. Therefore 2060 
Chiron is still in a minimum of activity close to that of 1983-1985 and 
of 1994-1995. (C) 1998 Elsevier Science Ltd. All rights reserved.

=============================================
(10) JOINT ASTEROID OBSERVATIONS BY ESO & KHARKIV OBSERVATORIES

V.G. Shevchenko*), I.N. Belskaya, V.G. Chiorny, J. Piironen, A. 
Erikson, G. Neukum & R. Mohamed: Asteroid observations at low phase 
angles. I. 50 Virginia, 91 Aegina and 102 Miriam. PLANETARY AND SPACE 
SCIENCE, 1997, Vol.45, No.12, pp.1615-1623

*) ASTRONOMICAL OBSERVATORY, BOX 515, S-75120 UPPSALA, SWEDEN

We present observations of magnitude-phase dependences of three 
low-albedo asteroids down to phase angles of 0.1-0.2 degrees. Data were 
obtained during 40 nights from 1994 to 1995 within the joint 
observational program at ESO and Kharkiv Astronomical Observatories 
with the aim to reach as low phase angles as possible. All three 
low-albedo asteroids may display a small nonlinear increase in 
magnitude-phase dependence at subdegree phase angles. The phase curves 
of 50 Virginia and 102 Miriam are poorly approximated by the HG 
function. Rotation periods of the asteroids were also determined: 
14.310+/-0.010 hours for 50 Virginia, 6.030+/-0.001 h for 91 Aegina and 
15.789+/-0.003 h for 102 Miriam. (C) 1998 Elsevier Science Ltd. All 
rights reserved.

===========================
(11) A NEW MODEL TO SIMULATE IMPACT BREAKUP

A. Cordelli & P. Farinella: A new model to simulate impact breakup
PLANETARY AND SPACE SCIENCE, 1997, Vol.45, No.12, pp.1639-1647

UNIVERSITY OF PISA, DIPARTIMENTO MATEMAT, GRP MECCAN SPAZIALE, VIA 
BUONARROTI 2, I-56127 PISA, ITALY

We have developed a preliminary version of a new type of code to 
simulate the outcomes of impacts between solid bodies, which we plan to 
further refine for application to both asteroid science and space 
debris studies. In the current code, colliding objects are modeled as 
two-dimensional arrays of finite elements, which can interact with each 
other in both an elastic and a shock-wave regime. The finite elements 
are hard spheres with a given value for mass and radius. When two of 
them come into contact the laws of inelastic scattering are applied, 
thus giving rise to the propagation of shock waves. Moreover each 
spherical elements interacts elastically with its nearest neighbours. 
The interaction force corresponds to that of a spring having an 
equilibrium length equal to the lattice spacing, and results into the 
propagation of elastic waves in the lattice. Dissipation effects are 
modeled by means of a dissipative force term proportional to the 
relative velocity, with a given characteristic time of decay. The 
possible occurrence of fractures in the material is model by assuming 
that when the distance of two neighbouring elements exceeds a threshold 
value, the binding force between them disappears for ever. This model 
requires finding a plausible correspondence between the input 
parameters appearing in the equations of motion, and the physical 
properties of real solid materials. Some of the required links are 
quite obvious (e.g., the relationship between mass of the elements and 
elastic constant on one side, and material density and sound velocity 
on the other side), some others a priori are unclear, and additional 
hypotheses on them must be made (e.g., on the restitution coefficient 
of inelastic scattering). Despite the preliminary character of the 
model, we have obtained some interesting results, which appear to mimic 
in a realistic way the outcomes of actual impacts. For instance, we 
have observed the formation of crates and fractures, and (for high 
impact energies) the occurrence of catastrophic breakup.. The masses and 
velocities of the fragments resemble those found in laboratory impact 
experiments. (C) 1998 Elsevier Science Ltd. All rights reserved.

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