Asteroid Proper Elements: The Big Picture

Four perturbation theories presently used to compute asteroid proper elements are reviewed, and their results are briefly discussed (Milani and Knežević, 1990, 1992, 1994, for low to moderate eccentricity/inclination main belt objects; Lemaitre and Morbidelli, 1994, for high e, I objects; Milani, 1993, for Trojans; Schubart, 1982, 1991 for Hildas). The most important recent improvements are described, in particular those pertaining to the upgrades of the previous analytic and semianalytic solutions. The dynamical structure of the asteroid main belt, as defined by the low order mean motion resonances and by linear and nonlinear secular resonances, is considered from the point of view of the effects of these resonances on the accuracy and/or reliability of the computation of proper elements and on the reliability of the identification of asteroid families.

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Higher Order and Iterative Theories to Compute Asteroid Mean Elements

International Astronomical Union Colloquium ◽

10.1017/s0252921100072717 ◽

1999 ◽

Vol 172 ◽

pp. 359-360 ◽

Cited By ~ 1

Author(s):

Z. Knežević ◽

A. Milani

Keyword(s):

Asteroid Belt ◽

Dynamical Structure ◽

Orbital Elements ◽

Mean Motion Resonances ◽

First Order ◽

Mean Motion ◽

Long Time ◽

The Mean ◽

Mean Elements ◽

Asteroid Families

Mean orbital elements are obtained from their instantaneous, osculating counterparts by removal of the short periodic perturbations. They can be computed by means of different theories, analytical or numerical, depending on the problem and accuracy required. The most advanced contemporary analytical theory (Knežević 1988) accounts only for the perturbing effects due to Jupiter and Saturn, to the first order in their masses and to degree four in eccentricity and inclination. Nevertheless, the mean elements obtained by means of this theory are of satisfactory accuracy for majority of the asteroids in the main belt (Knežević et al. 1988), for the purpose of producing large catalogues of mean and proper elements, to identify asteroid families, to assess their age, to study the dynamical structure of the asteroid belt and chaotic phenomena of diffusion over very long time spans. In the vicinity of the main mean motion resonances, however, especially 2:1 mean motion resonance with Jupiter, these mean elements are of somewhat degraded accuracy.

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Asteroid Proper Elements and the Dynamical Structure of the Asteroid Main Belt

Icarus ◽

10.1006/icar.1994.1020 ◽

1994 ◽

Vol 107 (2) ◽

pp. 219-254 ◽

Cited By ~ 142

Author(s):

Andrea Milani ◽

Zoran KnežEvić

Keyword(s):

Dynamical Structure ◽

Main Belt ◽

Proper Elements

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Asteroid Families Close to Mean Motion Resonances: Dynamical Effects and Physical Implications

Icarus ◽

10.1006/icar.1995.1181 ◽

1995 ◽

Vol 118 (1) ◽

pp. 132-154 ◽

Cited By ~ 66

Author(s):

A. Morbidelli ◽

V. Zappala ◽

M. Moons ◽

A. Cellino ◽

R. Gonczi

Keyword(s):

Mean Motion Resonances ◽

Mean Motion ◽

Asteroid Families

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Secular evolution of asteroid families: the role of Ceres

Proceedings of the International Astronomical Union ◽

10.1017/s1743921315008595 ◽

2015 ◽

Vol 10 (S318) ◽

pp. 46-54 ◽

Cited By ~ 2

Author(s):

Bojan Novaković ◽

Georgios Tsirvoulis ◽

Stefano Marò ◽

Vladimir Đošović ◽

Clara Maurel

Keyword(s):

Numerical Simulations ◽

Main Belt ◽

Secular Resonance ◽

Secular Evolution ◽

Secular Dynamics ◽

Proper Elements ◽

Post Impact ◽

Actual Shape ◽

Asteroid Families

AbstractWe consider the role of the dwarf planet Ceres on the secular dynamics of the asteroid main belt. Specifically, we examine the post impact evolution of asteroid families due to the interaction of their members with the linear nodal secular resonance with Ceres. First, we find the location of this resonance and identify which asteroid families are crossed by its path. Next, we summarize our results for three asteroid families, namely (1726) Hoffmeister, (1128) Astrid and (1521) Seinajoki which have irregular distributions of their members in the proper elements space, indicative of the effect of the resonance. We confirm this by performing a set of numerical simulations, showcasing that the perturbing action of Ceres through its linear nodal secular resonance is essential to reproduce the actual shape of the families.

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The Dynamics of the Trojan Asteroids

Symposium - International Astronomical Union ◽

10.1017/s0074180900046520 ◽

1994 ◽

Vol 160 ◽

pp. 159-174

Author(s):

Andrea Milani

Keyword(s):

State Of The Art ◽

Stability Boundary ◽

Synthetic Method ◽

Dynamical Structure ◽

Main Belt ◽

Trojan Asteroids ◽

Proper Elements ◽

Numerical Integrations ◽

The Stability ◽

The One

The state of the art in the dynamics of the Trojan asteroids has progressed rapidly, since it has been possible to perform numerical integrations of many orbits for millions of years. Accurate proper elements are now computed by the synthetic method, that is from the output of a numerical integration; their stability, at least for time spans of a few million years, is good. This has allowed identification of Trojan families with an automated procedure closely mimicking the one used in the main belt. Although the families identified in a reliable way are only four, the occurrence of significant collisional evolution, not unlike that of the main belt, can be confirmed. The dynamical structure of the Trojan cloud, including the location of the main secular resonances, can be deduced from the proper elements and frequencies by a simple fit. However, many problems are not solved: the origin of a significant percentage of chaotic orbits showing no indications of instability; the location of the stability boundary of the Trojan cloud; the origin of the high inclination of most Trojans. We also do not know if there are “Trojans” for some other planets beside Jupiter: only one Mars Trojan has been found.

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The relationship between the `limiting' Yarkovsky drift speed and asteroid families' Yarkovsky V-shape

Serbian Astronomical Journal ◽

10.2298/saj2000025m ◽

2020 ◽

pp. 25-41

Author(s):

I. Milic-Zitnik

Keyword(s):

Interesting Property ◽

Parent Body ◽

Mean Motion Resonances ◽

Mean Motion ◽

Drift Speed ◽

Yarkovsky Effect ◽

The Mean ◽

The Relationship ◽

Asteroid Families

The Yarkovsky effect is an important force to consider in order to understand the long-term dynamics of asteroids. This non-gravitational force affects the orbital elements of objects revolving around a source of heat, especially their semi-major axes. Following the recently defined `limiting' value of the Yarkovsky drift speed at 7x10-5 au/Myr in Milic Zitnik (2019) (below this value of speed asteroids typically jump quickly across the mean motion resonances), we decided to investigate the relation between the asteroid family Yarkovsky V-shape and the `limiting' Yarkovsky drift speed of asteroid's semi-major axes. We have used the known scaling formula to calculate the Yarkovsky drift speed (Spoto et al. 2015) in order to determine the inner and outer `limiting' diameters (for the inner and outer V-shape borders) from the `limiting' Yarkovsky drift speed. The method was applied to 11 asteroid families of different taxonomic classes, origin type and age, located throughout the Main Belt. Here, we present the results of our calculation on relationship between asteroid families' V-shapes (crossed by strong and/or weak mean motion resonances) and the `limiting' diameters in the (a, 1=D) plane. Our main conclusion is that the `breakpoints' in changing V-shape of the very old asteroid families, crossed by relatively strong mean motion resonances on both sides very close to the parent body, are exactly the inverse of `limiting' diameters in the a versus 1=D plane. This result uncovers a novel interesting property of asteroid families' Yarkovsky V-shapes.

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Extended Families in the Main Belt and in the Trojan Swarms

Highlights of Astronomy ◽

10.1017/s1539299600017032 ◽

2005 ◽

Vol 13 ◽

pp. 758-758 ◽

Cited By ~ 2

Author(s):

Zoran Knezevic ◽

Andrea Milani

Keyword(s):

Hubble Space Telescope ◽

Family Members ◽

Mean Motion Resonances ◽

Size Dependent ◽

Proper Elements ◽

Chaotic Diffusion ◽

Large Spread ◽

The Family ◽

Long Time ◽

Asteroid Families

The availability of highly accurate synthetic proper elements for a large number of asteroids made possible detailed studies of the structure of asteroid families. The entire region of the Vesta family is dominated by bodies with D < 7 km. The large spread of family members appears to be primarily due to Yarkovsky mobility, a strongly size-dependent. The proper elements of the asteroids the region (except close to mean motion resonances) are stable over very long time spans; thus chaotic diffusion could not play a significant role. The total volume of the family members with diameter less than 7 km amounts approximately to 6 x 104 cubic km, the volume of a crater with 100 km diameter and average depth 7 km. If the albedo feature, visible in the Hubble Space Telescope images, is really a crater its volume could be even larger. Thanks to the recently computed catalogs of proper elements for 1167 trojans, there are now confirmed dynamical families in the trojan swarms. This allows to begin to study the collisional evolution with constraints from observations.

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Mitigating the seismic pounding of multi-story buildings in series using linear and nonlinear fluid viscous dampers

Archives of Civil and Mechanical Engineering ◽

10.1007/s43452-021-00249-9 ◽

2021 ◽

Vol 21 (4) ◽

Author(s):

Hytham Elwardany ◽

Robert Jankowski ◽

Ayman Seleemah

Keyword(s):

Substantial Improvement ◽

Point Of View ◽

Steel Buildings ◽

Viscous Dampers ◽

Element Analysis ◽

Fluid Viscous Dampers ◽

Adjacent Buildings ◽

In Series ◽

Linear And Nonlinear ◽

Nonlinear Fluid

AbstractSeismic-induced pounding between adjacent buildings may have serious consequences, ranging from minor damage up to total collapse. Therefore, researchers try to mitigate the pounding problem using different methods, such as coupling the adjacent buildings with stiff beams, connecting them using viscoelastic links, and installing damping devices in each building individually. In the current paper, the effect of using linear and nonlinear fluid viscous dampers to mitigate the mutual pounding between a series of structures is investigated. Nonlinear finite-element analysis of a series of adjacent steel buildings equipped with damping devices was conducted. Contact surfaces with both contactor and target were used to model the mutual pounding. The results indicate that the use of linear or nonlinear dampers leads to the significant reduction in the response of adjacent buildings in series. Moreover, the substantial improvement of the performance of buildings has been observed for almost all stories. From the design point of view, it is concluded that dampers implemented in adjacent buildings should be designed to resist maximum force of 6.20 or 1.90 times the design independent force in the case of using linear or nonlinear fluid viscous dampers, respectively. Also, designers should pay attention to the design of the structural elements surrounding dampers, because considerable forces due to pounding may occur in the dampers at the maximum displaced position of the structure.

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