Doctoral Thesis

Faculty of Mathematics and Computer Science
"Babes-Bolyai" University, Cluj-Napoca, Romania

THE ORIGIN AND EVOLUTION OF CELESTIAL BODIES
GRAVITATING IN THE VICINITY OF EARTH'S ORBIT

Stefan Berinde

-doctoral thesis-

Research supervisor: Prof.Dr. Vasile Ureche

Date of public defence: June 14, 2002

Content

Introduction

Abbreviations

Chapter 1. Population description
1.1 Observational evidences
1.2 Observational biases

Chapter 2. Dynamics of close encounters
    2.1 The restricted three body problem
        2.1.1 Equations of motion
        2.1.2 Jacobi integral
        2.1.3 Tisserand criterion
        2.1.4 Lagrange equilibrium points
        2.1.5 Hill’s equations
    2.2 Opik’s geometric formalism
        2.2.1 Motion characteristics
        2.2.2 Motion outside the planetary sphere of action
        2.2.3 Motion inside the planetary sphere of action
        2.2.4 A complete map of orbital changes

Chapter 3. Characteristics of long-term dynamical evolution
    3.1 Chaotic behaviour
        3.1.1 Chaos in the planar, circular, restricted three-body problem
        3.1.2 Lyapounov exponents
        3.1.3 Effects of chaos on long-term numerical integrations
    3.2 Resonant motions
        3.2.1 Mean motion resonances
        3.2.2 Secular resonances
        3.2.3 Protection mechanisms
    3.3 Dynamical classifications
        3.3.1 Classification against minimal orbital intersection distance
        3.3.2 SPACEGUARD classification

Chapter 4. Source regions and dynamical transport mechanisms
    4.1 The main belt of asteroids as NEA source
        4.1.1 Dynamical structure of the asteroid belt
        4.1.2 Transport mechanisms to the inner solar system
        4.1.3 The role of inter-asteroidal collisions
        4.1.4 Estimating the mass of asteroids
    4.2 NEA asteroids of cometary origin
        4.2.1 Populations of bodies in the outer solar system
        4.2.2 Chaotic diffusion of bodies from the Kuiper belt to the inner solar system

Chapter 5. Methods of estimating the impact probability with the Earth
    5.1 Mean impact probabilities
        5.1.1 Extrapolated probabilities from the frequency of close encounters
        5.1.2 Averaged probabilities along the orbit
    5.2 Intrinsic impact probabilities
        5.2.1 Determination of the orbital uncertainty region
        5.2.2 Propagation of the orbital uncertainty region
        5.2.3 Analysis of the impact scenario in the target plane
        5.2.4 Identifying and cataloging close encounters
        5.2.5 Estimation of the intrinsic impact probability
        5.2.6 Monte-Carlo iterative sampling
    5.3 Quantifying the impact hazard
        5.3.1 Torino scale
        5.3.2 Palermo scale
        5.3.3 Consequences of the impact phenomenon

Chapter 6. The SolSyIn package
    6.1 Package description
    6.2 Radau-Everhart numerical integration method
        6.2.1 Description of used dynamical model
        6.2.2 Mathematical aspects
        6.2.3 The numerical algorithm
        6.2.4 Control of the integration precision
    6.3 A numerical example

List of figures

Bibliography

Index

An extended abstract (in English) is available here (PDF format, 0.5 Mb).

The full thesis (in Romanian) is available here (PDF format, 1.2 Mb).


	Related links: Personal report on dynamics of the asteroid (29075) 1950 DA - a potential impactor with the Earth The SolSyIn package Author homepage
Animation: some virtual asteroids from the orbital uncertainty region of the asteroid 2000 SG344 approaching the Earth on May 1, 2069 (projection on ecliptic plane).

Last change on April 23, 2002.