Harry Varvoglis

Aristotle University of Thessaloniki | AUTH · School of Physics

The increasing number of free-floating planets discovered in recent years confirms earlier theoretical predictions and leads us to believe that the possibility of such an object intruding an existing planetary system is not negligible, especially in dense clusters. We present a theoretical dynamical study on the interaction of a free-floating plane...

Along the subject line of this workshop, the common topic of the submissions is the field of extrasolar planetary systems with its multitude of facets ? from orbital dynamics to mutually destructive collisions, from binary star systems to Trojan planets to exocomets, from captured free-floating objects to artificial satellites. Despite the comparat...

Predicting biodiversity relaxation following a disturbance is of great importance to conservation biology. Recently-developed models of stochastic community assembly allow us to predict the evolution of communities on the basis of mechanistic processes at the level of individuals. The neutral model of biodiversity, in particular, has provided close...

The problem of the origin of asteroids residing in the Jovian first-order mean motion resonances is still open. Is the observed population survivors of a much larger population formed in the resonance in primordial times? Here, we study the evolution of 182 long-lived asteroids in the 2:1 Mean Motion Resonance, identified in Brož & Vokrouhlické (20...

In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of ex...

We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the planar to the spatial case. We find that such bifurcations exist only for planetary mass ratios $\rho=\frac{m_2}{...

After the detailed presentation of the evolution of concepts and ideas in various branches of physics, we can arrive at some interesting general conclusions concerning the dependence of this evolution on various parameters, such as the geographical area, the model for the development of research and the personality of scientists.

Motion was one of the earlier phenomena that were studied by ancient Greek natural philosophers. One might initially assume that motion is a characteristic of life: people and animals move freely, while dead men and stones do not. It is possible of course to make a rock to move, but this usually happens through the impulse given to it by a living b...

Modern universities are the result of many centuries of evolution. We can say that higher education has its roots in the teachings of natural philosophers of Ionia and Magna Graecia. However, strictly speaking, a master’s teaching to his students (for example, Socrates to Plato or Plato to Aristotle) cannot be regarded as a university course, since...

The history of any discipline is always based on written texts. In this way, to restrict ourselves to texts of Antiquity, the history of the Jewish people is based on the books of the Old Testament, the history of the Persian Wars on the books by Herodotus and the history of the Peloponnesian War on the books by Thucydides. Even the history of the...

During the Hellenistic period (The period that starts after the death of Alexander the Great), natural sciences continued to develop through the work of natural philosophers of Greek education and culture (not necessarily Greeks) mainly in Greek colonies and in Alexander’s empire, as well as in the mainland. More specifically, the great intellectua...

The evolution of physics did not come to an end in the dawn of the 20th century, as many physicists believed at that time and as school textbooks seem to imply sometimes. Simply, the new avenue opened by Galilean transformations had come to an end at the moment when Lorentz transformations were introduced. Experimental results accumulated in the ea...

The evolution of physics from the Renaissance until today could be the subject of a book thousands of pages long. But if a book is intended to help the readers in the “organization” of physics they already know into a “logical” structure, it should be limited to the major branches of this discipline. Furthermore, if this knowledge is of high school...

Our understanding of nature, and in particular of physics and the laws governing it, has changed radically since the days of the ancient Greek natural philosophers. This book explains how and why these changes occurred, through landmark experiments as well as theories that - for their time - were revolutionary. The presentation covers Mechanics, Op...

Discoveries of exoplanets orbiting evolved stars motivate critical examinations of the dynamics of N-body systems with mass-loss. Multiplanet evolved systems are particularly complex because of the mutual interactions between the planets. Here, we study the underlying dynamical mechanisms which can incite planetary escape in two-planet post-main-se...

Discoveries of exoplanets orbiting evolved stars motivate critical examinations of the dynamics of $N$-body systems with mass loss. Multi-planet evolved systems are particularly complex because of the mutual interactions between the planets. Here, we study the underlying dynamical mechanisms which can incite planetary escape in two-planet post-main...

GAIA is expected to greatly enhance our knowledge on the orbital, spin-state, spectral and size distribution of individual asteroids and asteroid families. Dynamical models, incorporating resonant phenomena and thermal (Yarkovsky/YORP) effects, can be used to understand the observations, in particular the orbital, size-frequency and spin-axis distr...

In a recent paper, published in Astrophys. Space Sci. (337:107, 2012) (hereafter paper ZZX) and entitled “On the triangular libration points in photogravitational restricted three-body problem with variable mass”, the authors study the location and stability of the generalized Lagrange libration points L 4 and L 5. However their study is flawed in...

The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-f...

The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model have been extensively studied in the literature, only few results about the dynamics of the elliptic model were...

In a previous work we studied the effects of (I) the J 2 and C 22 terms of the lunar potential and (II) the rotation of the primary on the critical inclination orbits of artificial satellites. Here, we show that, when 3rd-degree gravity harmonics are taken into account, the long-term orbital behavior and stability are strongly affected, especially...

A questionable approximation in the calculation of the period of revolution of a pair of extended bodies, appearing in the paper mentioned in the title, is pointed out. An exact method to perform this task is suggested.

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J 2 and C 22 terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument of pericenter do not remain both constant at the same...

The family of (490) Veritas is a young, dynamically heterogeneous asteroid family, located in the outer main belt. As such, it represents a valuable example for studying the effects of chaotic diffusion on the shape of asteroid families. The Veritas family can be decomposed into several groups, in terms of the principal mechanisms that govern the l...

When one thinks of the solar system, he has usually in mind the picture based on the solution of the two‐body problem approximation presented by Newton, namely the ordered clockwork motion of planets on fixed, non‐intersecting orbits around the Sun. However, already by the end of the 18th century this picture was proven to be wrong. As discussed by...

The family of (490) Veritas is a young, dynamically heterogeneous asteroid family, located in the outer main belt. We took advantage of the fact that it can be decomposed in several groups, in terms of the principal mechanisms that govern the local dynamics, to asses the age of the family. Using the members with the diffusive chaotic motion, we der...

All laws that describe the time evolution of a continuous system are given in the form of differential equations, ordinary (if the law involves one independent variable) or partial (if the law involves two or more independent variables). Historically the first law of this type was Newton's second law of motion. Since then Dynamics, as it is customa...

In the beginning we review briefly the evolution of the ideas on the motion of the bodies in our solar system, from Newton's clockwork Universe to the presently accepted ubiquity of chaotic transport in the asteroid belt. Then we discuss the result of chaotic motion, which is transport in phase space, and we introduce the concept of diffusion of an...

It is usually believed that we know everything to be known for any separable Hamiltonian system, i.e. an integrable system in which we can separate the variables in some coordinate system (e.g. see Lichtenberg and Lieberman 1992, Regular and Chaotic Dynamics, Springer). However this is not always true, since through the separation the solutions may...

In a recent paper [1] we estimated the topological dimension of trajectories belonging to three typical classes of the Restricted Three Body Problem (RTBP), namely regular, chaotic and stable chaotic. We found that stable chaotic trajectories seem to wonder in a phase space region where local integrals of motion exist, besides the already known iso...

A population of 23 asteroids is currently observed in a very unstable region of the main belt, the 7/3 Kirkwood gap. The small size of these bodies—with the notable exception of (677) Aaltje (∼ 30 km)—as well as the computation of their dynamical lifetimes (3 < T D < 172 Myr) shows that they cannot be on their primordial orbits, but were recently i...

In 1964 M. Hénon and, independently, V. Szebehely with G. Bozis presented the first numerical results, indicating the existence of a “new” local integral of motion in the circular restricted three-body problem. The first terms of an asymptotic expansion of this integral were later calculated by Contopoulos [1]. Several years later, the Celestial Me...

6.1 Introduction In recent decades it became evident that non-integrable, i.e. "chaotic", dynamical systems are the rule rather than the exception in nature. Many scientists however, especially astronomers working in Celestial Mechanics, have grown up in the belief that most systems of interest show a regular behavior. But methods devised for the s...

In this paper we present a comprehensive analysis of the dynamics in the region of the Veritas family, aiming to describe the principal mechanisms at work and provide a more reliable estimate of the diffusion rate. Our numerical integrations confirm previous results on the chaotic motion of the family members and on the resonances involved, but als...

In previous publications we suggested that stable chaos is related to the existence of local integrals of motion in the phase-space region occupied by the trajectory. In order to test this hypothesis we estimated, using a numerical method, the topological dimension, d3, of several trajectories in the 3-D embedding space of proper elements. Our firs...

We have shown, in previous publications, that stable chaos is associated with medium/high-order mean motion resonances with Jupiter, for which there exist no resonant periodic orbits in the framework of the elliptic restricted three-body problem. This topological “defect” results in the absence of the most efficient mechanism of eccentricity transp...

In a previous publication (Tsiganis et al. 2000, Icarus146, 240–252), we argued that the occurrence of stable chaos in the 12/7 mean motion resonance with Jupiter is related to the fact that there do not exist families of periodic orbits in the planar elliptic restricted problem and in the 3-D circular problem corresponding to this resonance. In th...

If an asteroid is located in a mean motion resonance with Jupiter, its orbital elements, especially the eccentricity, e, can be transported to Jupiter-crossing values due to chaotic motion. For resonances closer to Jupiter, such as those placed in the outer asteroid belt (defined here by 3.45AU ≤ a ≤ 3.90AU), a large fraction of orbits is expected...

One of the most interesting, newly discovered, phenomena in solar system dynamics is a type of asteroidal motion commonly referred to as stable chaos. An asteroid on stable chaotic motion (ASC) follows a strongly chaotic trajectory (as indicated by its short Lyapunov time, T L = 1 / λ, where λ is the Maximal Lyapunov Characteristic Number, LCN) and...

Numerical evidence is presented, indicating that the Coulomb three-body scattering problem possesses chaotic phase space regions for collision energies corresponding to the common classical approximation regime. Consequently, the stochasticity threshold of 100 eV, reported previously by Sattin and Salasnich, is extended by two orders of magnitude u...

Recent studies show that chaotic motion should be considered as the rule rather than the exception in the asteroid belt, if the pertur bations of many planets are taken into account. Assuming that asteroids are constantly diffus- ing away from the main belt, we may model their transport, i.e. the evolution of a distribution of initial conditions in...

The study of the motion of a point mass, moving in the gravitational field of two fixed attracting centers, is a problem first posed by Euler in the 18th century, as an intermediate step towards the solution of the famous three-body problem. Euler himself, in a series of three papers (Euler 1766a, 1766b and 1767), was able to integrate the equation...

Chaotic trajectories in Hamiltonian systems may have a peculiar evolution, owing to stickiness effects or migration to adjacent stochastic regions. As a result, the function χ(t), which measures the exponential divergence of nearby trajectories, changes its behaviour within different time intervals. We obtain such trajectories, through numerical in...

On May 9 the Minor Planet Center announced the re-discovery of the last `lost' minor planet, (719) Albert. In this paper we study its orbital evolution. We show that Albert follows an extremely chaotic orbit, typical of near-Earth asteroids (NEAs) that are extracted from main belt resonances through close planetary encounters. It will become an Ear...

We follow the evolution of distributions of real and fictitious asteroids, initially placed in the vicinity of the 12:7 mean motion resonance with Jupiter. Our results show that, besides the well-known example of 522-Helga, other stable chaotic asteroids could, in principle, exist in this region of the belt. Most of the particles, though, attain Ju...

We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then performing a power spectrum analysis of the series. Ordered trajectories present a spectrum that consists of a...

We study transport in a model perturbed integrable Hamiltonian system by calculating the volume, V(t), of elementary phase space cells visited by a trajectory, as a function of time. We use this function in order to "measure" the fractality of phase space. We argue that the "degree" of fractality is related to the well known difficulties in assigni...

A model, plane symmetric, 3-D potential, which preserves some features of galactic problems,is used in order to examine the phase space structure through the study of the properties of orbits crossing perpendicularly the plane of symmetry. It is found that the lines formed by periodic orbits, belonging to Farey sequences, are not smooth neither con...

The interaction of charged particles, moving in a uniform magnetic field, with a plane-polarized gravitational wave is considered using the Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact locations in phase space, where resonance overlapping occurs. We investigate the diffusion of orbits around e...

We study the resonant interaction of charged particles with a gravitational wave propagating in the non-empty interstellar space in the presence of a uniform magnetic field. It is found that this interaction can be cast in the form of a parametric resonance problem which, besides the main resonance, allows for the existence of many secondary ones....

Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The spacetime consists of one timelike dimension and two maximally symmetric subspaces, filled with matter in the form of an anisotropic fluid. Numerical integration of the cosmological field equations indicate...

Transport in Hamiltonian systems, in the case of strong perturbation, can be modeled as a diffusion process, with the diffusion coefficient being constant and related to the maximal Lyapunov number (Konishi 1989). In this respect the relation found by Lecar et al. (1992) between the escape time of asteroids, T E , and the Lyapunov time, T L , can b...

Transport in Hamiltonian systems, in the case of strong perturbation, can be modeled as a diffusion process , with the diffusion coefficient being constant and related to the maximal Lyapunov number (Konishi 1989). In this respect the relation found by Lecar et al. (1992) between the escape time of asteroids, T E , and the Lyapunov time, T L , can...

By using Lyapounov's direct method the authors examine the conditions under which stable solutions to the field equations for the scale function of the external space may be derived in the context of a five-dimensional quadratic theory of gravity. They show that the time evolution of the distance, in a diagram t-R, between the solution to the field...

The assumption that transport in a Hamiltonian system can be described as a normal diffusion process leads naturally to a power law dependence of the exit time, TE, on the Lyapunov time, TL=l/lambda, where by lambda we denote the maximal Lyapunov characteristic number, LCN. Since transport in perturbed integrable Hamiltonian systems can be modeled...

Stability features of dynamical systems are frequently attributed to the implications of the Kolmogoroff-Arnold-Moser (KAM) theorem. However, application of this theorem requires compact phase-space regions. This is not the case in the hyperbolic Coulomb three-body problem encountered in most of the classical trajectory Monte Carlo (CTMC) applicati...

The evolution of the eccentricity of particular asteroidal trajectories in the 2:1 resonance is analysed by a spectral scheme. This analysis is an alternative to the well known analysis based on the computation of Liapunov exponents. The method can be used to estimate the long time evolution of a trajectory from a segment considerably shorter than...

The propagation of a gravitational wave in the non-empty interstellar space, in the presence of a uniform magnetic field, is investigated. It is found that the type of interaction of the wave with the interstellar plasma depends on the direction of propagation of the gravitational wave with respect to the magnetic field. In the oblique and parallel...

In this paper we examine the statistical properties of transport, for orbits of fictitious asteroids initiated in three outer-belt resonances: the 7:4, 9:5 and 12:7 mean motion resonances of the 2-D elliptic restricted three-body problem. Two alternative approaches are used: (i) numerical integration of distributions of initial conditions and (ii)...

In a recent work (Varvoglis 1991) we proposed the use of a model dynamical system as a fast and effective method to study the motion of asteroids in the main asteroidal belt. This dynamical system is, essentially, a modified planar elliptical restricted three-body problem, in which the variation of Jupiter's eccentricity, caused by the perturbation...

The interaction of a charged particle, moving in a uniform magnetic field, with a gravitational wave is considered for two types of wave polarization (linear and circular) and for an arbitrary direction of propagation, with respect to the magnetic field. It is found that, in the oblique and perpendicular propagation cases, the motion of the particl...

The motion of charged particles (electrons or ions) is considered in a uniform magnetic field and a linearly polarized gravitational wave propagating along the x-axis. It is found numerically that for certain values of the amplitude of the wave and the relative frequency, nu = omega/Omega, (where by omega we denote the angular frequency of the wave...

A number of lunar flashes or transient lunar phenomena have been recorded. The latest observation was made in 1985 by a Greek astronomer who, together with colleagues at the University of Thessaloniki, concluded the flash was caused by a discharge close to the lunar surface. American astronomers have since proposed the flash was caused by satellite...

We present further evidence that the bright spot on the Moon observed on May 23, 1985, was a natural phenomenon that occurred slightly above the lunar surface. The interpretation that the spot could be attributed to an instantaneous reflection from a satellite's solar panel fails to explain several important characteristics of the observation.

Many trajectories of the third body are integrated numerically in a modified elliptical restricted three body problem (ERTBP), in which the eccentricity, e, of the orbit of the second primary varies sinusoidally with time. It is found that, in the case of the 2:1 resonance, the introduction of the time variability of e modifies significantly the be...

The present small amount of water in the atmosphere of Venus, in connection with the estimated short time scale of water loss from this planet, has lead to the hypothesis that the water concentration in the Venusian atmosphere is in a dynamical equilibrium, where the losses are counter-balanced by a suitable water source. The main candidate water s...

The stochastic non-resonant energization of ions in non-sinusoidal coherent plane-polarized magnetosonic waves is investigated. It is found that, as in the case of sinusoidal magnetosonic waves, the process does not follow quasi-linear theory, i.e. it is a diffusion in velocity space, but with a diffusion coefficient D ν–α, α ≈ 1, instead of D ν–3....

We present photographic evidence of a very short duration, strong flash from the surface of the Moon (near an irregularly shaped crater in Palus Somni). The flash covered a region roughly 22 by 18 km wide with a total energy of the order of 1017 erg. The event is established to be slightly above the surface of the Moon. An explanation is proposed i...

In a model galaxy composed of a relativistically active nucleus, a main body, and a halo, all three components considered as homogeneous prolate ellipsoids, we explore the probable association of the internal characteristics of the nucleus and the observed orbits of the stars near the surface of the main body. Using the authors’ theoretical framewo...

The diffusion due to stochasticity is explored numerically in a simple model that represents the plane of symmetry of a nonrotating distorted galaxy. The onset of large scale stochasticity is studied in a Hamiltonian system of two degrees of freedom that may represent the inner parts of a deformed galactic model. When the energy is small, the stoch...

The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold...

The ordered or chaotic behaviour of charged particle trajectories in the static magnetic field of the Astron thermonuclear reactor is numerically investigated. Despite the fact that the corresponding Hamiltonian function is of class C**0, from which it follows that this dynamical system does not possess true phase space invariant tori for any numer...

It is shown that no conflicts need to arise between results on the stochastic properties of a dynamical system obtained through the method of the surface of section mapping and results obtained through the Hedlund-Hopf-Lobachevsky-Hadamard theorem.

The characteristic curves of several families of periodic orbits in a two-dimensional quartic potential field symmetric with respect to both axes x and y are explored. Two types of families are found: (a) regular families which are connected with the families of the unperturber system and (b) irregular families not connected with the above. It is s...

The motion of test ions in a magnetosonic plasma wave is considered, and the 'stochasticity threshold' of the wave's amplitude for the onset of chaotic motion is estimated. It is shown that for wave amplitudes above the stochasticity threshold, the evolution of an ion distribution can be described by a diffusion equation with a diffusion coefficien...

The large scale chaotic motion of a charged particle in a homogeneous static magnetic field and a longitudinal electrostatic wave is discussed. A formula for estimating the stochasticity threshold alpha thr of the wave amplitude from the wave frequency nu and the propagation angle phi is proposed. For ϕ = π/2 and phi approximately = π/4 this formul...

The model advanced by Fisk (1978) to explain the anomalous enhancements in the abundance of some ionic species in energetic solar particle flux measurements at about 1 AU is revised by including the proper nonlinear physics of particle energization by electrostatic ion cyclotron (EIC) waves. The revised model contains two basic concepts by Fisk: th...

The problem of constructing the stochasticity criterion of a degenerate near-integrable dynamical system is considered. We show that in certain cases the above criterion can be found as the limit of the corresponding stochasticity criteria of a family of non-degenerate systems, whose limit is the degenerate one.

The abundance anomalies associated with 3He-rich flares, are attributed to the intrinsically anomalous acceleration behavior of species with A/Q less than 3, in the presence of hydrogen cyclotron waves. While the overall model is along the lines of Fisk's (1978) proposal, the difficulties associated with triggering of nonhydrogenic cyclotron waves...

The abundance anomalies associated with /sup 3/He-rich flares, are attributed to the intrinsically anomalous acceleration behavior of species with A/Q less than 3, in the presence of hydrogen cyclotron waves. While the overall model is along the lines of Fisk's (1978) proposal, the difficulties associated with triggering of nonhydrogenic cyclotron...

A theoretical framework is developed for the construction of a formal, third integral of motion in the post-Newtonian approximation of general relativity, which will be valid for a test particle moving in the four-dimensional spacetime of a gravitating source. The source is composed of a bounded, perfect-fluid mass with a plane of symmetry, and wit...

. We examine whether the macroscopically measured diffusion rate in the chaotic region of a time-perturbed classical pendulum depends on the value of the maximalLyapunov characteristic number, #. In this respect we calculate the functions #(l), w(l), #(#) and w(#), where l denotes the physical length of the pendulum, # the strength of the perturbat...

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle t...

It is well known since the 19th century that the Kirkwood gaps, observed in the distribution of orbital periods of the asteroids, correspond to simple commensurabilities with the orbital period of Jupiter. Furthermore it is now widely accepted that the main gap-depletion mechanism is related to the chaotic motion of asteroids, generated in the vici...

We use a running window on the AsDys catalogue of asteroids and create groups of varying proper semi-major axis values. We calculate, for each such group, the distribution of asteroids with respect to proper eccentricity and inclination. We plot the distribution parameters as a function of the semi-major. We see that the graphs are related to the r...

The abundance anomalies associated with ³He-rich flares are attributed to the intrinsically anomalous acceleration behavior of species with A/Q