Dynamical erosion of asteroid groups in the region of the Pallas family

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An analysis of the region of the Phocaea dynamical family

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nebular gas drag and co-orbital system dynamics

Aims. We study trajectories of planetesimals whose orbits decay due to gas drag in a primordial solar nebula and are perturbed by the gravity of the secondary body on an eccentric orbit whose mass ratio takes values from mu(2) = 10(-7) to mu(2) = 10(-3) increasing ten times at each step. Each planetesimal ultimately suffers one of the three possible fates: (1) trapping in a mean motion resonance with the secondary body; (2) collision with the secondary body and consequent increase of its mass; or (3) diffusion after crossing the orbit of the secondary body.Methods. We take the Burlirsh-Stoer numerical algorithm in order to integrate the Newtonian equations of the planar, elliptical restricted three-body problem with the secondary body and the planetesimal orbiting the primary. It is assumed that there is no interaction among planetesimals, and also that the gas does not affect the orbit of the secondary body.Results. The results show that the optimal value of the gas drag constant k for the 1: 1 resonance is between 0.9 and 1.25, representing a meter size planetesimal for each AU of orbital radius. In this study, the conditions of the gas drag are such that in theory, L4 no longer exists in the circular case for a critical value of k that defines a limit size of the planetesimal, but for a secondary body with an eccentricity larger than 0.05 when mu(2) = 10(-6), it reappears. The decrease of the cutoff collision radius increase the difusions but does not affect the distribution of trapping. The contribution to the mass accretion of the secondary body is over 40% with a collision radius 0.05R(Hill) and less than 15% with 0.005R(Hill) for mu(2) = 10(-7). The trappings no longer occur when the drag constant k reachs 30. That means that the size limit of planetesimal trapping is 0.2 m per AU of orbital radius. In most cases, this accretion occurs for a weak gas drag and small secondary eccentricity. The diffusions represent most of the simulations showing that gas drag is an efficient process in scattering planetesimals and that the trapping of planetesimals in the 1: 1 resonance is a less probable fate. These results depend on the specific drag force chosen.

EXPANSION OF THE DISTURBING FUNCTION FOR HIGH ECCENTRICITY AND LARGE-AMPLITUDE OF LIBRATION

Following some ideas, developed by Woltjer (1928), Message (1989), Yokoyama (1988, 1989) and Duriez (1990) an expansion of the disturbing function is given for high values of the eccentricity and large amplitude of libration. The classical expansion can be obtained as a particular case of the present model. Several asteroids with high eccentricity and large amplitude of libration are tested and the results are much better than those obtained from the classical theory.

Simple generalization of Wisdom's perturbative method

A simple generalization of Wisdom's perturbative method, as originally proposed by Wisdom (1985), is obtained. Any number of resonant cosines can be handled and the method can also accommodate more involved disturbing functions. Averaged trajectories are easily obtained by drawing level curves of the action. Here, the method is first tested for simple models of 3:1 and 2:1 resonant problems. Comparisons with numerical integration and surface-section curves show very good agreements.

Collisions with the Earth: the Moon's contribution

In the present work is analyzed the contribution of the Moon on the collisional process of the Earth with asteroids (NEOs). The dynamical system adopted is the restricted four-body problem Sun-Earth-Moon-particle. Using a simple analytical approach one can verify that, the orbit of an object can be significantly affected by the Moon's gravitational field when their relative velocity is smaller than 5 km/s. Therefore, the present work is based on hypothetical asteroids whose velocities relative to Moon are of the order of 1 km/s. In fact, there are several real objects (NEOs) with such velocities at the point they cross the Earth's orbit. The net results obtained indicate that the Moon helps to avoid collisions (2.6%) more than it contributes to extra collisions (0.6%). (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

Irregular Satellites of Jupiter: a study of the capture direction

The irregular satellites of Jupiter are believed to be captured asteroids or planetesimals. In the present work is studied the direction of capture of these objects as a function of their orbital inclination. We performed numerical simulations of the restricted three-body problem, Sun-Jupiter-particle, taking into account the growth of Jupiter. The integration was made backward in time. Initially, the particles have orbits as satellites of Jupiter, which has its present mass. Then, the system evolved with Jupiter losing mass and the satellites escaping from the planet. The reverse of the escape direction corresponds to the capture direction. The results show that the Lagrangian points L1 and L2 mainly guide the direction of capture. Prograde satellites are captured through these two gates with very narrow amplitude angles. In the case of retrograde satellites, these two gates are wider. The capture region increases as the orbital inclination increases. In the case of planar retrograde satellites the directions of capture cover the whole 360 degrees around Jupiter. We also verified that prograde satellites are captured earlier in actual time than retrograde ones.

Resonance and chaos .2. Exterior resonances and asymmetric libration

The motion of a test particle in the vicinity of exterior resonances is examined in the context of the planar, circular, restricted three-body problem. The existence of asymmetric periodic orbits associated with the 1 : n resonances (where n = 2, 3, 4, 5) is confirmed; there is also evidence of asymmetric resonances associated with larger values of n. A detailed examination of the evolution of the family of orbits associated with the 1:2 resonance shows the sequence that leads to asymmetric libration. on the basis of numerical studies of the phase space it is concluded that the existence of asymmetric libration means that the region exterior to the perturbing mass is more chaotic than the interior region. The apparent absence of 'particles' in 1 : n resonances in the solar system may reflect this inherent bias.

The Aster Project: Flight to a Near-Earth Asteroid

The information on the project being developed in Brazil for a flight to binary or triple near-Earth asteroid is presented. The project plans to launch a spacecraft into an orbit around the asteroid and to study the asteroid and its satellite within six months. Main attention is concentrated on the analysis of trajectories of flight to asteroids with both impulsive and low thrust in the period 2013-2020. For comparison, the characteristics of flights to the (45) Eugenia triple asteroid of the Main Belt are also given.

On the first nu(6) anti-aligned librating asteroid family of Tina

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stability regions around the components of the triple system 2001 SN263

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Resonance and chaos: II. Exterior resonances and asymmetric libration

The motion of a test particle in the vicinity of exterior resonances is examined in the context of the planar, circular, restricted three-body problem. The existence of asymmetric periodic orbits associated with the 1 : n resonances (where n = 2, 3, 4, 5) is confirmed; there is also evidence of asymmetric resonances associated with larger values of n. A detailed examination of the evolution of the family of orbits associated with the 1:2 resonance shows the sequence that leads to asymmetric libration. On the basis of numerical studies of the phase space it is concluded that the existence of asymmetric libration means that the region exterior to the perturbing mass is more chaotic than the interior region. The apparent absence of 'particles' in 1 : n resonances in the solar system may reflect this inherent bias.

Time analysis for temporary gravitational capture: Satellites of Uranus

We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of different capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elements - inclination (i), longitude of the node (Ω), argument of pericenter (ω), and time of pericenter passage (τ) - are first taken to be zero. Then we investigate the cases with ω = 90°, 180°, and 270°. We also present a sample of results for Ω = 90°, considering the cases i = 60°, 120°, 150°, and 180°. Special attention is given to the influence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0° to 180° in steps of 10°. The success of the final stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60°-70° and 160°. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

ASTER: A Brazilian mission to an asteroid

The first Brazilian mission to an asteroid is being planned. The target is the asteroid 2001 SN263, which has a NEA orbit of class AMOR. Spectral analysis indicated that this is a C-type asteroid. This type of asteroids are dark and difficult to be studied from Earth. They hold clues of the initial stages of planetary formation and also the origin of water and life on Earth. In fact, radar data showed that 2001 SN263 is composed of three bodies with diameters of about 2.8 km, 1.1 km and 0.4 km. Therefore, the spacecraft will have the opportunity to explore three bodies on the same trip. The mission is scheduled to be launched in 2015, reaching the asteroid in 2018. It will be used a small spacecraft (150 kg) with 30 kg for the payload. The set of scientific instruments being considered to explore the target of this mission include an Imaging Camera, a Laser Rangefinder, an Infrared Spectrometer, a Synthetic Aperture Radar and a Mass Spectrometer. The main measurements to be made include the bulk properties (size, shape, mass, density, dynamics, spin state), the internal properties (structure, gravity field) and surface properties (mineralogy, morphology, elemental composition). The mission also opens an opportunity for some relevant experiments, not directly related to the target. Two such experiments will take benefit from being on board of the spacecraft along the journey to the asteroid system, which will take about three years. The first is an astrobiology experiment. The main goal of this experiment is to determine the viability of the microorganisms survival in extraterrestrial environments simulated in laboratory (chemical atmosphere, temperature, desiccation, vacuum, microgravity and radiation). The second experiment is a plasma package. The main objectives of this experiment are to study the structure and electrodynamics of plasma along the trajectory, the plasma instability processes and the density and temperature of plasma of solar wind origin along the trajectory and near the asteroids. This mission represents a great challenge for the Brazilian space program. It is being structured to allow the full engagement of the Brazilian universities and technological companies in all the necessary developments to be carried out. In this paper, we present some aspects of this mission and details of the payload that will be used and the scientific expectations. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

The aster mission: Exploring for the first time a triple system asteroid

2001 SN263 is a triple system asteroid. Although it was discovery in 2001, in 2008 astronomical observation carried out by Arecibo observatory revealed that it is actually a system with three bodies orbiting each other. The main central body is an irregular object with a diameter about 2.8 km, while the other two are small objects with less than 1 km across. This system presents an orbital eccentricity of 0.47, with perihelion of 1.04 and aphelion of 1.99, which means that it can be considered as a Near Earth Object. This interesting system was chosen as the target for the Aster mission - first Brazilian space exploration undertaking. A small spacecraft with 150 kg of total mass, 30 kg of payload with 110 W available for the instruments, is scheduled to be launched in 2015, and in 2018 it will approach and will be put in orbit of the triple system. This spacecraft will use electric propulsion and in its payload it will carry image camera, laser rangefinder, infrared spectrometer, mass spectrometer, and experiments to be performed in its way to the asteroid. This mission represents a great challenge for the Brazilian space program. It is being structured to allow the full engagement of the Brazilian universities and technological companies in all the necessary developments to be carried out. In this paper, we present some aspects of this mission, including the transfer trajectories to be used, and details of buss and payload subsystems that are being developed and will be used. Copyright ©2010 by the International Astronautical Federation. All rights reserved.