Detection of Collisional Asteroid Orbits Under Observable Nonlinearity in the Problem of Orbit Improvement

Solar System Research - A method has been developed for detecting collisional orbits of asteroids in the initial confidence region with a noticeable nonlinearity in the problem of improving their...     

The Impact Effect Callculator of Celestial Body Impacts to the Earth: The Constructor of Hazardous Orbits

Quick assessment of hazardous effects from impacts of large celestial bodies is achieved through the development of a new consequence calculator. A distinctive feature of this calculator is a new block, the Hazardous-Orbit Constructor, which simulates the conditions of entry of a celestial body into the Earth’s atmosphere and determines the orbital parameters of the body based on given atmospheric entry conditions. This block is used to simulate the atmospheric entry conditions of known asteroids and meteoroids and to determine the orbital parameters of known bolides leading to meteorite fall events. For the case of asteroid 2008 TC3 and the P?ibram meteorite, it is shown that within the potential impact area of the celestial body, the atmospheric entry angle may vary considerably.     

On the Possibility of Deflecting an Asteroid from Collision with the Earth Using the Kinetic Method

The possibilities of deflecting an asteroid from its collision course with the Earth by changing its velocity with an impact are considered. Using the asteroid Apophis as an example, the time dependence of the positions and sizes of the keyholes leading to collision is studied. It has been found that the possibility of deflecting this asteroid usually exists, and the impact can be accomplished in principle, given the capabilities of modern space technology. A change in the velocity should be performed before the encounter of 2029 in order to use the gravitational maneuver effect. The possible accuracy of determining Apophis’ orbit and the keyholes that lead to collision and are associated with the resonance returns are considered.     

On the Distance Function Between Two Keplerian Elliptic Orbits

The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.     

Earth impact probability of the Asteroid (25143) Itokawa to be sampled by the spacecraft Hayabusa

The Japanese spacecraft Hayabusa is planed to reach the Asteroid Itokawa in September 2005, and to bring back some samples of its surface to Earth in 2007. We have studied the future possible evolution of this asteroid by integrating numerically over 100 Myr a set of 39 initially indistinguishable orbits (clones), obtained either by small variations of the nominal initial conditions, or by using different computers (introducing different round-off errors). The results indicate that an Earth impact of this 500-m-size asteroid is likely within a million years, which is only a factor of four larger than the average impact frequency of asteroids of this size. The mission Hayabusa may thus sample a good candidate for being among the next 500-m-size Earth impactors.     

An Algebraic Method to Compute the Critical Points of the Distance Function Between Two Keplerian Orbits

We describe an efficient algorithm to compute all the critical points of the distance function between two Keplerian orbits (either bounded or unbounded) with a common focus. The critical values of this function are important for different purposes, for example to evaluate the risk of collisions of asteroids or comets with the Solar system planets. Our algorithm is based on the algebraic elimination theory: through the computation of the resultant of two bivariate polynomials, we find a 16th degree univariate polynomial whose real roots give us one component of the critical points. We discuss also some degenerate cases and show several examples, involving the orbits of the known asteroids and comets.      

Resonant dynamics of Medium Earth Orbits: space debris issues

The Medium Earth Orbit region is the home of the navigation constellations. It is shown how the orbits of these constellations of satellites are strongly affected by the so-called inclination dependent luni-solar resonances. The analytical theory of these resonances is recalled and a large set of numerical integrations is used to investigate the stability of the orbits of the constellations over very long time spans. The stability issue is important in the definition of possible disposal strategies for the constellation spacecraft, after their end-of-life. Two possible disposal strategies are envisaged involving either stable or unstable orbits (from the eccentricity growth point of view). In particular it is shown how, to have disposal orbits with moderately short lifetime (of the orders of 40–50 years), a very large disposal maneuver would be required to rise the inital eccentricity to values above ~ 0.3.     

On the Trajectories of Asteroid Encounters with the Earth for 2015 RN35 and Apophis

A great number of probable encounters of asteroid 2015 RN35 with the Earth have been found; many of them were unknown earlier. The main characteristics and properties of the corresponding trajectories have been obtained. Probable impacts of the asteroid Apophis with the Earth are also discussed. The results suggest that the multitudes of potential impacts of hazardous asteroids with the Earth can be and must be analyzed in more detail. Such an analysis is required to plan and implement the measures on preventing the asteroid impact hazard.     

Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.     

Solar Sail Halo Orbits at the Sun–Earth Artificial L 1 Point

Halo orbits for solar sails at artificial Sun–Earth L₁ points are investigated by a third order approximate solution. Two families of halo orbits are explored as defined by the sail attitude. Case I: the sail normal is directed along the Sun-sail line. Case II: the sail normal is directed along the Sun–Earth line. In both cases the minimum amplitude of a halo orbit increases as the lightness number of the solar sail increases. The effect of the z-direction amplitude on x- or y-direction amplitude is also investigated and the results show that the effect is relatively small. In case I, the orbit period increases as the sail lightness number increases, while in case II, as the lightness number increases, the orbit period increases first and then decreases after the lightness number exceeds ~0.01.     

Fast Periodic Transfer Orbits in the Sun–Earth–Moon Quasi-Bicircular Problem

Starting from the identification and classification of a family of fast periodic transfer orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), and using analytic continuation techniques, we find two unstable periodic orbits in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). The orbits found perform periodic Earth–Moon transfers with a period of approximately 29.5 days.     

2009年若干典型低轨空间区域空间碎片分布仿真

空间碎片在太空中的累积越来越多,它们主要聚集在离地球表面2000km高度以下空间区域内.空间碎片引起的空间"污染"越来越威胁到在轨工作飞行器的安全.这里主要对600km、700km和800km轨道高度,倾角分别为30°、60°和98°的低轨道空间区域的空间碎片分布进行了仿真计算.可以为在轨飞行器安全运行及未来飞行器在空间布局决策提供一定参考.     

Impact solutions of Asteroid 2007 WD5 with Mars

A method for computing impact probabilities between asteroids and the planet Mars is presented that uses impact clones and validation analysis based on a normal distribution of computed errors. This method uses OrbFit software, and we present a calculation of the impact probabilities between Asteroid 2007 WD₅ and Mars, which passed within about 20,000 km of the martian surface on January 30, 2008. This method can be generalized for computing impact probabilities between asteroids and other planets including Earth. Presented method applies in principal the same technique already in use for years at the JPL NASA and by the group of researchers at the University of Pisa [Milani, A., Chesley, S.R., Sansaturio, M.E., Tommei, G., Valsecchi, G.B., 2005a. Icarus 173, 362].     

Abrupt alteration of Asteroid 2004 MN4's spin state during its 2029 Earth flyby

We predict that when Asteroid 2004 MN4 passes 5.6±1.4 Earth radii from Earth's center on April 13, 2029, terrestrial torques during the flyby will alter its spin state in a dramatic manner that will be observable using groundbased telescopes. Although the asteroid will most likely not undergo catastrophic disruption, it may be subject to localized failure across its surface and interior, providing a unique opportunity to measure otherwise inaccessible mechanical properties of an asteroid.     

The Contribution of Asteroid Dust to the Interplanetary Dust Cloud: The Impact of ULYSSES Results on the Understanding of Dust Production in the Asteroid Belt and of the Formation of the IRAS Dust Bands

Investigations of the zodiacal dust cloud give evidence for a significant contribution of asteroidal dust to the interplanetary dust cloud, a result which can now be compared to measurements of the ULYSSES dust detector during its passage of the asteroid belt. Especially we discuss the ULYSSES data with respect to the IRAS dust bands and consider geometric selection effects for the detector. From calculations of radiation pressure forces, we conclude that particles in the IRAS dust bands with massesm≥ 10⁻¹²g will stay in bound orbits after their release from asteroid fragmentation. This is already in the mass range (10⁻¹⁶–10⁻⁷g) of particles detectable with the dust detector onboard ULYSSES. The absence of these particles in the ULYSSES data cannot be explained exclusively in terms of their small detection probability. Thus we conclude that the size distribution of particles in the IRAS dust bands most probably cannot be continued to the submicrometer range. Concerning the global structure of the inner zodiacal cloud (i.e., about solar distancer< 3.5 AU) the ULYSSES data are not inconsistent with present models. Recent estimates of the total mass of the interplanetary cloud require a dust production rate of about 10¹⁴g/year of which a significant amount is assumed to result from the asteroids. Our estimate for the production of dust particles in an IRAS dust band, based on the assumption that the dust band results from a single destruction of an asteroid of 100 km size, yields a production rate of 10¹⁰g/year. Other models of the IRAS dust bands suggest production rates up to 10¹²g/year and also cannot provide a significant source of the dust cloud.     

Multifractal Fits to the Observed Main Belt Asteroid Distribution

Dohnanyi's (J. W. Dohnanyi, 1969, J. Geophys. Res.74, 2531-2554) theory predicts that a collisional system such as the asteroidal population of the main belt should rapidly relax to a power-law stationary size distribution of the kind N(m)∝m^−α, with α very close to 11/6, provided all the collisional response parameters are independent of size. The actual asteroid belt distribution at observable sizes, instead, does not exhibit such a simple fractal size distribution.We investigate in this work the possibility that the corresponding cumulative distribution may be instead fairly fitted by multifractal distributions. This multifractal behavior, in contrast with the Dohnanyi fractal distribution, is related to the release of his hypothesis of self-similarity.     

Impact orbits of the asteroid 2009 FJ with the Earth

We show how to calculate the impact orbits of dangerous asteroids using the freely available the OrbFit software, and compare our results with impact orbits calculated using Sitarski??s independent software (Sitarski, 1999; 2000; 2006). The new method is tested on asteroid 2009 FJ. Using the OrbFit package to integrate alternate orbits along the line of variation (Milani et al., 2002; 2005a; 2005b), we identify impact orbits and can plot paths of risk for the Earth or any other body in the Solar System. We present the orbital elements of asteroid 2009 FJ and its ephemerides, along with uncertainties, for the next 100 years. This paper continues a long-term research program on impact solutions for asteroids (Wlodarczyk, 2007; 2008; 2009).     

Implementation of the First Asteroid Landing

Spacecraft have successfully landed on the Moon, Venus, and Mars, and have penetrated the atmosphere of Jupiter. On 2001 February 12, the Near-Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft landed on the surface of the asteroid (433) Eros after a year of observations in orbit about the asteroid. NEAR Shoemaker was not designed to land on an asteroid, complicating the design of operations needed to accomplish this feat. However, the NEAR Shoemaker team wanted to attempt a landing after the year of orbital operations that consumed most of the remaining spacecraft fuel, operations funding, and planned Deep Space Network tracking. This would be a fitting end to the mission, and it would be possible to obtain images at much greater resolution during the descent than could be obtained from orbit. The operations were more successful than the NEAR Shoemaker team had hoped, obtaining 70 high-resolution images during the descent and two weeks of gamma-ray spectrometer data from the surface after the successful soft landing.     

On the Stochasticity of the Asteroid Belt

The study of the stochasticity of the asteroid belt requires the analysis of a large number of orbits. We detect the dynamical character of a set of 5 400 asteroids using the Fast Lyapunov Indicator, a method of analysis closely related to the computation of the Lyapunov Characteristic Exponents, but cheaper in computational time. For both regular and chaotic orbits we try to associate the motion to the underlying resonances network. For it we consider different methods of classification of rational numbers proposed by number theory, and we choose the one which seems to be strictly related to the dynamical behaviour of a system. This revised version was published online in July 2006 with corrections to the Cover Date.