Intermittent Trajectories in the 3/1 Jovian Resonance

The statistical behaviour of intermittent trajectories at the 3/1resonance is investigated. The elliptic planar restricted three-body problemis used as a model. Distribution functions for time intervals D betweeneccentricity bursts are obtained and theoretically interpreted. For smallervalues of D the distribution is found to be of Poisson type, while in itstail it is described by a power law D. This change in thedistribution occurs for values of D in the range10⁵10⁶Jupiter periods. The power-lawindexfor the integral distributions lies in the range (-2,-1) and istrajectory dependent. The algebraic decay in the tails of the distributionsis explained by the phenomenon of sticking of orbits to the chaos borderduring long intervals between bursts.     

Dynamics of Earth‐crossing asteroids: the protected Toro orbits

Some asteroids in Earth‐crossing orbits avoid close approaches by entering in a mean motion resonance whenever the distance between the two orbits is small. These orbits are ‘Toro class’ according to the classification of (Milani et al., 1989). This protection mechanism can be understood by a semi‐averaged model, in which the fast variables are removed and the dynamical variables are the critical argument and the semimajor axis, with dependence upon a slow parameter. The adiabatic invariant theory can be applied to this model and accounts for all the qualitative features of the orbits in this class, including the onset of the libration when the orbit distance is small. Because of the neglected perturbations by the other planets, this theory is approximate and the adiabatic invariant is conserved only with low accuracy moreover, the Toro state can be terminated by a close approach to another planet (typically Venus). “Would you tell me, please, which way I ought to go from here?” “That depends a good deal on where you want to get to,” said the Cat. Alice in Wonderland, L. Carroll     

Periodic orbit families near the 4:1 jovian resonance

An enlarged averaged Hamiltonian is introduced to compute several families of periodic orbits of the planar elliptic 3-body problem, in the Sun–Jupiter–Asteroid system, near the 4:1 resonance. Four resonant critical point families are found and their stability is studied. The families of symmetric periodic orbits of the elliptic problem appear near the corresponding fixed points computed in this model. There is a good agreement for moderate eccentricity of the asteroid for three of these families, whereas the remaining family cannot be considered as a family of periodic orbits of the real model. This revised version was published online in July 2006 with corrections to the Cover Date.     

On symmetrical planetary corotations

Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) _jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– _jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev ₅-resonance. This paper presents the symmetric solutions =0 (mod ), = _jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.     

Asteroid 2002NY40 as a source of meteorite-dropping bolides

The existence of asteroidal meteoroid streams capable of producing meteorite-dropping bolides has long being invoked, but evidence is scarce. Recent modelling of previously reported associations suggests that the time-scales to keep the orbital coherence of these streams producing meteorites are too short. We present an unequivocal association between near earth object (NEO) 2002NY40 and at least one bright fireball detected over Finland in 2006 August. Another two additional fireballs recorded from Spain and Finland seem to be related, together producing a fireball-producing stream (β Aquarids). On the basis of historical data, the 2006 finding suggests the existence of a meteoroid complex capable of producing meteorites. Taking into account present time-scales for orbital decoherence, if 2002NY40 has large meteoroids associated with it, such behaviour would be the consequence of a relatively recent asteroidal fragmentation. Supporting our claim, the heliocentric orbits of two recently discovered NEOs, 2004NL8 and 2002NY40, were found to exhibit a good similarity to each other and also to the orbits of the three bolides. The fireball spectra of the two Finish bolides showed that the chemical abundances of these objects are consistent with the main elements found in chondrites. This result is consistent with the probable Low iron, Low metal (LL) chondritic mineralogy of asteroid 2002NY40. Consequently, this asteroid may be delivering LL chondrites to the Earth. Additional fireball reports found in the literature suggest that the associated β Aquarid complex may have been delivering meteorites to the Earth during, at least, the last millennium.     

A radar survey of M- and X-class asteroids

We observed ten M- and X-class main-belt asteroids with the Arecibo Observatory's S-band (12.6 cm) radar. The X-class asteroids were targeted based on their albedos or other properties which suggested they might be M-class. This work brings the total number of main-belt M-class asteroids observed with radar to 14. We find that three of these asteroids have rotation rates significantly different from what was previously reported. Based on their high radar albedo, we find that only four of the fourteen—16 Psyche, 216 Kleopatra, 758 Mancunia, and 785 Zwetana—are almost certainly metallic. 129 Antigone has a moderately high radar albedo and we suggest it may be a CH/CB/Bencubbinite parent body. Three other asteroids, 97 Klotho, 224 Oceana, and 796 Sarita have radar albedos significantly higher than the average main belt asteroid and we cannot rule out a significant metal content for them. Five of our target asteroids, 16 Psyche, 129 Antigone, 135 Hertha, 758 Mancunia, and 785 Zwetana, show variations in their radar albedo with rotation. We can rule out shape and composition in most cases, leaving variations in thickness, porosity, or surface roughness of the regolith to be the most likely causes. With the exception of 129 Antigone, we find no hydrated M-class asteroids (W-class; Rivkin, A.S., Howell, E.S., Lebofsky, L.A., Clark, B.E., Britt, D.T., 2000. Icarus 145, 351-368) to have high radar albedos.     

Asteroids on Earth-like orbits and their origin

The orbit of 1991 VG and a set of other asteroids whose orbits are very similar to that of the Earth have been examined. Its origin has been speculated to be a returning spacecraft, lunar ejecta or a low-inclination Amor- or Apollo-class object. The latter is arguably the more likely source, which has been investigated here. The impact probability for these objects has been calculated, and while it is larger than that of a typical near-Earth asteroid (NEA), it is still less than 1:200 000 over the next 5000 yr. In addition, the probability of an NEA ever ending up on an Earth-like orbit has been obtained from numerical simulations and turned out to be about 1:20 000, making this a rare class of objects. The typical time spent in this state is about 10 000 yr, much less than the typical NEA lifetime of 10 Myr.     

Meteoroids, Meteors, and the Near-Earth Object Impact Hazard

In considering the modern-day hazard from infalling near-Earth asteroids and comets, the focus has shifted toward the smallest, most frequent impacts that can do damage on the ground, like the 1908 Tunguska aerial burst. There is considerable uncertainty about the potential for damage by objects in the range 20 to 100 m diameter. Since smaller, less dangerous, meter-sized meteoroids are part of a continuum of small interplanetary bodies, derived by a collisional cascade and Yarkovsky spin-up, research on such phenomena by meteor scientists can shed light on a vital question that will soon have great practical relevance as new telescopic searches for near-Earth asteroids come on line: what is the threshold size between harmless high-altitude airbursts and impacts that can cause lethal damage on the ground?