121 research outputs found

    The ω\omega-limit set in a positively invariant compact region and a new description of the Lorenz attractor

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    The ω\omega-limit set in a compact positively invariant region R⊂RnR \subset \mathbb{R}^n has been identified for n=1n=1, 2, and 3, with examples in each case. It has been shown that the ω\omega-limit set becomes more complex as nn increases from 1 to 3, and we expect this to also be true for n>3n>3. Our example for n=3n=3 is the Lorenz equations, for which we have shown that its ω\omega-limit set is a {\em twisted torus

    Long-term impact risk for (101955) 1999 RQ36

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    The potentially hazardous asteroid (101955) 1999 RQ36 has the possibility of collision with the Earth in the latter half of the 22nd century, well beyond the traditional 100-year time horizon for routine impact monitoring. The probabilities accumulate to a total impact probability of approximately 10E-3, with a pair of closely related routes to impact in 2182 comprising more than half of the total. The analysis of impact possibilities so far in the future is strongly dependent on the action of the Yarkovsky effect, which raises new challenges in the careful assessment of longer term impact hazards. Even for asteroids with very precisely determined orbits, a future close approach to Earth can scatter the possible trajectories to the point that the problem becomes like that of a newly discovered asteroid with a weakly determined orbit. If the scattering takes place late enough so that the target plane uncertainty is dominated by Yarkovsky accelerations then the thermal properties of the asteroid,which are typically unknown, play a major role in the impact assessment. In contrast, if the strong planetary interaction takes place sooner, while the Yarkovsky dispersion is still relatively small compared to that derived from the measurements, then precise modeling of the nongravitational acceleration may be unnecessary.Comment: Reviewed figures and some text change

    The Impact Trajectory of Asteroid 2008 TC3

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    Asteroid 2008 TC3 was the rst asteroid ever discovered before reaching Earth. By using the almost 900 astrometric observations acquired prior to impact we estimate the trajectory of 2008 TC3 and the ground-track of the impact location as a function of altitude. For a reference altitude of 100 km the impact location 3- formal uncertainty is a 1.4 km 0.15 km ellipse with a semimajor axis azimuth of 105. We analyze the contribution of modeling errors and nd that the second-order zonal harmonics of the Earth gravity eld moves the ground-track by more than 1 km and the location along the ground-track by more than 2 km. Non-zonal and higher order harmonics only change the impact prediction by less than 20 m. The contribution of the atmospheric drag to the trajectory of 2008 TC3 is at the numerical integration error level, a few meters, down to an altitude of 50 km. Integrating forward to lower altitudes and ignoring the break-up of 2008 TC3, the atmospheric drag causes an along-track error that can be as large as a few kilometers at sea level. The locations of the recovered meteorites is consistent with the computed ground-track

    Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact

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    Binary near-Earth asteroid (65803) Didymos is the target of the proposed NASA Double Asteroid Redirection Test (DART), part of the Asteroid Impact & Deflection Assessment (AIDA) mission concept. In this mission, the DART spacecraft is planned to impact the secondary body of Didymos, perturbing mutual dynamics of the system. The primary body is currently rotating at a spin period close to the spin barrier of asteroids, and materials ejected from the secondary due to the DART impact are likely to reach the primary. These conditions may cause the primary to reshape, due to landslides, or internal deformation, changing the permanent gravity field. Here, we propose that if shape deformation of the primary occurs, the mutual orbit of the system would be perturbed due to a change in the gravity field. We use a numerical simulation technique based on the full two-body problem to investigate the shape effect on the mutual dynamics in Didymos after the DART impact. The results show that under constant volume, shape deformation induces strong perturbation in the mutual motion. We find that the deformation process always causes the orbital period of the system to become shorter. If surface layers with a thickness greater than ~0.4 m on the poles of the primary move down to the equatorial region due to the DART impact, a change in the orbital period of the system and in the spin period of the primary will be detected by ground-based measurement.Comment: 8 pages, 7 figures, 2 tables, accepted for publication in MNRA
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