121 research outputs found
The -limit set in a positively invariant compact region and a new description of the Lorenz attractor
The -limit set in a compact positively invariant region has been identified for , 2, and 3, with examples in each
case. It has been shown that the -limit set becomes more complex as
increases from 1 to 3, and we expect this to also be true for . Our
example for is the Lorenz equations, for which we have shown that its
-limit set is a {\em twisted torus
Long-term impact risk for (101955) 1999 RQ36
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
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
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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