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Register a new userComparing Analytical and Numerical Approaches to Meteoroid Orbit Determination using Hayabusa Telemetry
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Added by
Trent Jansen-Sturgeon Mr
Publication date
2018
fields
Physics
and research's language is
English
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Fireball networks establish the trajectories of meteoritic material passing through Earths atmosphere, from which they can derive pre-entry orbits. Triangulated atmospheric trajectory data requires different orbit determination methods to those applied to observational data beyond the Earths sphere-of-influence, such as telescopic observations of asteroids. Currently, the vast majority of fireball networks determine and publish orbital data using an analytical approach, with little flexibility to include orbital perturbations. Here we present a novel numerical technique for determining meteoroid orbits from fireball network data and compare it to previously established methods. The re-entry of the Hayabusa spacecraft, with its known pre-Earth orbit, provides a unique opportunity to perform this comparison as it was observed by fireball network cameras. As initial sightings of the Hayabusa spacecraft and capsule were made at different altitudes, we are able to quantify the atmospheres influence on the determined pre-Earth orbit. Considering these trajectories independently, we found the orbits determined by the novel numerical approach to align closer to JAXAs telemetry in both cases. Comparing the orbits determined from the capsules re-entry shows the need for an atmospheric model, which the prevailing analytical approach lacks. Using simulations, we determine the atmospheric perturbation to become significant at ~90 km; higher than the first observations of typical meteorite dropping events. Using further simulations, we find the most substantial differences between techniques to occur at both low entry velocities and Moon passing trajectories. These regions of comparative divergence demonstrate the need for perturbation inclusion within the chosen orbit determination algorithm.
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We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (DMRG and Exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.
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Based on telescopic observations of Jupiter-family comets (JFCs), there is predicted to be a paucity of objects at sub-kilometre sizes. However, several bright fireballs and some meteorites have been tenuously linked to the JFC population, showing metre-scale objects do exist in this region. In 2017, the Desert Fireball Network (DFN) observed a grazing fireball that redirected a meteoroid from an Apollo-type orbit to a JFC-like orbit. Using orbital data collected by the DFN, in this study, we have generated an artificial dataset of close terrestrial encounters that come within $1.5$ lunar distances (LD) of the Earth in the size-range of $0.01-100$kg. This range of objects is typically too small for telescopic surveys to detect, so using atmospheric impact flux data from fireball observations is currently one of the only ways to characterise these close encounters. Based on this model, we predict that within the considered size-range $2.5times 10^{8}$ objects ($0.1%$ of the total flux) from asteroidal orbits ($T_{J}>3$) are annually sent onto JFC-like orbits ($2<T_{J}<3$), with a steady-state population of about $8times 10^{13}$ objects. Close encounters with the Earth provide another way to transfer material to the JFC region. Additionally, using our model, we found that approximately $1.96times 10^{7}$ objects are sent onto Aten-type orbits and $sim10^{4}$ objects are ejected from the Solar System annually via a close encounter with the Earth.
Fireball observations from camera networks provide position and time information along the trajectory of a meteoroid that is transiting our atmosphere. The complete dynamical state of the meteoroid at each measured time can be estimated using Bayesian filtering techniques. A particle filter is a novel approach to modelling the uncertainty in meteoroid trajectories and incorporates errors in initial parameters, the dynamical model used and observed position measurements. Unlike other stochastic approaches, a particle filter does not require predefined values for initial conditions or unobservable trajectory parameters. The Bunburra Rockhole fireball (Spurny et al. 2012), observed by the Australian Desert Fireball Network (DFN) in 2007, is used to determine the effectiveness of a particle filter for use in fireball trajectory modelling. The final mass is determined to be $2.16pm1.33, kg$ with a final velocity of $6030pm216, m,s^{-1}$, similar to previously calculated values. The full automatability of this approach will allow an unbiased evaluation of all events observed by the DFN and lead to a better understanding of the dynamical state and size frequency distribution of asteroid and cometary debris in the inner solar system.
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