High-Fidelity Multiple-Flyby Trajectory Optimization Using Multiple-Shooting

Rendering a complex spacecraft trajectory in high fidelity can be an expensive endeavor, both computationally and from a human time/cost standpoint. However, in many cases, a low-fidelity trajectory that reasonably approximates a high-fidelity counterpart is much easier to obtain. Thus, it is important to have an efficient process for converting a trajectory from lower-fidelity model to high fidelity. We present a method for converting low-fidelity trajectories into high fidelity that relies on multiple shooting, nonlinear programming, and numerical integration. The procedure converts any zero-radius sphere-of-influence gravity-assist events to fully integrated flyby events. Several numerical examples are presented that showcase the flexibility of the high-fidelity rendering process across multiple mission types and flight regimes

Global Optimization of N-Maneuver, High-Thrust Trajectories Using Direct Multiple Shooting

The performance of impulsive, gravity-assist trajectories often improves with the inclusion of one or more maneuvers between flybys. However, grid-based scans over the entire design space can become computationally intractable for even one deep-space maneuver, and few global search routines are capable of an arbitrary number of maneuvers. To address this difficulty a trajectory transcription allowing for any number of maneuvers is developed within a multi-objective, global optimization framework for constrained, multiple gravity-assist trajectories. The formulation exploits a robust shooting scheme and analytic derivatives for computational efficiency. The approach is applied to several complex, interplanetary problems, achieving notable performance without a user-supplied initial guess

Optimization of the Lucy Interplanetary Trajectory via Two-Point Direct Shooting

Lucy is NASAs next Discovery-class mission and will explore the Trojan asteroids in the Sun-Jupiter L4 and L5 regions. This paper details the design of Lucys interplanetary trajectory using a two-point direct shooting transcription, nonlinear programming, and monotonic basin hopping. These techniques are implemented in the Evolutionary Mission Trajectory Generator (EMTG), a trajectory optimization tool developed at NASA Goddard Space Flight Center. We present applications to the baseline trajectory design, Monte Carlo analysis, and operations

Application and Analysis of Bounded-Impulse Trajectory Models with Analytic Gradients

In the companion paper, analytic methods were presented for computing the Jacobian entries for two-sided direct shooting trajectory models that utilize the bounded-impulse approximation. In this paper we discuss practical implementation considerations. Efficient computation of the mathematical components required to compute the partials is discussed and a guiding numerical example is provided for validation purposes. A solar electric power model suitable for preliminary mission design is presented, including a method for handling thruster cut-off events that result in non-smooth derivatives. The challenges associated with incorporating the SPICE ephemeris system into an optimization framework are discussed and an alternative is presented that results in smooth time partials. Application problems illustrate the benefits of employing analytic Jacobian calculations vs. using the method of finite differences. The importance of accurately modeling hardware and operational constraints at the preliminary design stage, and the benefits of using an analytic Jacobian in a solver that combines the monotonic basin hopping heuristic method with a local gradient search are also explored

Analytic Gradient Computation for Bounded-Impulse Trajectory Models Using Two-Sided Shooting

Many optimization methods require accurate partial derivative information in order to ensure efficient, robust, and accurate convergence. This work outlines analytic methods for computing the problem Jacobian for two different bounded-impulse spacecraft trajectory models solved using two-sided shooting. The specific two-body Keplerian propagation method used by both of these models is described. Methods for incorporating realistic operational constraints and hardware models at the preliminary stage of a trajectory design effort are also demonstrated and the analytic methods derived are tested for accuracy using automatic differentiation. A companion paper will solve several relevant problems that show the utility of employing analytic derivatives, i.e. compared to using derivatives found using finite differences

Particle Acceleration in Supernova Remnants and the Production of Thermal and Nonthermal Radiation

If highly efficient, cosmic ray production can have a significant effect on the X-ray emission from SNRs as well as their dynamical evolution. Using hydrodynamical simulations including diffusive shock acceleration, we produce spectra for both the thermal and nonthermal forward shock emission. For a given ambient density and explosion energy, we find that the position of the forward shock at a given age is a strong function of the acceleration efficiency, providing a signature of cosmic-ray production. Using an approximate treatment for the ionization state of the plasma, we investigate the effects of slow vs. rapid heating of the postshock electrons on the ratio of thermal to nonthermal X-ray emission at the forward shock. We also investigate the effects of magnetic field strength on the observed spectrum for efficient cosmic-ray acceleration. The primary effect of a large field is a considerable flattening of the nonthermal spectrum in the soft X-ray band. Spectral index measurements from X-ray observations may thus be indicators of the postshock magnetic field strength. The predicted gamma-ray flux from inverse-Compton (IC) scattering and neutral pion decay is strongly affected by the ambient conditions and, for the particular parameters used in our examples, the IC emission at E ~ 1 TeV exceeds that from pion decay, although at both lower and higher energies this trend is reversed for cases of high ambient density. More importantly, high magnetic fields produce a steepening of the electron spectrum over a wide energy range which may make it more difficult to differentiate between IC and pion-decay emission solely by spectral shape.Comment: 30 pages, 12 figures, submitted to ApJ January 200

Refining Lucy Mission Delta-V During Spacecraft Design Using Trajectory Optimization Within High-Fidelity Monte Carlo Maneuver Analysis

Recent advances linking medium-fidelity trajectory optimization and high-fidelity trajectory propagation/maneuver design software with Monte Carlo maneuver analysis and parallel processing enabled realistic statistical delta-V estimation well before launch. Completing this high-confidence, refined statistical maneuver analysis early enabled release of excess delta-V margin for increased dry mass margin for the Lucy Jupiter Trojan flyby mission. By 3.3 years before launch, 16 of 34 TCMs had 1000 re-optimized trajectory design samples, yielding tens of m/s lower 99%-probability delta-V versus targeting maneuvers to one optimal trajectory. One year later, 1000 re-optimized samples of all deterministic maneuvers and subsequent flybys further lowered estimated delta-V

Thermal X-ray Emission and Cosmic Ray Production in Young Supernova Remnants

We have developed a simple model to investigate the modifications of the hydrodynamics and non-equilibrium ionization X-ray emission in young supernova remnants due to nonlinear particle acceleration. In nonlinear, diffusive shock acceleration, the heating of the gas to X-ray emitting temperatures is strongly coupled to the acceleration of cosmic ray ions. If the acceleration is efficient and a significant fraction of the shock ram energy ends up in cosmic rays, compression ratios will be higher and the shocked temperature lower than test-particle, Rankine-Hugoniot relations predict. We illustrate how particle acceleration impacts the interpretation of X-ray data using the X-ray spectra of Kepler's remnant, observed by ASCA and RXTE. The thermal X-ray emission provides important constraints on the efficiency of particle acceleration, in complement to nonthermal emission. X-ray data from Chandra and XMM Newton, plus radio observations, will be essential to quantify nonlinear effects.Comment: 4 pages, 3 figures, accepted in ApJ Letter

Broad-band Observations and Modeling of the Shell-Type Supernova Remnant G347.3-0.5

The supernova remnant G347.3--0.5 emits a featureless power-law in X-rays, thought to indicate shock-acceleration of electrons to high energies. We here produce a broad-band spectrum of the bright NW limb of this source by combining radio observations from the Australia Telescope Compact Array (ATCA), X-ray observations from the Advanced Satellite for Cosmology and Astrophysics (ASCA), and TeV gamma-ray observations from the CANGAROO imaging Cerenkov telescope. We assume this emission is produced by an electron population generated by diffusive shock acceleration at the remnant forward shock. The nonlinear aspects of the particle acceleration force a connection between the widely different wavelength bands and between the electrons and the unseen ions, presumably accelerated simultaneously with the electrons. This allows us to infer the relativistic proton spectrum and estimate ambient parameters such as the supernova explosion energy, magnetic field, matter density in the emission region, and efficiency of the shock acceleration process. We find convincing evidence that the shock acceleration is efficient, placing >25% of the shock kinetic energy flux into relativistic ions. Despite this high efficiency, the maximum electron and proton energies, while depending somewhat on assumptions for the compression of the magnetic field in the shock, are well below the observed `knee' at about 10^{15} eV in the Galactic cosmic-ray spectrum.Comment: Submitted to ApJ, 22 pages, 5 figure

A Search for Oxygen in the Low-Density Lyman-alpha Forest Using the Sloan Digital Sky Survey

We use 2167 Sloan Digital Sky Survey (SDSS) quasar spectra to search for low-density oxygen in the Intergalactic Medium (IGM). Oxygen absorption is detected on a pixel-by-pixel basis by its correlation with Lyman-alpha forest absorption. We have developed a novel Locally Calibrated Pixel (LCP) search method that uses adjacent regions of the spectrum to calibrate interlopers and spectral artifacts, which would otherwise limit the measurement of OVI absorption. Despite the challenges presented by searching for weak OVI within the Lyman-alpha forest in spectra of moderate resolution and signal-to-noise, we find a highly significant detection of absorption by oxygen at 2.7 < z < 3.2 (the null hypothesis has a chi^2=80 for 9 data points). We interpret our results using synthetic spectra generated from a lognormal density field assuming a mixed quasar-galaxy photoionizing background (Haardt & Madau 2001) and that it dominates the ionization fraction of detected OVI. The LCP search data can be fit by a constant metallicity model with [O/H] = -2.15_(-0.09)^(+0.07), but also by models in which low-density regions are unenriched and higher density regions have a higher metallicity. The density-dependent enrichment model by Aguirre et al. (2008) is also an acceptable fit. All our successful models have similar mass-weighted oxygen abundance, corresponding to [_MW] = -2.45+-0.06. This result can be used to find the cosmic oxygen density in the Lyman-alpha forest, Omega_(Oxy, IGM) = 1.4(+-0.2)x10^(-6) = 3x10^(-4) Omega_b. This is the tightest constraint on the mass-weighted mean oxygen abundance and the cosmic oxygen density in the Lyman-alpha forest to date and indicates that it contains approximately 16% of metals produced by star formation (Bouch\'e et al. 2008) up to z = 3.Comment: 12 pages, 9 figures. Accepted by ApJ (minor changes