- Caltech JPL Principal EngineerMission Designedit
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The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists.... more
The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimi...
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The Genesis mission will launch in 2001, sending the spacecraft into a halo orbit about the Sun-Earth L1 point to collect and return solar wind samples to the Earth for analysis in 2003. One of the most constraining aspects of the mission... more
The Genesis mission will launch in 2001, sending the spacecraft into a halo orbit about the Sun-Earth L1 point to collect and return solar wind samples to the Earth for analysis in 2003. One of the most constraining aspects of the mission design is the requirement to return to the designated landing site (the Utah Test and Training Range, UTTR) during daylight hours. The ongoing mission design has led the development of a family of solutions that characterize a broad range of conditions at Earth entry. Characterizing this family provides insight into the possible existence of additional trajectories while also helping to narrow the search space by indicating where additional solutions are unlikely to exist; this contributes to a more efficient utilization of mission design resources.
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As the fifth mission of NASA's Directory Program, Genesis is designed to collect solar wind samples for approximately two years in a halo orbit near the Sun-Earth L(sub 1) Lagrange point for return to the Earth.
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In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 parsecs). Since then, the interest in the detection of extra-solar planets, in order to learn about the origin, evolution, and composition of... more
In 1995, Mayor and Queloz [a] detected for the first time a planet orbiting a nearby star (15.4 parsecs). Since then, the interest in the detection of extra-solar planets, in order to learn about the origin, evolution, and composition of planetary systems, has grown tremendously and ...
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Results of a systems concepts study for a Titan Probe were examined. The key tradeoffs performed are described in detail. Mass breakdown of each Probe subsystem or major element were given. The mission analysis performed to determine... more
Results of a systems concepts study for a Titan Probe were examined. The key tradeoffs performed are described in detail. Mass breakdown of each Probe subsystem or major element were given. The mission analysis performed to determine compliance with the high altitude sampling and descent time requirements are described. The baseline Descent Module design was derived. The element of the
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Europa is a premier target for advancing both planetary science and astrobiology, as well as for opening a new window into the burgeoning field of comparative oceanography. The potentially habitable subsurface ocean of Europa may harbor... more
Europa is a premier target for advancing both planetary science and astrobiology, as well as for opening a new window into the burgeoning field of comparative oceanography. The potentially habitable subsurface ocean of Europa may harbor life, and the globally young and comparatively thin ice shell of Europa may contain biosignatures that are readily accessible to a surface lander. Europa’s icy shell also offers the opportunity to study tectonics and geologic cycles across a range of mechanisms and compositions. Here we detail the goals and mission architecture of the Europa Lander mission concept, as developed from 2015 through 2020. The science was developed by the 2016 Europa Lander Science Definition Team (SDT), and the mission architecture was developed by the preproject engineering team, in close collaboration with the SDT. In 2017 and 2018, the mission concept passed its mission concept review and delta-mission concept review, respectively. Since that time, the preproject has ...
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An investigation of the topology of flow in the equilibrium region of the Planar Circular Restricted Three-Body Problem is presented. By utilizing a homeomorphic mapping we are able to visualize trajectories in the energy surface... more
An investigation of the topology of flow in the equilibrium region of the Planar Circular Restricted Three-Body Problem is presented. By utilizing a homeomorphic mapping we are able to visualize trajectories in the energy surface directly, giving insight into the governing role of invariant manifolds. We show that manifolds govern the flow of objects by physically blocking trajectories exterior to the manifold tubes in the energy surface from transiting. We demonstrate that transit orbits must flow inside invariant manifolds and pass through Lyapunov orbits in phase space, although they may appear to wander outside when projected in configuration space. Through a numerical investigation of transit orbits, we show manifolds govern the flow of objects over a wider range of energies than previously proven, controlling transit for energies at least as high as C = C(L_5)
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In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason... more
In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason the Hill’s surfaces or the families of halo orbits have been extensively studied in the frame of the circular restricted three body problem. It is our opinion that their natural extensions to the ER3BP have not been studied enough. We divide the position space into forbidden subegions, subregions of motion and low-velocity subregions. We use these notions to define necessary condition for a transfer trajectory in the ER3BP. Also we compute branches of elliptic halo orbits bifurcating from halo orbits in the circular restricted three body problem. The new periodic orbits have principal periods and stability properties different from those of the originating halo orbit.
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ABSTRACT The article develops a method for the exploration of a concept of autonomous navigation constellations in the Earth-Moon system. This concept consists of using autonomous GPS-like beacons on three-body periodic orbits to provide... more
ABSTRACT The article develops a method for the exploration of a concept of autonomous navigation constellations in the Earth-Moon system. This concept consists of using autonomous GPS-like beacons on three-body periodic orbits to provide navigation services to an end-user in the larger Earth-Moon neighborhood. The autonomy of the constellation spacecraft would be achieved using LiAISON navigation as introduced by Hill, Born, and Lo. The article focuses on the problem of orbit down-selection for such a concept, which is approached by formulating an optimization problem. The discussion of potential cost functions and the resulting simplifications of the problem are addressed. A continuation based method that leverages the structure of periodic orbits in the circular restricted three-body problem is then proposed to analyze the problem. The method allows notably for a succinct representation of the solution space as a one-dimensional graph that highlights local and global extrema of the optimization problem. Illustration of the method using a simplified down-selection metric is discussed to balance the strengths and limitations of the approach.
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ABSTRACT We present preliminary results of tomographic imaging of the 20 keV to 1800 keV gamma-ray sky using Radon Transforms and data from the BATSE experiment on the Compton Gamma Ray Observatory. The method uses Earth occultation, with... more
ABSTRACT We present preliminary results of tomographic imaging of the 20 keV to 1800 keV gamma-ray sky using Radon Transforms and data from the BATSE experiment on the Compton Gamma Ray Observatory. The method uses Earth occultation, with the 0.2 degree angular response characteristic of the atmospheric limb, together with the all-sky coverage of the BATSE instrument to produce 2-dimensional maps of the sky from the count data from the eight BATSE detectors. We have initially used the Linear Radon Transform (LRT), though this limits us to imaging small ( 4x4o) regions of the sky where the earth limb can be approximated as a straight line. As the orbit of the spacecraft precesses over a 51-day period, the earth limb sweeps across the sky at different orientations, though never sampling the full 180o range of angles. The large and complex variation of the background counting rate common to all high-energy instruments in low-earth orbit is subtracted from the raw data prior to the imaging steps using our earlier work in modeling the background variability (Ling et al. 2000). Summing the 16 BATSE LAD energy channels into four broad bands (23-98 keV, 98-230 keV, 230-595 keV, and 595-1798 keV), we are able to detect and position the Crab Nebula and the nearby transient GRO J0422+32 using only a single 51 day precession cycle, with source location accuracy of the order of 1o in each band. We confirm earlier work by Zhang et al (1993) for applying the LRT technique to the BATSE data, extend their work to cover more source regions, and produce images at higher energies. We also discuss the extension of our method to Generalized Radon Transforms, e.g. the Spherical Cap Radon Transform, which would allow us to image larger regions of the sky.
Research Interests: Count data, Radon, Dimensional, Low Earth Orbit, Sky, and 4 moreGamma Ray, Radon Transform, High energy, and Aas
... 80201 Kathleen C. Howell, Brian Barden, Roby Wilson Purdue University, West Lafayette, IN 47907 Abstract ... As the hook takes the load, it is pulled free of its attachment to the pole, transferring the load to the retrieval cable. On... more
... 80201 Kathleen C. Howell, Brian Barden, Roby Wilson Purdue University, West Lafayette, IN 47907 Abstract ... As the hook takes the load, it is pulled free of its attachment to the pole, transferring the load to the retrieval cable. On ...
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A fundamental problem in spacecraft mission design is to find a free flight path from one place to another with a given transfer time. This problem for paths in a central force field is known as Lambert's problem. Although this is an... more
A fundamental problem in spacecraft mission design is to find a free flight path from one place to another with a given transfer time. This problem for paths in a central force field is known as Lambert's problem. Although this is an old problem, we take a new approach. Given two points in the plane, we produce the conic parameters for all conic paths between these points. For a given central force gravitational parameter, the travel time between the launch and destination points is computed along with the initial and final velocities for each transfer conic. For a given travel time, we calculate the parameters for a transfer conic having that travel time.
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A navigation and communications network is proposed to support an anticipated need for infrastructure in the Earth-Moon system. Periodic orbits will host the constellations while a novel, autonomous navigation strategy will guide the... more
A navigation and communications network is proposed to support an anticipated need for infrastructure in the Earth-Moon system. Periodic orbits will host the constellations while a novel, autonomous navigation strategy will guide the spacecraft along their path strictly based on satellite-to-satellite telemetry. In particular, this paper investigates the second stage of a larger constellation optimization scheme for multi-spacecraft systems. That is, following an initial orbit down-selection process, this analysis provides insights into the ancillary problem of spacecraft placement. Two case studies are presented that consider configurations of up to four spacecraft for a halo orbit and a cycler trajectory.
The set of trajectories leaving/impacting the surface of the Galilean satellites of Jupiter is analyzed from theoretical and computational viewpoints in the circular restricted three body problem in order to characterize the sensitive... more
The set of trajectories leaving/impacting the surface of the Galilean satellites of Jupiter is analyzed from theoretical and computational viewpoints in the circular restricted three body problem in order to characterize the sensitive impact regions for spacecraft trajectory ap- plications, as well as the main dynamical structures influencing this set of trajectories. A set of escape/impact dynamical maps as a func- tion of the Jacobi constant has been computed and their analysis, using a two body approximation and the stable/unstable manifolds associated with the colinear libration point dynamics, is presented. While the results mainly focus on the planar problem, the two body analysis also considers the spatial problem.
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energyorbittransferswouldsignificantlylowerthecostofestablishingandmaintaining small lunar communication relay constellations in halo orbits. Autonomous orbit determination would allow the constellation to navigate without expensive... more
energyorbittransferswouldsignificantlylowerthecostofestablishingandmaintaining small lunar communication relay constellations in halo orbits. Autonomous orbit determination would allow the constellation to navigate without expensive Earth-based tracking assets. For libration point orbits, both relative and absolute autonomous orbit determination is possible using only satellite-to-satellite tracking such as crosslink range or Doppler. The spacecraft could be used as mobile tracking stations to provide navigation as well as communications. Low-energy lunar transfers could be used to place more mass into lunar halo orbits than conventional trajectories, and using these low-energy transfers, it should be possible to launch the entire constellation on a single vehicle.
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We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing... more
We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids.
Research Interests: Mechanical Engineering, Applied Mathematics, Computer Science, Physics, Molecular modeling, and 9 moreThree body problem, Graph Partitioning, Chemical Reaction, Numerical Analysis and Computational Mathematics, Tree Structure, Dynamic System, Bifurcation and Chaos, Invariant Set, and Computational Techniques
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Abstract—Achieving longer mission duration, increased science return, and flexability for follow on observations motivated by unanticipated discoveries is facilitated through improvements in trajectory generation, particularly with... more
Abstract—Achieving longer mission duration, increased science return, and flexability for follow on observations motivated by unanticipated discoveries is facilitated through improvements in trajectory generation, particularly with respect to computational efficiency of computing near-optimal solutions of constrained optimization problems. Practical complications to be faced also include solving an ensemble of constrainted optimization prob-lems for random initial and/or final states, uncertainty in the dy-namics, and quantifying state measurement error during tracking and navigation. Here we formulate a probabilistic approach to control allowing convergence to optimal solutions over an entire set of boundary conditions, as well as allowing other sources of uncertainty to be included. Furthermore, we use insight provided from a global view of phase space structure (i.e. a “dynamical systems ” viewpoint of the free trajectories) to guide computation and improve efficiency of trajecto...
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In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less ΔV than a standard Hohmann transfer to the Moon. In this paper, we apply the same dynamical systems techniques used to... more
In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less ΔV than a standard Hohmann transfer to the Moon. In this paper, we apply the same dynamical systems techniques used to produce the “Petit Grand Tour” of Jovian moons to reproduce a Hiten-like mission. We decouple the Sun-Earth-Moon- Spacecraft 4-body problem into two 3-body problems. Using the invariant manifold theory of the Lagrange points of the 3-body systems, we are able to construct low energy transfer trajectories from the Earth and ballistic capture trajectories at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations.
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The Multi-Moon Orbiter concept is introduced, wherein a single spacecraft orbits several moons of Jupiter, allowing long duration observations. The ∆V requirements for this mission can be low if ballistic captures and resonant gravity... more
The Multi-Moon Orbiter concept is introduced, wherein a single spacecraft orbits several moons of Jupiter, allowing long duration observations. The ∆V requirements for this mission can be low if ballistic captures and resonant gravity assists by Jupiter’s moons are used. For example, using only 22 m/s, a spacecraft initially injected in a jovian orbit can be directed into a capture orbit around Europa, orbiting both Callisto and Ganymede enroute. The time of flight for this preliminary trajectory is four years, but may be reduced by striking a compromise between fuel and time optimization during the inter-moon transfer phases.
The Terrestrial Planet Finder (TPF) is one of the center pieces of NASA's Origins Program. The goal of TPF is to identify terrestrial planets around stars nearby the Sun. For this purpose, a space-based interferometer with a baseline... more
The Terrestrial Planet Finder (TPF) is one of the center pieces of NASA's Origins Program. The goal of TPF is to identify terrestrial planets around stars nearby the Sun. For this purpose, a space-based interferometer with a baseline of approximately 100 m is required. To achieve such a large baseline, a distributed system of five spacecraft flying in formation is an efficient approach. Since the TPF instruments need a cold and stable environment, a halo orbit about 4 is ideal. First, we describe formation flight near the Lagrange point is feasible for the TPF mission. Second, we propose a novel approach for human servicing of Lagrange point missions by placing a Lunar service station in an Lunar Ll orbit. The TPF spacecraft can be transferred to a Lunar L1 orbit in a few days and requires relatively little delta-V. This efficient transfer results from the system of low energy pathways connecting the entire Solar System generated by the Lagrange points. The halo orbits are the p...