Publications

This page highlights select works only, and is not always up-to-date. My Google Scholar page is probably the most comprehensive list. Planetary science works are differentiated from engineering with a saturn emoji 🪐.

This page is auto-generated from a .bib file by jekyll-scholar.

2025

1. A Monomial Method for Nonlinear Optimization in Astrodynamics

   Ethan R. Burnett, and Francesco Topputo

   AAS Spaceflight Mechanics Meeting, paper AAS 25-218, Jan 2025

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   This paper introduces a monomial method for rapidly solving a variety of nonlinear optimization problems astrodynamics. Using differential algebra to compute Taylor expansions of given nonlinear functions, the result is a function of multivariate monomials up to the order of truncation. These monomials are interrelated. We use this fact to approximate nonlinear functions in Euclidean space by linear functions on a Riemannian manifold, wherein the problem can be solved with speed and stability, leveraging numerical schemes for optimization on manifolds. The method could prove advantageous in contexts requiring the repeated solution of similar optimization problems, for which the expansion can be reused, or for particularly tricky optimization problems where a combination of rapid sampling and gradient-based methods need to be used. In this introductory work we lay the foundations and explore two simple example applications: 1) computing periodic orbits, and 2) computing/continuing optimal impulsive transfers.

2. Trajectory Design in Multi-Body Models via Homotopic Convex Optimization

   Christian Hofmann, Hakan Chunton, Kai Xi, and 4 more authors

   (submitted to Astrodynamics), Jan 2025

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   The Moon will play a central role in upcoming human space exploration efforts, with numerous missions planned in the near future. Designing trajectories for spacecraft in the cislunar region requires advanced methods that account for the dynamics of complex multi-body systems. This work presents a sequential convex programming (SCP) framework for optimizing both impulsive and continuous-thrust trajectories within the restricted three- and four-body models, with a subsequent transition to high-fidelity ephemeris models. We employ a pulsating-rotating frame, use a homotopic approach and leverage the Sundman transformation to improve convergence. The proposed method is demonstrated through simulations in the Sun-perturbed Earth–Moon system and the Moon-perturbed Sun–Earth system. The high accuracy and robustness make SCP an excellent choice even for solving highly nonlinear problems.

3. Convex Trajectory Optimization via Monomial Coordinates Transcription for Cislunar Rendezvous

   Omar Regantini, Ethan R Burnett, Antonio Rizza, and 2 more authors

   arXiv preprint (submitted to JGCD), Jan 2025

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   This paper proposes a nonlinear guidance algorithm for fuel-optimal impulsive trajectories for rendezvous operations close to a reference orbit. The approach involves overparameterized monomial coordinates and a high-order approximation of the dynamic flow precomputed using Differential Algebra, which eliminates the need for real-time integration. To address non-convexity in the monomial coordinate formulation of the guidance problem, Sequential Convex Programming is applied. Using the methodology presented in this paper, repeatedly evaluating the nonlinear dynamics is not necessary, as in shooting or collocation methods. Instead, only the monomial equations require updating between iterations, drastically reducing computational burden. The proposed algorithm is tested in the Circular Restricted Three-Body Problem framework with the target spacecraft on a Near-Rectilinear Halo Orbit. The results demonstrate stability, efficiency, and low computational demand while achieving minimal terminal guidance errors. Compared to linear methods, this nonlinear convex approach exhibits superior performance in open-loop propagation of impulsive maneuvers in cislunar space, particularly in terms of accuracy. These advantages make the algorithm an attractive candidate for autonomous onboard guidance for rendezvous operations in the cislunar domain.

4. Rapid nonlinear convex guidance using a monomial method

   Ethan R. Burnett, and Francesco Topputo

   Journal of Guidance, Control, and Dynamics, Apr 2025

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   This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization with impulsive maneuvers, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs overparameterized monomial coordinates and precomputed fundamental solution expansions to facilitate rapid optimization while minimizing real-time computational requirements. The fundamental solution expansions are precomputed about an uncontrolled reference trajectory using differential algebra. Unlike traditional approaches that repeatedly evaluate the nonlinear dynamics and constraints as part of complex shooting or collocation-based schemes, this method replaces the nonlinearity inherent to dynamics and constraint functions entirely with a computationally simpler manifold constraint. With this approach, trajectory optimization is posed efficiently as a path-planning problem on the manifold. This problem is entirely convex except for the manifold constraint, readily lending itself to solution via sequential convex programming. We demonstrate the effectiveness of our approach in computing fast and accurate delta-V optimal solutions for long-range spacecraft rendezvous, including problems with nonlinear state constraints.

2024

1. 🪐 Numerical inference of viscoelastic properties in tidal models of rubble pile asteroids

   Ethan R. Burnett, Iosto Fodde, and Fabio Ferrari

   EGU General Assembly, abstract EGU24-17927, Apr 2024

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2023

1. 🪐 Astrobiology eXploration at Enceladus (AXE): A New Frontiers Mission Concept Study

   K. Marshall Seaton, Szilárd Gyalay, Gaia Stucky Quay, and 17 more authors

   The Planetary Science Journal, Jun 2023

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   The Saturnian moon Enceladus presents a unique opportunity to sample the contents of a subsurface liquid water ocean in situ via the continuous plume formed over its south polar terrain using a multi-flyby mission architecture. Previous analyses of the plume’s composition by Cassini revealed an energy-rich system laden with salts and organic compounds, representing an environment containing most of the ingredients for life as we know it. Following in the footsteps of the Cassini-Huygens mission, we present Astrobiology eXploration at Enceladus (AXE), a New Frontiers class Enceladus mission concept study carried out during the 2021 NASA Planetary Science Summer School program at the Jet Propulsion Laboratory, California Institute of Technology. We demonstrate that a scientifically compelling geophysical and life-detection mission to Enceladus can be carried out within the constraints of a New Frontiers-5 cost cap using a modest instrument suite, requiring only a narrow angle, high-resolution telescopic imager, a mass spectrometer, and a high-gain antenna for radio communications and gravity science measurements. Using a multi-flyby mission architecture, AXE would evaluate the habitability and potential for life at Enceladus through a synergistic combination of in situ chemical analysis measurements aimed at directly detecting the presence of molecular biosignatures, along with geophysical and geomorphological investigations to contextualize chemical biosignatures and further evaluate the habitability of Enceladus over geologic time.

2. 🪐 Spin–orbit coupling of Europa’s ice shell and interior

   Ethan R. Burnett, and Paul O. Hayne

   Icarus, Jun 2023

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   Europa is an icy ocean world, differentiated into a floating ice shell and solid interior, separated by a global ocean. The classical spin–orbit coupling problem considers a satellite as a single rigid body, but in the case of Europa, the existence of the subsurface ocean enables independent motion of the ice shell and solid interior. This paper explores the spin–orbit coupling problem for Europa from a dynamical perspective, yielding illuminating analytical and numerical results. We determine that the spin behavior of Europa is influenced by processes not captured by the classical single rigid body spin–orbit coupling analysis. The tidal locking process for Europa is governed by the strength of gravity-gradient coupling between the ice shell and solid interior, with qualitatively different behavior depending on the scale of this effect. In this coupled rigid model, the shell can potentially undergo large angular displacements from the solid interior, and the coupling plays an outsize role in the dynamical evolution of the moon, even without incorporating the dissipative effects of shell non-rigidity. We additionally discuss the effects of a realistic viscoelastic shell, and catalogue other torques that we expect to be sub-dominant in Europa’s spin dynamics, or whose importance is unknown. Finally, we explore how the choice of tidal model affects the resulting equilibrium spin state.

3. Energy reference guidance for drag-modulated aerocapture

   Samuel W. Albert, Ethan R. Burnett, Hanspeter Schaub, and 2 more authors

   Advances in Space Research, Jun 2023

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   Aerocapture is a method of achieving orbit insertion via a single pass through the atmosphere of the central body. Single-event jettison drag modulation is a simple way of achieving control during atmospheric flight by effecting a discrete change in the aerodynamics of the vehicle. A novel guidance algorithm, energy reference guidance, is developed and implemented for a reference scenario of a small satellite aerocapture demonstration at Earth, and is compared to the baseline numerical predictor–corrector solution. The new approach is shown to achieve equivalent apoapsis targeting performance as the baseline algorithm with significantly lower CPU demand during atmospheric flight, although more onboard memory is required in exchange. The relationship between targeting performance and required memory is quantitatively explored for the new algorithm; the selected configuration generates approximately 3.3 MB of data, which is expected to be well within the capability of relevant avionics systems.

4. Chance-Constrained, Drift-Safe Guidance for Spacecraft Rendezvous

   A. W. Berning Jr., E. R. Burnett, and S. Bieniawski

   AAS Rocky Mountain GNC Conference, paper no. AAS 23-115, Jun 2023

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   A robust drift-safe rendezvous trajectory optimization tool is developed in this work, with applications to orbital rendezvous and proximity operations. The method is based on direct collocation and utilizes a sequential convex programming framework, and is extended from previous work to include passive safety constraints. The tool is then paired with a dispersion analysis framework to allow trajectories to be optimized subject to plant, navigation, and actuator uncertainties. The timing, direction, and magnitude of orbital maneuvers are optimized subject to the expected propellant usage, for a given navigation system performance. Representative trajectories are presented for the LEO flight regime, but the approach can also be applied to GEO and NRHO with minimal modification.

2022

1. Approximating orbits in a rotating gravity field with oblateness and ellipticity perturbations

   Ethan R. Burnett, and Hanspeter Schaub

   Celestial Mechanics and Dynamical Astronomy, Jun 2022

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   This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for the orbit radius and other elements. The conservation of the Jacobi integral is used to make the problem solvable to first order in the perturbations. The solutions are characterized as small deviations from an unperturbed circular orbit. The approximations are developed for near-circular orbits with initial mean motion n0 around a body with rotation rate c. The approximations are shown to be valid for values of angular rate ratio Gamma = c/n0 > 1, with accuracy decreasing as Gamma approaches 1, and singularities at and near Gamma = 1. Extensions of the methodology to eccentric orbits are discussed, with commentary on the challenges of obtaining generally valid solutions for both near-circular and eccentric orbits.

2. Spacecraft Relative Motion Dynamics and Control Using Fundamental Modal Solution Constants

   Ethan R. Burnett, and Hanspeter Schaub

   Journal of Guidance, Control, and Dynamics, Aug 2022

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   This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental modal solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of fundamental and geometrically insightful modal motions. These fundamental motions are obtained using the Lyapunov–Floquet theory. In the case that the dynamics are perturbed by the action of a controller or by unmodeled dynamics, the weights on each fundamental solution are allowed to vary as in a variation-of-parameters approach, and in this manner function as state variables. This methodology reveals interesting insights about satellite relative motion and enables elegant control approaches. This approach can be applied in any dynamical environment as long as the chief orbit is periodic, and this is demonstrated with results for relative motion analysis and control in the eccentric Keplerian problem and in the circular restricted three-body problem. Some commentary on the extension of the methodology beyond the periodic chief orbit case is also provided. This is a promising and widely applicable new approach to the close-proximity satellite relative motion problem.

3. Geometric Perspectives on Fundamental Solutions in the Linearized Satellite Relative Motion Problem

   Ethan R. Burnett, and Hanspeter Schaub

   Acta Astronautica, Jan 2022

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   Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite relative motion solutions for linearization about a closed chief orbit. By identifying the analytic relationship between Lyapunov–Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration of the types of close-proximity natural relative motion available in various applications. The approach is demonstrated for the Keplerian relative motion problem with general eccentricities in multiple coordinate representations. The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.

2021

1. Study of highly perturbed spacecraft formation dynamics via approximation

   Ethan. R. Burnett, and Hanspeter Schaub

   Advances in Space Research, Jan 2021

   Satellite Constellations and Formation Flying

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   This paper explores methods for approximating and analyzing the dynamics of highly perturbed spacecraft formations with an emphasis on computationally efficient approaches. This facilitates on-board computation or rapid preliminary mission design analysis. Perturbed formation dynamics are often approximated as linear time-varying (LTV) systems, for which Floquet theory can be used to analyze the degree of system instability. Furthermore, the angular momentum of the relative orbital state can be computed with the approximate dynamics to provide additional insight. A general methodology is developed first and then applied to the problem of unstable formation dynamics in asteroid orbits. Here the dominant perturbative effects due to low-order gravitational harmonics and solar radiation pressure are modeled. Numerical simulations validate the approach and illustrate the approximation accuracy achieved.

2. Spacecraft formation and orbit control using differential attitude-dependent solar radiation pressure

   Ethan R. Burnett, and Hanspeter Schaub

   Advances in Space Research, Jan 2021

   Satellite Constellations and Formation Flying

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   This paper introduces a linear model for spacecraft formation dynamics subject to attitude-dependent solar radiation pressure (SRP) disturbance, with the SRP model accounting for both absorption and specular/diffuse reflection. Spacecraft attitude is represented in modified Rodriguez parameters (MRPs), which also parameterize the orientation of individual facets for a spacecraft with fixed geometry. Compared to earlier work, this model incorporates analytic approximation of the SRP-perturbed chief orbit behavior in a manner enabling its use in applications with infrequent guidance updates. Control examples are shown for single-plate representations of hypothetical spacecraft with generally realistic optical parameters. The results demonstrate the validity of the model and the feasibility of SRP-based formation and rendezvous control in orbits around small bodies and in high orbits around the Earth such as the GEO belt.

3. 🪐 Europa’s hemispheric color dichotomy as a constraint on non-synchronous rotation

   Ethan R. Burnett, and Paul O. Hayne

   Icarus, Aug 2021

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   Europa’s surface reflectance exhibits a pronounced hemispheric dichotomy, which is hypothesized to form due to enhanced irradiation of the trailing hemisphere by energetic particles entrained in the jovian magnetosphere. We propose that this pattern can only persist if the timescale for discoloration is much shorter than that of Europa’s rotation relative to the synchronous state, and provide a means for constraining the rotation rate using the observed color pattern. By decomposing the longitudinal ultraviolet and visible color variations from Voyager data into sine and cosine terms, we find no detectable signature of non-synchronous rotation (NSR). This same conclusion is reached with two observational models of discoloration: one representing an actively discoloring surface, and the other assuming that the present-day exogenic discoloration on the surface is in steady-state. Magnitudes of the expected signature are presented as functions of the age of the crater Pwyll, which is used to constrain the timescale of discoloration. Furthermore, we develop a physical model of discoloration to validate the geometric models, producing consistent results. The failure to identify a signature of NSR using Europa’s hemispheric color dichotomy magnifies the outstanding problem of the origin of the stress to explain Europa’s pervasive tectonic features.

2020

1. Unit Sphere-Constrained and Higher Order Interpolations in Laplace’s Method of Initial Orbit Determination

   Ethan R. Burnett, Andrew J. Sinclair, and Carolyn C. Fisk

   The Journal of the Astronautical Sciences, Aug 2020

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   This paper explores an alternative interpolation approach for the line-of-sight measurements in Laplace’s method for angles-only initial orbit determination (IOD). The classical implementation of the method uses Lagrange polynomials to interpolate three or more unit line-of-sight (LOS) vectors from a ground-based or orbiting site to an orbiting target. However, such an approach does not guarantee unit magnitude of the interpolated line-of-sight path except at the measurement points. The violation of this constraint leads to unphysical behavior in the derivatives of the interpolated line-of-sight history, which can lead to poor initial orbit determination (IOD) performance. By adapting a spherical interpolation method used in the field of computer graphics, we can obtain an interpolated line-of-sight history that is always unit norm. This new spherical interpolation method often leads to significant performance improvements in Laplace’s IOD method, with comparable robustness to measurement noise as the traditional interpolation methods. This paper also demonstrates the benefit of interpolating through more than three data points, which is easily enabled up to an arbitrary number of measurements by recursive definitions of the interpolations.