D. J. Scheeres

University of Colorado Boulder | CUB · Department of Aerospace Engineering Sciences (AES)

A semi-analytical uncertainty propagation conjunction analysis toolkit is presented for short-term and long-term conjunctions in the near-Earth space. The primary purpose of this user-accessible toolkit is to provide a fast and reliable method to predict collisions between space objects; and to present an alternative to the existing computationally...

It is essential to develop accurate tools for uncertainty propagation and conjunction assessment for cislunar region. In this paper, Gaussian Mixture Models (GMMs) and State Transition Tensors (STTs) are used in the Circular Restricted Three-Body Problem to propagate system uncertainty accurately and efficiently. The GMM splitting is performed alon...

The Keplerian orbital elements make up a set of parameters that uniquely describe a two-body trajectory. Once perturbations are imposed on two-body dynamics, one often studies the time evolution of the orbital elements. Moving in complexity beyond two-body perturbations [that is, studying the dynamics in the circular restricted three-body problem (...

This work presents a study of the dynamics in the vicinity of the stable $L_2$ halo orbits in the Earth-Moon system of the circular restricted three-body problem. These solutions include partially elliptic, partially hyperbolic, and elliptic quasi-halo orbits. The first two types of orbits are 2-dimensional quasi-periodic tori, whereas the elliptic...

Impulsive maneuver design between quasi-periodic orbits (QPOs) remains a prevalent problem in astrodynamics. Challenges associated with the higher-dimensional nature of QPOs present difficulties when using existing approaches to design transfers between them. This paper establishes a methodology to abate these issues. Fundamental to the approach is...

On April 13, 2029, the asteroid (99942) Apophis will have a close approach to Earth and be observed with optical telescopes and the DSN’s Goldstone planetary radar in the weeks before and after closest approach. This paper will describe how these observations can be leveraged to provide information on Apophis’ interior and to detect shifts within i...

The catalog of km-sized near-Earth objects (NEOs) is nearly complete. Typical impact monitoring analyses search for possible impacts over the next 100 yr and none of the km-sized objects represent an impact threat over that time interval. Assessing the impact risk over longer timescales is a challenge since orbital uncertainties grow. To overcome t...

The future of space exploration requires a thorough understanding of spacecraft dynamics in the Earth-Moon system. Often neglected when studying motion in this system is the gravitational influence of the Sun. This paper leverages the Hill restricted four- body problem (HR4BP), a time-periodic generalization of the circular restricted three-body pr...

Ground-based characterization of spacecraft targets prior to mission operations is critical to properly plan and execute measurements. Understanding surface properties, such as mineralogical composition and phase curves (expected brightness at different viewing geometries), informs data acquisition during the flybys. Binary near-Earth asteroids (NE...

The catalog of km-sized near-Earth objects (NEOs) is nearly complete. Typical impact monitoring analyses search for possible impacts over the next 100 years and none of the km-sized objects represent an impact threat over that time interval. Assessing the impact risk over longer time scales is a challenge since orbital uncertainties grow. To overco...

Ground-based characterization of spacecraft targets prior to mission operations is critical to properly plan and execute measurements. Understanding surface properties, like mineralogical composition and phase curves (expected brightness at different viewing geometries) informs data acquisition during the flybys. Binary near-Earth asteroids (NEA) (...

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on September 26, 2022 as a planetary defense test. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defense,...

Some active asteroids have been proposed to be the result of impact events. Because active asteroids are generally discovered serendipitously only after their tail formation, the process of the impact ejecta evolving into a tail has never been directly observed. NASA's Double Asteroid Redirection Test (DART) mission, apart from having successfully...

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on September 26, 2022 as a planetary defense test1. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defense,...

While no known asteroid poses a threat to Earth for at least the next century, the catalog of near-Earth asteroids is incomplete for objects whose impacts would produce regional devastation1,2. Several approaches have been proposed to potentially prevent an asteroid impact with Earth by deflecting or disrupting an asteroid1-3. A test of kinetic imp...

Some active asteroids have been proposed to be the result of impact events1. Because active asteroids are generally discovered serendipitously only after their tail formation, the process of the impact ejecta evolving into a tail has never been directly observed. NASA's Double Asteroid Redirection Test (DART) mission2, apart from having successfull...

Autonomous capabilities could be an essential aspect of future near-Earth asteroid exploration missions, enabling a fleet of low-cost spacecraft to be distributed to various targets for increased scientific and engineering returns. This paper studies the design of an adaptive offline policy for a surface imaging task under the influence of maneuver...

This work develops a long-term conjunction toolkit by combining an efficient and accurate semi-analytical uncertainty propagation method, realistic dynamics, and an encounter model. The epoch Gaussian uncertainty distribution is split into smaller Gaussian Mixture Model components. These mixture components are propagated individually using State Tr...

Gaussian Mixture Models and State Transition Tensors are combined to propagate state uncertainty to demonstrate an analytical and accurate future uncertainty and conjunction assessment. The initial uncertainty distribution is split into a Gaussian Mixture Model to reduce the size of covariance associated with each mixture component. This reduction...

An algorithm to compute a quasi-periodic orbit by targeting the frequencies of the orbit is presented. The algorithm requires a known solution and a set of frequencies to target. The algorithm makes use of a pre-existing quasi-periodic orbit computational scheme to continue the solutions toward the targeted frequencies. The algorithm is tested on t...

There are destabilizing resonances in medium Earth orbit due to third body effects from the Sun and Moon. Objects in the region suffer a growth of eccentricity dependent on their initial conditions. This study focuses on how debris objects from a fragmentation event would interact with the chaotic dynamics of the area. The debris clouds are studied...

This paper proposes a semianalytical measure of nonlinearity (MoN) based on tensor eigenpairs. Approximating nonlinear dynamics via local linearization is a common practice that is used to enable analytical methods in dynamics, control, navigation, and uncertainty propagation. However, these linear approximations are only applicable near the linear...

The propagation of small bodies in the solar system is driven by the combination of planetary encounters that cause abrupt changes in their orbits and secular long-term perturbations. We propose a propagation strategy that combines both of these effects into a single framework for long-term, rapid propagation of small bodies in the inner solar syst...

Traditional concerns regarding spacecraft estimation are exacerbated in cislunar space due to highly nonlinear dynamics, limited observational information, and increasingly overloaded Earth-based resources. These concerns motivate the investigation of space-based navigation and observation capabilities which lend themselves to autonomy. This paper...

In this paper, we use a soft-sphere discrete element method code to simulate the transmission and study the attenuation of a seismic wave. Then, we apply our findings to the different space missions that have had to touch the surface of different small bodies in the solar system. Additionally, we do the same in regard to the seismic wave generated...

There’s recently been an increased interest in exploring the very low Earth orbits (VLEO) for sustained satellite operations and as parking orbits before raising the satellite to its operational altitude. With increasing congestion in Low Earth Orbit (LEO) and its associated collision risks, VLEO could provide an additional orbital regime where sat...

We explore the effects of the 2029 Earth encounter on asteroid (99942) Apophis' non-principal axis spin state, leveraging refined orbit, spin state, and inertia information provided by more recent optical and radar observations. Propagating the asteroids' coupled orbit and rigid body attitude dynamics through the flyby, we present the range of poss...

Spin state predictions for defunct satellites in geosynchronous earth orbit (GEO) are valuable for active debris removal and servicing missions as well as material shedding studies and attitude-dependent solar radiation pressure (SRP) modeling. Previous studies have shown that solar radiation torques can explain the observed spin state evolution of...

Synchronous binary asteroids can experience libration about their tidally-locked equilibrium, which will result in energy dissipation. This is an important topic to the Asteroid Impact and Deflection Assessment, where excitation caused by the DART kinetic impact in the Didymos binary asteroid system may be reduced through dissipation before Hera ar...

We explore the effects of the 2029 Earth encounter on asteroid (99942) Apophis’ non-principal axis spin state, leveraging refined orbit, spin state, and inertia information provided by more recent optical and radar observations. Propagating the asteroids’ coupled orbit and rigid body attitude dynamics through the flyby, we present the range of poss...

Synchronous binary asteroids can experience libration about their tidally-locked equilibrium, which will result in energy dissipation. This is an important topic to the Asteroid Impact and Deflection Assessment, where excitation caused by the DART kinetic impact in the Didymos binary asteroid system may be reduced through dissipation before Hera ar...

Gaussian Mixture Models and State Transition Tensors are combined in a semi-analytical GMM-STT method to nonlinearly propagate uncertainty accurately and efficiently. This method previously defined in Khatri and Scheeres is combined with a more accurate dynamical system to match full Keplerian, J2, and Solar Radiation Pressure dynamics. An averaged...

In this paper we use a Soft-Sphere Discrete Element method code to simulate the transmission and study the attenuation of a seismic wave. Then, we apply our findings to the different space missions that have had to touch the surface of different small bodies. Additionally, we do the same in regards to the seismic wave generated by the hypervelocity...

Local linearization is often used to enable analytical methods in spacecraft dynamics, navigation, and control. However, the linear approximation becomes inaccurate at large distances from the linearization point and/or when the underlying dynamical system is strongly nonlinear. As a result, linearization-based methods like the finite time Lya-puno...

Heteroclinic connections present opportunities for spacecraft to access regions of space without expending propellant. These dynamical structures will play an important role as the Earth-Moon regime is exploited moving forward. The objective of this work is to compute all of the connections between the first and second libration points in the Earth...

This paper utilizes Koopman operator theory to generate robust optimal control laws for nonlinear systems with control-dependent noise. The Koopman operator is a theoretical, infinite-dimensional linear operator that characterizes the evolution of a nonlinear dynamical system in function space, i.e., the dynamics of a nonlinear system can be descri...

Quasi-halo orbits in the circular restricted three-body problem are quasi-periodic orbits that exist about the periodic halo orbits. A quasi-periodic orbit is an orbit diffeomorphic to a quasi-periodic torus that moves on at least a two-dimensional manifold in phase space and does not repeat itself. Given plans for the future Lunar Gateway, the L2...

Reachable and controllable sets for electric propulsion spacecraft are important to many problems including: dynamic replanning, robust mission design, space situational awareness, assessing advanced concepts, and threat assessments. Current methods result in a two-point boundary value problem or are limited in their application. We solve the reach...

Understanding and predicting the long-term spin state evolution of defunct satellites and rocket bodies is important for solar radiation pressure modeling, space domain awareness, and active debris removal (ADR). Dynamical modeling and observations indicate that defunct geosynchronous satellite spin states are primarily driven by solar radiation to...

NASA's Double Asteroid Redirection Test (DART) spacecraft is planned to impact the natural satellite of (65803) Didymos, Dimorphos, around 23:14 UTC on 26 September 2022, causing a reduction in its orbital period that will be measurable with ground-based observations. This test of kinetic impactor technology will provide the first estimate of the m...

When the OSIRIS-REx spacecraft pressed its sample collection mechanism into the surface of Bennu, it provided a direct test of the poorly understood near-subsurface physical properties of rubble-pile asteroids, which consist of rock fragments at rest in microgravity. Here, we find that the forces measured by the spacecraft are best modeled as a gra...

The propagation of small bodies in the Solar system is driven by the combination of planetary encounters that cause abrupt changes in their orbits and secular long-term perturbations. We propose a propagation strategy that combines both of these effects into a single framework for long-term, rapid propagation of small bodies in the inner Solar Syst...

Modern space missions demand that vehicles operate in multi-body environments. Further, they will require that spacecraft are able to coordinate with each other to complete complex objectives. We present an impulsive control strategy for driving spacecraft to bounded relative trajectories. The approach is grounded in dynamical systems theory. The i...

Cislunar space is an exciting frontier for space system development, particularly with respect to formation flying because of modular and sustainable architectures like the Lunar Gateway. This motivates the development of autonomous cislunar formation flight capabilities to alleviate logistical challenges and facilitated understanding of proximity...

Asteroid 469219 Kamo’oalewa, also named 2016 HO3, is a small-size fast-rotating near-Earth asteroid, which is a potential target for future explorations. Owing to its weak gravity and fast spin rate, the dynamics on the surface or in the vicinity of 2016 HO3 are significantly different from those of planets or other small bodies explored in previou...

One of the Janus mission flyby targets, 1991 VH, exhibits signs of chaotic dynamics. Observations show the orbit and secondary spin periods are changing over time. We use a high-fidelity numeric model to simulate the system under a variety of initial conditions, and find the dynamics are sensitive to the secondary's shape, spin, and orientation. Ce...

An accurate estimation of upper atmospheric densities is crucial for precise orbit determination (POD), prediction of low Earth orbit satellites, and scientific studies of the Earth's atmosphere. But densities estimated using satellite tracking data are always uncertain up to the drag‐coefficient assumed in the inversion method. This work develops...

Capability for spacecraft to autonomously explore near-Earth asteroids (NEAs) could be an essential aspect of future NEA missions, enabling a fleet of low-cost spacecraft to be distributed to various targets for increased scientific and engineering returns. During the proximity operation, an autonomous spacecraft needs to estimate its position, vel...

This paper introduces a new technique for directly controlling the missed thrust recovery margin (MTRM) of a low-thrust spacecraft trajectory. MTRM is defined here as the longest amount of time a spacecraft may coast away from a nominal trajectory while still being able to reach a terminal manifold once thruster operations are resumed. The “virtual...

Understanding long term stability in the GNSS region is crucial to maintaining this orbital regime. Averaged dynamics pose a useful tool for running long term analysis on these orbits for low computational power and quick run times. Because this region is subject to luni-solar resonances, averaged dynamics do not necessarily closely match the actua...

We present a study of the current state of knowledge concerning spacecraft operations and potential hazards while operating near a comet nucleus. Starting from simple calculations comparing the cometary coma environment to benign conditions on Earth, we progress to sophisticated engineering models of spacecraft behavior, and then confront these mod...

The many small-body exploration missions that have occurred over the last few decades have shown that small solar system objects are covered with granular material of varying depth. These missions have also observed that granular materials are mobilized from the surfaces at speeds on the order of escape speed by different contributing mechanisms. T...

View Video Presentation: https://doi.org/10.2514/6.2022-1274.vid This work presents a preliminary exploration of optimal maneuver strategies for two Earth-orbiting spacecraft to avoid a collision. A cooperative approach explores the Pareto-optimal trade-off in fuel use for each spacecraft for both to successfully avoid a collision while starting an...

View Video Presentation: https://doi.org/10.2514/6.2022-1571.vid Combining observations of a binary asteroid system’s mutual orbit with a dynamic model of the system’s motion can lead to an estimate of the bodies’ mass properties. A simplified planar model of binary asteroid dynamics using a second degree gravity field is sufficient to estimate the...

View Video Presentation: https://doi.org/10.2514/6.2022-2459.vid Quasi-halo orbits in the circular restricted three-body problem are quasi-periodic orbits that exist about the periodic halo orbits. A quasi-periodic orbit is an orbit that moves on at least a 2-dimensional manifold in phase space but does not repeat. Given plans for the future Lunar...

View Video Presentation: https://doi.org/10.2514/6.2022-2468.vid The OSIRIS-REx mission to asteroid (101955) Bennu resulted in the most detailed and accurate model to date of a small, rubble-pile asteroid. This paper provides a detailed dynamical systems analysis of orbital motion in the vicinity of Bennu, leveraging the final physical model estima...

Recent developments in the field of Scientific Machine Learning have lead to new techniques that allow for the combination of mechanistic and data-driven approaches for modelling dynamical systems. Utilizing two of these methods, Universal Differential Equations and Symbolic Regression, this work demonstrates a robust manner to uncover unmodelled p...

The NASA Double Asteroid Redirection Test (DART) mission is a planetary defense-driven test of a kinetic impactor on Dimorphos, the satellite of the binary asteroid 65803 Didymos. DART will intercept Dimorphos at a relative speed of ∼6.5km s−1, perturbing Dimorphos’s orbital velocity and changing the binary orbital period. We present three independ...

In this paper, the structural stability of a fast-spinning small body is investigated. In particular, a nonlinear yield condition in tensile stress is applied to estimate the required cohesion in a fast-spinning small body. The least upper bound of required cohesion is investigated for both ellipsoid and irregular shape models. The stress state of...

The Double Asteroid Redirection Test (DART) mission will be the first test of a kinetic impactor as a means of planetary defense. In late 2022, DART will collide with Dimorphos, the secondary in the Didymos binary asteroid system. The impact will cause a momentum transfer from the spacecraft to the binary asteroid, changing the orbit period of Dimo...

We present a study of the current state of knowledge concerning spacecraft operations and potential hazards while operating near a comet nucleus. Starting from some simple back of the envelope calculations comparing the cometary coma environment to benign conditions on Earth, we progress to sophisticated engineering models of spacecraft behavior, a...

The Double Asteroid Redirection Test (DART) mission will be the first test of a kinetic impactor as a means of planetary defense. In late 2022, DART will collide with Dimorphos, the secondary in the Didymos binary asteroid system. The impact will cause a momentum transfer from the spacecraft to the binary asteroid, changing the orbit period of Dimo...

Autonomous capability could be a pivotal element for future near-Earth asteroid (NEA) exploration, where a fleet of low-cost spacecraft is distributed to various targets for increased scientific and engineering returns. A challenge in proximity operations at NEAs is a significant a priori uncertainty in a target’s physical parameters, such as its size...

Gaussian Mixture Models and State Transition Tensors are combined to propagate state uncertainty to demonstrate an analytical and accurate future uncertainty and conjunction assessment. The initial uncertainty distribution is split into a Gaussian Mixture Model to reduce the size of covariance associated with each mixture component. This reduction...

Traditional concerns regarding space domain awareness are exacerbated in cislunar space due to highly nonlinear dynamics, limited viewing geometries, and increasingly overloaded Earth-based resources. These concerns motivate the investigation of space-based navigation and observation capabilities which lend themselves to autonomy. This paper expand...

Exploration of asteroid (101955) Bennu by the OSIRIS-REx mission has provided an in-depth look at this rubble-pile near-Earth asteroid. In particular, the measured gravity field and the detailed shape model of Bennu indicate significant heterogeneities in its interior structure, compatible with a lower density at its center. Here we combine gravity...