Survey on studies about model uncertainties in small body explorations

Currently, the explorations of small solar system bodies (asteroids and comets) have become more and more popular. Due to the limited measurement capability and irregular shape and diverse spin status of the small body, uncertainties on the parameters of the system and s/c executions are a practical and troublesome problem for mission design and operations. The sample-based Monte Carlo simulation is primarily used to propagate and analyze the effects of these uncertainties on the surrounding orbital motion. However, it is generally time-consuming because of large samples required by the highly nonlinear dynamics. New methods need to be applied for balancing computational efficiency and accuracy. To motivate this research area and facilitate the mission design process, this review firstly discusses the dynamical models and the different methods of modeling the mostly related gravitational and non-gravitational forces. Then the main uncertainties in these force models are classified and analyzed, including approaching, orbiting and landing. Then the linear and nonlinear uncertainty propagation methods are described, together with their advantages and drawbacks. Typical mission examples and the associated uncertainty analysis, in terms of methods and outcomes, are summarized. Future research efforts are emphasized in terms of complete modelling, new mission scenarios, and application of (semi-) analytical methods in small body explorations

Analytic initial relative orbit solution for angles-only space rendezvous using hybrid dynamics method

A closed-form solution to the angles-only initial relative orbit determination (IROD) problem for space rendezvous with non-cooperated target is developed, where a method of hybrid dynamics with the concept of virtual formation is introduced to analytically solve the problem. Emphasis is placed on developing the solution based on hybrid dynamics (i.e., Clohessy-Wiltshire equations and two-body dynamics), obtaining formation geometries that produce relative orbit state observability, and deriving the approximate analytic error covariance for the IROD solution. A standard Monte Carlo simulation system based on two-body dynamics is used to verify the feasibility and evaluate the performance proposed algorithms. The sensitivity of the solution accuracy to the formation geometry, observation numbers is presented and discussed

1:1 resonance capture of a low-thrust spacecraft around Vesta

Vesta is the second largest celestial object in the main asteroid belt and it was visited and studied by the DAWN mission in 2011. The spacecraft used solar-electric propulsion that generates continuous low-thrust. As the spacecraft slowly descends from high altitude mission orbit (HAMO) to low altitude mission orbit (LAMO), it crosses the 1:1 resonance, putting the spacecraft at risk of being permanently trapped at this altitude. The objective of this paper is to analyze the probability that the spacecraft has to be captured into the 1:1 resonance with Vesta. Firstly, we model the dynamics considering the irregular gravitational field up to the fourth-order and degree and the thrust constant in magnitude and opposite to the velocity direction of the spacecraft. Then, we calculate the probability of capture for orbits with different combinations of the semi-major axis and true anomaly. In addition, we simplify the dynamical model by considering the harmonic terms related to the 1:1 resonance and the second-order degree harmonics, respectively. It is found that the simplified models are not capable of estimating this probability promisingly. Therefore, through pure numerical simulations of the complete model, we investigate the sensitivity of this capture to different orbital geometries and physical properties of the spacecraft. The results show that the probability of capture is more dependent on the value of the mass of the spacecraft and the magnitude of the thrust, and is less dependent on the value of the specific impulse. In addition, it is found that the spacecraft is more prone to be captured into the 2:3 resonance with Vesta if the descent starts from a non-polar orbit

Dynamics around equilibrium points of uniformly rotating asteroids

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families

Hamiltonian model of a low-thrust spacecraft's capture into 1:1 resonance around Vesta

Vesta is the second largest celestial object of the main asteroid belt and it was visited and investigated by the DAWN mission in 2011. The spacecraft used solar-electric propulsion that generates continuous low-thrust. As the spacecraft slowly descends from high altitude mission orbit (HAMO) to low altitude mission orbit (LAMO), it crosses the 1:1 resonance, putting the spacecraft at risk of being permanently trapped at this altitude. The objective of this paper is to develop a hamiltonian model that represents the phenomenon, which is used as a bases for estimating the probability of capture using the adiabatic invariant theory. Firstly, we define the hamiltonian considering the irregular gravitational field up to the second order and degree and the thrust constant in magnitude and opposite to the velocity direction of the spacecraft. Then, we expand the model around the resonance which results the hamiltonian to be reduced in a pendulum-like expression. The reduced model is validated against numerical simulations and is proven to be a good approximation of the dynamic

Design and Analysis of Robust Ballistic Landings on the Secondary of a Binary Asteroid

ESA's Hera mission aims to visit binary asteroid Didymos in late 2026, investigating its physical characteristics and the result of NASA's impact by the DART spacecraft in more detail. Two CubeSats on-board Hera plan to perform a ballistic landing on the secondary of the system, called Dimorphos. For these types of landings the translational state during descent is not controlled, reducing the spacecrafts complexity but also increasing its sensitivity to deployment maneuver errors and dynamical uncertainties. This paper introduces a novel methodology to analyse the effect of these uncertainties on the dynamics of the lander and design a trajectory that is robust against them. This methodology consists of propagating the uncertain state of the lander using the non-intrusive Chebyshev interpolation (NCI) technique, which approximates the uncertain dynamics using a polynomial expansion, and analysing the results using the pseudo-diffusion indicator, derived from the coefficients of the polynomial expansion, which quantifies the rate of growth of the set of possible states of the spacecraft over time. This indicator is used here to constrain the impact velocity and angle to values which allow for successful settling on the surface. This information is then used to optimize the landing trajectory by applying the NCI technique inside the transcription of the problem. The resulting trajectory increases the robustness of the trajectory compared to a conventional method, improving the landing success by 20 percent and significantly reducing the landing footprint.Comment: 34 pages, 15 figure

Design of ganymede-synchronous frozen orbit around Europa

A Ganymede-synchronous frozen orbit around Europa provides a stable spatial geometry between a Europa probe and a Ganymede lander, which facilitates the observation of Ganymede and data transmission between probes. However, the third-body gravitation perturbation of Ganymede continues to accumulate and affect the long-term evolution of the Europa probe. In this paper, the relative orbit of Ganymede with respect to Europa is considered to accurately capture the perturbation potential. The orbital evolution behaviors of the Europa probe under the non-spherical gravitation of Europa and the third-body gravitation of Jupiter and Ganymede are studied based on a double-averaging framework. Then, the initial orbital conditions of the Ganymede-synchronous frozen orbit are developed. A station-keeping maneuver was performed to maintain the orbital elements to achieve the Ganymede-synchronous and frozen behaviors. A numerical simulation showed that the consumption for orbital maintenance is acceptablePeer ReviewedPostprint (published version

Leveraging the ground-track resonance capture and escape for precise and efficient orbital transfers

Vesta, the second largest celestial object in the main asteroid belt, was visited and studied by the Dawn mission in 2011. The spacecraft employed solar-electric propulsion, which generated continuous low-thrust. During the slow descent from high altitude mission orbit (HAMO) to low altitude mission orbit (LAMO), the spacecraft encountered the 1:1 ground-track resonance, with the potential of being captured and trapped in it. The objective of this paper is to present a workflow for designing orbit transfers from HAMO to LAMO by leveraging the effects of the 1:1 ground-track resonance, achieved only by adjusting the thrust magnitude value throughout the descent. Firstly, the dynamics are modeled by considering the irregular gravitational field up to the fourth order and degree, while the thrust remains constant in magnitude and opposes the velocity direction of the spacecraft. Subsequently, a reference case of capture into the 1:1 ground-track resonance is considered, and the effects of the resonance on the trajectory of the spacecraft are described. Following that, the workflow adopted for designing orbit transfers during Dawn's approach phase is presented, and a case study is conducted to apply the workflow. This paper contributes to raising awareness regarding the risk of resonance capture and highlights strategies for escaping such resonances, thereby facilitating the design of future space missions to asteroids

The capture probability of Dawn into ground-track resonances with Vesta

The Dawn spacecraft approached the asteroid Vesta and descended from a high-altitude mission orbit to a low-altitude mission orbit using lowthrust propulsion. During this descent, the spacecraft crossed the 2:3 and 1:1 ground-track resonances with Vesta, which posed a risk of capture that might strongly perturb the spacecraft's orbit. This study analyzes the effects of these resonances on the spacecraft's orbital elements and estimates the probability of capture into it through Monte Carlo simulations. Specifically, a comprehensive investigation is performed to assess the effects of 1:1 and 2:3 ground-track resonances on the semi-major axis, eccentricity, and inclination. The dynamical model includes the gravitational field of Vesta using a spherical harmonics approximation up to the 4th degree and order and the low-thrust acceleration that is assumed to be opposite to the spacecraft’s velocity vector direction. It is observed that the eccentricity evolution is mostly influenced by the 2:3 groundtrack resonance which results in a large variation when the spacecraft crosses that ground-track resonance, while the semi-major axis and inclination are mostly influenced by the 1:1 ground-track resonance. Then, the probability of capture into 1:1 ground-track resonance is found to have a negative correlation with the spacecraft's thrust magnitude and the probability of capture into 2:3 ground-track resonance is found to arise as the spacecraft's mass increases. It is found that for circular orbits below a certain inclination value the spacecraft's trajectory is subject to the "automatic entry into libration" phenomenon, due to the singularity in the Hamiltonian function. This research contributes to the design of successful transfer strategies when crossing resonance for future missions

Escape strategies from the capture into 1:1 resonance using low-thrust propulsion

Vesta is the second largest celestial object of the main asteroid belt and it was visited and studied by the DAWN mission in 2011. The spacecraft used solar-electric propulsion that generates continuous low-thrust. As the spacecraft slowly descends from high altitude mission orbit (HAMO) to low altitude mission orbit (LAMO), it crosses the 1:1 ground-track resonance, with the risk of being captured by this resonance and being trapped at this altitude. The objective of this paper is to analyze different escape strategies from the 1:1 resonance with Vesta based on the change in the low-thrust magnitude. Firstly, the dynamics is modelled considering the irregular gravitational field up to the fourth order and degree and the thrust constant in magnitude and opposite to the velocity direction of the spacecraft. Then, a reference case of capture into 1:1 resonance is considered and the effects of the resonance on the spacecraft's trajectory are described. A Monte Carlo analysis is performed to study the probability of escape from 1:1 resonance as a function of the thrust magnitude. The analysis reveals that there are regions in which the escape from the 1:1 resonance requires more thrust with respect to other ones. Additionally, some cases require to increase the thrust magnitude over the operational limit, making the escape impossible by only increasing the thrust magnitude. This paper contributes to increase the awareness on the risk of resonance capture and the strategies to escape for designing future space missions to asteroids