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

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

Semi-analytical estimation of the probability of capture into ground-track resonances of Dawn around Vesta

The DAWN mission demonstrated the feasibility of utilizing low-thrust propulsion for extended periods of time. The mission involves approaching asteroid Vesta from a high-altitude mission orbit (HAMO) to a low-altitude mission orbit (LAMO). As the spacecraft descends towards the asteroid, there is a likelihood that it might be captured by the 1:1 ground-track resonance. This occurs when the spacecraft encounters the same gravitational configuration at each revolution, which leads to significant changes in the orbital's eccentricity and inclination. With the increasing trend of using low-thrust propulsion in space exploration, it is essential to investigate the probability of capture into resonance for low-thrust spacecraft. This research focuses on developing a semi-analytical methodology to estimate the probability of a low-thrust spacecraft’s capture into 1:1 ground-track resonance of a low-thrust spacecraft around an asteroid in the context of the Dawn mission. Firstly, the two-degree-of-freedom Hamiltonian dynamical model of the 1:1 ground-track resonance around an asteroid is defined taking into account perturbations from the irregular gravitational field up to the second order and continuous low thrust that is constant in magnitude and always in the opposite direction of the spacecraft’s velocity. Then, the effect of low-thrust on these degrees of freedom is characterized by analyzing their rate of change as a function of the thrust magnitude and the expressions are averaged over the mean anomaly. Finally, the probability of capture into resonance is estimated as a function of the energy balance, which is evaluated as it crosses the separatrix using a global adaptive quadrature method. The results are validated against numerical simulations using the equations of motion derived from the Hamiltonian of the dynamics. Beside, we we also study the probability of capture given different thrust magnitudes and different orbit geometries in terms of semimajor axis, eccentricity, and inclination. Finally, the semi-analytical approach is applied to estimate the probability of capture into 2:3 ground-track resonance. This research makes a significant contribution to the field of astrodynamics by systematically analysing the probability of low-thrust spacecraft’s capture into resonances around asteroids, and also to efficient and robust mission design

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

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

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

Semi-analytical estimation of the probability of capture into 1:1 ground-track resonance of a low-thrust spacecraft around an asteroid

This paper presents a semi-analytical methodology to estimate the probability of capture into 1:1 ground-track resonance of a low-thrust spacecraft around an asteroid. The system dynamics are described by a Hamiltonian model that considers the perturbations from the irregular gravitational field up to the second order and degree, and the continuous low thrust that remains constant in magnitude and is always in the direction opposite to the spacecraft’s velocity. The model focuses on the equatorial case of the 1:1 ground-track resonance. When a trajectory is close to the resonance location, its behavior becomes non-deterministic, making it necessary to estimate the probability of capture into resonance. A fourth-order polynomial is used to numerically approximate the separatrices of the resonance region, while the change of the system’s energy balance when the trajectory crosses the separatrices is determined with a global adaptive quadrature method. Subsequently, the probability of capture into resonance is estimated, and the accuracy of the results is verified by comparing them to numerical simulations based on the perturbed Hamilton’s equations of motion. This research makes a significant contribution to the field of astrodynamics by systematically and efficiently analyzing the probability of low-thrust spacecraft capture into ground-track resonance around asteroids