Independent deep-space exploration with CubeSats, where the spacecraft independently propels itself from Earth orbit to deep-space, is currently not possible due to the lack of high-V propulsion systems compatible with the small form factor. The ion Electrospray Propulsion System (iEPS) under development at the Massachusetts Institute of Technology's Space Propulsion Laboratory is a promising technology due to its inherently small size and high efficiency. However, current electrospray thrusters have demonstrated lifetimes (500 hours) below the required firing time for an electrospray-thruster-propelled CubeSat to escape from Earth starting from geostationary orbit (8000 hours). To bypass this lifetime limitation, a stage-based approach, analogous to launch vehicle staging, is proposed where the propulsion system consists of a series of electrospray thruster arrays and fuel tanks. As each array reaches its lifetime limit, the thrusters and fuel tanks are ejected from the spacecraft exposing a new array to continue the mission. This work addresses the technical feasibility of a spacecraft with a stage-based electrospray propulsion system for a mission from geostationary orbit to near-Earth asteroid 2010 UE51 through a NASA Jet Propulsion Laboratory Team Xc concurrent design center study. Specific goals of the study were to analyze availability of CubeSat power systems that could support the propulsion system and any other avionics as well as requirements for attitude control and communication between the spacecraft and Earth. Two bounding cases, each defined by the maturity of the iEPS thrusters, were considered. The first case used the current demonstrated performance metrics of iEPS on a 12U CubeSat bus while the second case considered expected near-term increases in iEPS performance metrics on a 6U CubeSat bus. A high-level overview of the main subsystems of the CubeSat design options is presented, with a particular focus on the propulsion, power, attitude control, and communication systems, as they are the primary drivers for enabling the stage-based iEPS CubeSat architecture.

The Dawn spacecraft conducted two extended missions at Ceres following the completion of the primary mission in June 2016. The final orbit of the second extended mission was designed to have a 35-km periapsis altitude for 10x higher-resolution science. The mission ended in this orbit when the spacecraft ran out of attitude control propellant. In this paper, we describe the final orbit and discuss the challenges of flying this low at Ceres. We also include our stability analysis showing the spacecraft will remain in orbit for more than 20 years, as stipulated by the planetary protection requirements.

On Oct. 31st, 2018, the Dawn spacecraft completed its space journey covering more than 11 years including exploration of Vesta and Ceres, two protoplanets in the main asteroid belt. After successfully completing its prime mission at the dwarf planet Ceres, the Dawn mission was extended twice to pursue new scientific objectives. The second extended mission at Ceres, and the final mission for Dawn, presented a series of challenges that were new to the experienced and accomplished Dawn navigation team. This paper discusses mission design and navigational experiences and challenges during Dawn’s final transfer and orbit at Ceres. Topics include reference orbit design of the final science orbit, mission design and planning for the transfer, periapsis targeting over a surface feature, and analysis for planetary protection requirements.

In this paper we describe a prototype low-thrust optimization software being developed at JPL. The software tool is based on a collocation algorithm where a trajectory discretization is fitted and adjusted until the underlying dynamics equations of motion are satisfied. The resulting large scale non-linear programming problem may either be optimized with IPOPT or KNITRO. The user specifies path constraints, boundary constraints, and objectives. We describe the collocation algorithm as well as mesh refinement strategies, and apply the software tool to solve various example problems.

We present and discuss trajectory characteristics of low-thrust spacecraft thrusting along the instantaneous velocity vector toward escape. The behavior of the osculating eccentricity is examined, in which eccentricity decreases to a minimum before quickly increasing toward escape (e = 1). We find that the argument of periapsis replaces true anomaly as the fast time variable, and the spacecraft escapes near an osculating true anomaly of 90 degrees. This behavior was observed by the authors while designing thrusting maneuvers for the Dawn spacecraft. In this paper the dynamical theory governing these observations is discussed and explored with numerical simulations.

Wide-ranging transfer capabilities are necessary to support the development of cislunar space. But, low-thrust transfers between stable periodic orbits are challenging in this regime. Transfer design between such orbits cannot leverage the unstable manifold structures typically employed. Thus, a methodology for constructing these transfers, based on collocation, is demonstrated. Initial guesses comprised of coast arcs along periodic orbits as well as intermediate trajectory arcs from other periodic orbits are converged into feasible transfers and then refined using continuation and optimization strategies. This process applies to various spacecraft configurations and results are validated in a higher-fidelity model. Practical examples demonstrate collocation as a robust approach for computing low-thrust transfers.

Dawn is NASA's ninth Discovery class mission. The Dawn spacecraft was designed to orbit both the giant asteroid Vesta and the dwarf planet Ceres in succession, a mission only made possible by the high efficiency of ion propulsion. While the same spacecraft visited both bodies, the mission planning and maneuver execution at the two bodies were necessarily very different. The mission at Vesta benefited from at least three functioningreaction control wheels. At Ceres, all maneuvering and coasting during transfers was done without reaction wheel control due to the loss of the second of four wheels while departing Vesta. Loss of the second wheel made conserving attitude control propellant (hydrazine) critical to achieving mission success at Ceres. To save hydrazine, avoiding unnecessary coasting and attitude turns became essential during the interplanetary cruise to Ceres and for all transfers once at Ceres. In contrast, operations at Vesta did not need to avoid coasting. Operating at Ceres requires being farther from the Sun. Greaterheliocentric distances (approaching 3 AU (Astronomical Units) make Dawn's attitude control constraints while maneuvering more restrictive as a result of reduced control authority.

On October 23, 2015, the Dawn spacecraft left the High Altitude Mapping Orbit (HAMO) around Ceres and began its final decent to the Low Altitude Mapping Orbit (LAMO), arriving on December 15. The transfer between the two science orbits, a tight spiraling trajectory with over 100 revolutions, required the operations team to perform weekly maneuver designs for a period of 50 days. While the first six weeks of the transfer executed as planned, unexpectedly the spacecraft incurred a multi-sigma delivery error to the final science orbit that was subsequently clean-up at the first orbit maintenance maneuver. In this paper we discuss the design architecture for the transfer in detail, including challenges the team faced in flying the transfer and lessons learned.

The Dawn spacecraft arrived at the dwarf planet Ceres in early 2015 after a two and a half-year cruise in deep space after departing Vesta. The nominal plan for Dawn included successively lower science orbits, the last of which is called the Low Altitude Mapping Orbit that also serves as the disposal orbit after the end of mission. Prior to Dawn’s arrival at Ceres, it was identified that Dawn would have to meet planetary protection requirements at Ceres by remaining on a stable orbit for 20 years past the end of the mission. With little a priori knowledge on Ceres’ interior we analyzed what gravitational perturbations influence the long-term dynamical evolution of Dawn around Ceres and validated that the gravitational model of Ceres with the then-current best estimate of the density distribution model does not exceed the permissible bounds. The forward modeling of gravity fields from various shape models and density distribution was deemed valid to satisfy the planetary protection guidelines. This analysis was further confirmed after a new shape model based on the actual optical images was created. The gravity field as measured in the High Altitude Mapping Orbit also fits within the bounds of gravitational field studied pre-arrival at Ceres to substantiate our methodology used to satisfy the planetary protection requirement.

In mid-2014 the Dawn team finalized preparations for the spacecraft’s approach to Ceres. The design was the product of careful planning that began several years in advance, when the spacecraft left Vesta in September 2012. However, a few months prior to the anticipated start of approach, the spacecraft entered a safe mode. While temporary loss of thrust for ion propulsion missions is usually not mission-critical, it still presents many challenges. The safing event occurred at a time when thrusting to match Ceres’ orbital velocity was most effective, which meant the spacecraft must fly past Ceres before capturing into orbit. The new approach geometry changed the team’s strategy for navigating the spacecraft safely into orbit around Ceres with optical data. In this paper we describe the challenges of navigating the Dawn spacecraft into orbit around Ceres, including the safing event and re-design of the approach architecture.

Tisserand-leveraging transfers (TILTs) are introduced as a new method for computing low-Delta v orbit transfers with the help of third-body perturbations. The TILTs can mitigate the costs and risk of planetary missions by reducing the orbit insertion maneuver requirements while maintaining short flight times. TILTs connect two flybys at the minor body with an impulsive maneuver at an apse. Using the circular, restricted three-body problem, TILTs extend the concept of v-infinity leveraging beyond the patched-conics domain. In this paper, a new method is presented to compute TILTs and to patch them together to design low-energy transfers. The presented solutions have transfer times similar to the high-energy solutions, yet the Delta v cost is significantly reduced. For this reason, TILTs are used in the reference endgame of ESA's new mission option to Ganymede, JUICE, which is also presented here. JUICE's low-energy endgame halves the cost of similar high-energy endgames, which makes TILTs a mission-enabling technology for JUICE. The "lunar resonances" of SMART-1 are also explained in terms of low-thrust TILTs, suggesting future application of TILTs and low-thrust TILTs to design missions to the Moon and to other small-body destinations.

The Global Trajectory Optimization Competition was initiated in 2005 by the Advanced Concepts Team of the European Space Agency. The Outer Planets Mission Analysis Group of the Jet Propulsion Laboratory, winner of GTOC1, organized the following edition in 2006. All the following editions were organized by the winners of the previous competition edition: the Aerospace Propulsion Group of the Dipartimento di Energetica of the Politecnico di Torino, then the Interplanetary Mission Analysis team of the Centre National d’Etudes Spatieles de Toulouse. Finally, the team of Faculty of Mechanics andMathematics of Lomonosov Moscow State University, winner of the GTOC4, was very pleased to organize the fifth edition of the GTOC. In these notes we describe the problem we chose to release and some of the work done to verify the results returned by the various teams.

Quasi-terminator orbits are introduced as a class of quasi-periodic trajectories in the solar radiation pressure (SRP) perturbed Hill dynamics. These orbits offer significant displacements along the Sun-direction without the need for station-keeping maneuvers. Thus, quasi-terminator orbits have application to primitive-body mapping missions, where a variety of observation geometries relative to the Sun (or other directions) can be achieved. This paper describes the characteristics of these orbits as a function of normalized SRP strength and invariant torus frequencies and presents a discussion of mission design considerations for a global surface mapping orbit design.

Quasi-terminator orbits are a class of quasi-periodic orbits around a primitive body that exist in the vicinity of the well-known terminator orbits. The inherent stability of quasi-terminator trajectories and their wide variety of viewing geometries make them a very compelling option for primitive body mapping missions. In this paper, we discuss orbit design methodologies for selection of an appropriate quasi-terminator orbit that would meet the needs of a specific mission. Convergence of these orbits in an eccentric, higher-fidelity model is also discussed with an example case at Bennu, the target of the upcoming NASA's OSIRIS-REx mission.

Several broad search strategies were considered. These were coupled with three guiding philosophies. First, the one relied on most heavily, was the creation of ‘long-chain backbones,’ that is, long sequences of asteroid rendezvous by one probe. The Mothership and other probe trajectories were then built up, in that order, based on the long-chain backbone. The second and lesser used approach was to design first Mothership trajectories, a ‘Mothership backbone,’ wherein the mother would drop-off probes at a series of asteroids, followed by probe trajectories starting at these asteroids and returning to the mother at a final asteroid. The third philosophy was that all of these chains would be initially designed assuming the Mothership would rendezvous with asteroids for probe pick-up and drop-off. Once good candidates were found, this assumption was lifted and separation and rejoining of mother and probes was permitted to occur away from asteroids in order to boost the mass performance and the asteroid count. Various approaches were taken in building the long-chain backbones and the Mothership backbones. The most promising that we found was based on combinatorial analyses of Lambert solutions, dubbed ‘STAR’ by the developer of the method at JPL. In the STAR approach, a grid is made for the times at the various bodies, and all Lambert solutions are computed between the bodies, subject to v∞ and flight-time constraints. Then the Lambert fits are combined to form an end-to-end impulsive trajectory. At each combinatorial step, the combinations are iteratively pruned by a variety of criteria, such as ∆V , flight time, and asteroids visited, to avoid an explosion in the number of combinations that must be carried forward. The promising chains were then passed to a local optimiser for propellant mass optimisation. Another approach was to build up chains, one asteroid at a time, pruning and adjusting weighting factors as the chain grew, but with attention to retaining diversity. Candidate asteroids to be added were selected based on Lambert-arc ∆V and on the phase-free proximity quotients Q and he. The candidates would then be passed to the local optimiser, whereafter a screened subset of the converged solutions would be retained for the next step. This approach was slower and less effective than the STAR approach, probably due to the relatively high thrust level which allowed short transfer arcs to arise and be reasonably well modelled by Lambert arcs. Ant colony optimisation, particle swarm optimisation, and genetic algorithms were also used for chainbuilding. These methods also used Lambert-arc ∆V and Q and he to find long chains. The methods sought chains of a fixed length, iteratively selecting, retaining, and recombining sub-chains as the ‘free variables’ or ‘particles’. The better chains were again passed to a local optimiser. Close approaches were also studied as a possible filter for finding chains of asteroids. A database of close approaches for all asteroids over the entire date window was created and studied for chains of close approaches. Similarly, some thought was given to identifying time-varying regions of high asteroid density. Clustering techniques based on Q and he were also studied to identify sub-groups of asteroids that might

We present the methods and results of the Jet Propulsion Laboratory team in the 5 Global Trajectory Optimization Competition. Our broad-search strategy utilized several recently developed phase-free metrics for rapidly narrowing the search options. Two different, adaptive, branch-and-prune strategies were employed to build up asteroid sequences using a rendezvousflyby-rendezvous building block, with a robust local optimizer in the loop. The best of these sequences were refined end-to-end using the same direct optimizer, to yield the winning 18-point, 18-asteroid solution.

Quasi-terminator orbits are introduced as a class of quasi-periodic trajectories in the solar radiation pressure (SRP) perturbed Hill dynamics. These orbits offer significant displacements along the Sun-direction without the need for station-keeping maneuvers. Thus, quasi-terminator orbits have application to primitive-body missions, where a variety of observation geometries relative to the Sun (or other directions) can be achieved. This paper describes the characteristics of these orbits as a function of normalized SRP strength and invariant torus frequency ratio and presents a discussion of mission design considerations for a global surface mapping orbit design.

Global mapping campaigns are part of most primitive body exploration missions. However, designing a mapping orbit without station keeping maneuvers is challenging due to the highly perturbed environment near small bodies. In this paper, we present a new design methodology to support mapping campaigns using 'quasi-terminator' orbits, a class of quasi-periodic orbits that exist in the vicinity of the well-known terminator orbits. The inherent stability of quasi-terminator trajectories and their wide variety of viewing geometries make them a very compelling option for mapping campaigns. A high-fidelity test case solution is also presented to prove the existence of these mapping orbits in full ephemeris.