A General Approach to the Geostationary Transfer Orbit Mission Recovery

This paper discusses recovery scenarios for geosynchronous satellites injected in a non-nominal orbit due to a launcher underperformance. The theory on minimum-fuel orbital transfers is applied to develop an operational tool capable to design a recovery mission. To obtain promising initial guesses for the recovery three complementary techniques are used: p-optimized impulse function contouring, a numerical impulse function minimization and the solutions to the switching equations. The tool evaluates the feasibility of a recovery with the on-board propellant of the spacecraft and performs the complete mission design. This design takes into account for various mission operational constraints such as e.g., the requirement of multiple finite-duration burns, third-body orbital perturbations, spacecraft attitude constraints and ground station visibility. In a final case study, we analyze the consequences of a premature breakdown of an upper rocket stage engine during injection on a geostationary transfer orbit, as well as the possible recovery solution with the satellite on-board propellant

Braid Entropy of Two-Dimensional Turbulence

The evolving shape of material fluid lines in a flow underlies the quantitative prediction of the dissipation and material transport in many industrial and natural processes. However, collecting quantitative data on this dynamics remains an experimental challenge in particular in turbulent flows. Indeed the deformation of a fluid line, induced by its successive stretching and folding, can be difficult to determine because such description ultimately relies on often inaccessible multi-particle information. Here we report laboratory measurements in two-dimensional turbulence that offer an alternative topological viewpoint on this issue. This approach characterizes the dynamics of a braid of Lagrangian trajectories through a global measure of their entanglement. The topological length of material fluid lines can be derived from these braids. This length is found to grow exponentially with time, giving access to the braid topological entropy . The entropy increases as the square root of the turbulent kinetic energy and is directly related to the single-particle dispersion coefficient. At long times, the probability distribution of is positively skewed and shows strong exponential tails. Our results suggest that may serve as a measure of the irreversibility of turbulence based on minimal principles and sparse Lagrangian data

LightForce Photon-Pressure Collision Avoidance: Efficiency Assessment on an Entire Catalogue of Space Debris

The potential to perturb debris orbits using photon pressure from ground-based lasers has been confirmed by independent research teams. Two useful applications of this scheme are protecting space assets from impacts with debris and stabilizing the orbital debris environment, both relying on collision avoidance rather than de-orbiting debris. This paper presents the results of a new assessment method to analyze the efficiency of the concept for collision avoidance. Earlier research concluded that one ground based system consisting of a 10 kW class laser, directed by a 1.5 m telescope with adaptive optics, can prevent a significant fraction of debris-debris collisions in low Earth orbit. That research used in-track displacement to measure efficiency and restricted itself to an analysis of a limited number of objects. As orbit prediction error is dependent on debris object properties, a static displacement threshold should be complemented with another measure to assess the efficiency of the scheme. In this paper we present the results of an approach using probability of collision. Using a least-squares fitting method, we improve the quality of the original TLE catalogue in terms of state and co-state accuracy. We then calculate collision probabilities for all the objects in the catalogue. The conjunctions with the highest risk of collision are then engaged by a simulated network of laser ground stations. After those engagements, the perturbed orbits are used to re-assess the collision probability in a 20 minute window around the original conjunction. We then use different criteria to evaluate the utility of the laser-based collision avoidance scheme and assess the number of base-line ground stations needed to mitigate a significant number of high probability conjunctions. Finally, we also give an account how a laser ground station can be used for both orbit deflection and debris tracking

Mars Sample Return Using Commercial Capabilities: ERV Trajectory and Capture Requirements

Mars Sample Return was presented as the highest priority planetary science mission of the next decade [1]. Lemke et al. [2] present a Mars Sample Return mission concept in which the sample is returned directly from the surface of Mars to an Earth orbit. The sample is recovered in Earth Orbit instead of being transferred between spacecraft in Mars Orbit. This paper provides the details of this sample recovery in Earth orbit and presents as such a sub-element of the overall Mars sample return concept given in [2]. We start from the assumption that a Mars Ascent Vehicle (MAV), initially landed on Mars using a modified SpaceX Dragon capsule, has successfully delivered the sample, already contained within an Earth Return Vehicle (ERV), to a parking orbit around Mars. From the parking orbit, the ERV imparts sufficient Delta-V to inject itself into an earthbound trajectory and to be captured into an Earth orbit eventually. We take into account launch window and Delta-V considerations as well as the additional constraint of increased safety margins imposed by planetary protection regulations. We focus on how to overcome two distinct challenges of the sample return that are driven by the issues of planetary protection: (1) the design of an ERV trajectory meeting all the requirements including the need to avoid contamination of Earth's atmosphere; (2) the concept of operations for retrieving the Martian samples in Earth orbit in a safe way. We present an approach to retrieve the samples through a rendezvous between the ERV and a second SpaceX Dragon capsule. The ERV executes a trajectory that brings it from low Mars orbit (LMO) to a Moon-trailing Earth orbit at high inclination with respect to the Earth-Moon plane. After a first burn at Trans-Earth Injection (TEI), the trajectory uses a second burn at perigee during an Earth flyby maneuver to capture the ERV in Earth orbit. The ERV then uses a non-propulsive Moon flyby to come to a near-circular Moon-trailing orbit. To perform the Earth Orbit Rendezvous (EOR), a second Dragon capsule is then launched from Earth and a similar lunar flyby is performed to rendezvous with the ERV. The requirements for rendezvous, close proximity operations and capture of the sample canister are described. A concept of operations for sample retrieval is presented along with design specifications of the ERV, the required modifications to the Dragon capsule, as well as the hardware, software, sensors, actuators, and capture mechanisms used. In our concept, a container is mounted to the front hatch of Dragon, capable of accommodating the sample canister and sealing it from the rest of the capsule. The sample canister is captured using a robotic arm with a magnetic grappling mechanism. Dragon then performs a propulsive maneuver to return to Earth for a controlled re-entry while the ERV (sans sample container) is left in the Moon trailing orbit. Contingency cases and related mitigation strategies are also discussed, including the advantages and disadvantages of performing the ERV rendezvous with a crew

Mars Sample Return Using Commercial Capabilities: Mission Architecture Overview

Mars Sample Return (MSR) is the highest priority science mission for the next decade as recommended by the recent Decadal Survey of Planetary Science. This paper presents an overview of a feasibility study for an MSR mission. The objective of the study was to determine whether emerging commercial capabilities can be used to reduce the number of mission systems and launches required to return the samples, with the goal of reducing mission cost. We report the feasibility of a complete and closed MSR mission design using the following scenario that covers three synodic launch opportunities, beginning with the 2022 opportunity: A Falcon Heavy injects a SpaceX Red Dragon capsule and trunk onto a Trans Mars Injection (TMI) trajectory. The capsule is modified to carry all the hardware needed to return samples collected on Mars including a Mars Ascent Vehicle (MAV), an Earth Return Vehicle (ERV), and hardware to transfer a sample collected in a previously landed rover mission to the ERV. The Red Dragon descends to land on the surface of Mars using Super Sonic Retro Propulsion (SSRP). After previously collected samples are transferred to the ERV, the single-stage MAV launches the ERV from the surface of Mars. The MAV uses a storable liquid bi-propellant propulsion system to deliver the ERV to a Mars phasing orbit. After a brief phasing period, the ERV, which also uses a storable bi-propellant system, performs a Trans Earth Injection (TEI) burn. Upon arrival at Earth, the ERV performs Earth and lunar swing-bys and is placed into a lunar trailing circular orbit - an Earth orbit, at lunar distance. A later mission, using Dragon and launched by a Falcon Heavy, performs a rendezvous with the ERV in the lunar trailing orbit, retrieves the sample container and breaks the chain of contact with Mars by transferring the sample into a sterile and secure container. With the sample contained, the retrieving spacecraft makes a controlled Earth re-entry preventing any unintended release of pristine martian materials into the Earth's biosphere. The analysis methods employed standard and specialized aerospace engineering tools. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships (MERs). The architecture was iterated until overall mission convergence was achieved on at least one path. Subsystems analyzed in this study include support structures, power system, nose fairing, thermal insulation, actuation devices, MAV exhaust venting, and GN&C. Best practice application of loads, mass growth contingencies, and resource margins were used. For Falcon Heavy capabilities and Dragon subsystems we utilized publically available data from SpaceX, published analyses from other sources, as well as our own engineering and aerodynamic estimates. Earth Launch mass is under 11 mt, which is within the estimated capability of a Falcon Heavy, with margin. Total entry masses between 7 and 10 mt were considered with closure occurring between 9 and 10 mt. Propellant mass fractions for each major phase of the EDL - Entry, Terminal Descent, and Hazard Avoidance - have been derived. An assessment of the effect of the entry conditions on the thermal protection system (TPS), currently in use for Dragon missions, shows no significant stressors. A useful payload mass of 2.0 mt is provided and includes mass growth allowances for the MAV, the ERV, and mission unique equipment. We also report options for the MAV and ERV, including propulsion systems, crewed versus robotic retrieval mission, as well as direct Earth entry. International planetary protection policies as well as verifiable means of compliance will have a large impact on any MSR mission design. We identify areas within our architecture where such impacts occur. We also describe preliminary compliance measures that will be the subject of future work. This work shows that emerging commercial capabilities as well as new methodologies can be used to efficiently support an important planetary science objective. The work also has applications for human exploration missions that use propulsive EDL technique

Trajectory Design from GTO to Near-Equatorial Lunar Orbit for the Dark Ages Radio Explorer (DARE) Spacecraft

The trajectory design for the Dark Ages Radio Explorer (DARE) mission concept involves dropping the DARE spacecraft off in a generalized geosynchronous transfer orbit (GTO) as a secondary payload. From GTO, the spacecraft is then required to enter a near-equatorial lunar orbit that is stable (i.e., no station-keeping maneuvers are required) and yields the required number of cumulative hours (1,000) for science measurements while in the lunar farside radio quiet cone over a span of three years. Preliminary and expected results of the corresponding trajectory design are presented herein

LightForce Photon-Pressure Collision Avoidance: Updated Efficiency Analysis Utilizing a Highly Parallel Simulation Approach

This paper provides an updated efficiency analysis of the LightForce space debris collision avoidance scheme. LightForce aims to prevent collisions on warning by utilizing photon pressure from ground based, commercial off the shelf lasers. Past research has shown that a few ground-based systems consisting of 10 kilowatt class lasers directed by 1.5 meter telescopes with adaptive optics could lower the expected number of collisions in Low Earth Orbit (LEO) by an order of magnitude. Our simulation approach utilizes the entire Two Line Element (TLE) catalogue in LEO for a given day as initial input. Least-squares fitting of a TLE time series is used for an improved orbit estimate. We then calculate the probability of collision for all LEO objects in the catalogue for a time step of the simulation. The conjunctions that exceed a threshold probability of collision are then engaged by a simulated network of laser ground stations. After those engagements, the perturbed orbits are used to re-assess the probability of collision and evaluate the efficiency of the system. This paper describes new simulations with three updated aspects: 1) By utilizing a highly parallel simulation approach employing hundreds of processors, we have extended our analysis to a much broader dataset. The simulation time is extended to one year. 2) We analyze not only the efficiency of LightForce on conjunctions that naturally occur, but also take into account conjunctions caused by orbit perturbations due to LightForce engagements. 3) We use a new simulation approach that is regularly updating the LightForce engagement strategy, as it would be during actual operations. In this paper we present our simulation approach to parallelize the efficiency analysis, its computational performance and the resulting expected efficiency of the LightForce collision avoidance system. Results indicate that utilizing a network of four LightForce stations with 20 kilowatt lasers, 85% of all conjunctions with a probability of collision Pc > 10 (sup -6) can be mitigated

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table

Trajectory Design from GTO to Near-Equatorial Lunar Orbit for the Dark Ages Radio Explorer (DARE) Spacecraft

The trajectory design for the Dark Ages Radio Explorer (DARE) mission concept involves launching the DARE spacecraft into a geosynchronous transfer orbit (GTO) as a secondary payload. From GTO, the spacecraft then transfers to a lunar orbit that is stable (i.e., no station-keeping maneuvers are required with minimum perilune altitude always above 40 km) and allows for more than 1,000 cumulative hours for science measurements in the radio-quiet region located on the lunar farside