Multi-Mission Earth Entry Vehicle Design Trade Space and Concept Development Strategy

This presentation was part of the session : Sample Return ChallengesSixth International Planetary Probe WorkshopIn recent years the sample return mission concept has gradually grown increased favor over in-situ missions. The successes of the Stardust and Genesis missions have clearly highlighted the advantages of bringing samples back to Earth where they can be studied in much greater detail by more powerful instruments, examined by a much wider scientific community, and preserved over an extended period of time. With growing interest in the Moon, asteroids, comets, and particularly Mars, more and more sample return missions are sure to find their way into the space exploration roadmap. This paper will outline an approach to be taken to develop a flexible Earth Entry Vehicle (EEV) design concept which can be utilized by multiple sample return missions. The multi-mission EEV concept will be based on the Mars Sample Return (MSR) EEV design which is driven by minimizing risk associated with sample containment. However, not all sample return missions will need to meet the rigorous planatery protection requirements of MSR. The goal of this study will be to provide a foundation by which individual missions can build upon to optimize an EEV design which meets their specific needs while preserving as many common elements as possible. This multi-mission EEV concept could then provide a platform by which technologies, design elements, processes, etc., can be developed and even flight tested prior to implemention on MSR. This approach could not only significantly reduce the risk and associated cost in development of the MSR EEV, but also by leveraging common design elements, all sample return missions will benefit.NAS

Regular del Pezzo surfaces with irregularity

We construct the first examples of regular del Pezzo surfaces for which the irregularity (i.e. the dimension of the first cohomology group of the structure sheaf) is nonzero. We also find a restriction on the integer pairs that are possible as the anti-canonical degree and irregularity of such a surface.Comment: 23 pages, 1 figure (on page 2

Law in numbers: the poiesis of the crowd

Having written on protest and its variant forms for some years now, whether in squats or on the streets, through law or otherwise1, it has become more and more apparent how the right to dissent is altering, with the definite feel there are diminishing spaces in which to resist

Extension of the proximity-quotient control law for low-thrust propulsion

In this paper, the proximity quotient control law, first developed by Petropoulos, is extended to account for both third body effects and solar radiation pressure based on the mission requirements for a hypothetical NEO deflection mission to the asteroid Apophis using a solar sublimation deflection technique. The perturbing effect of solar radiation pressure becomes relevant when dealing with large optics in space. Equations for the disturbing acceleration are derived for the perturbations, then analytically incorporated into the equations determining the rate-of-change in time of the orbital elements, and tested using a Earth-asteroid transfer. Another specific variant of the control law is developed for the orbital maintenance of the spacecraft formation in the vicinity of the NEO

Extension of the proximity-quotient control law for low-thrust propulsion

In this paper, the proximity quotient control law, first developed by Petropoulos, is extended to account for both third body effects and solar radiation pressure. The perturbing effect of solar radiation pressure becomes relevant when dealing with solar sails, or large optics in space. Equations for the disturbing acceleration and disturbing potential function were derived for the perturbations, then analyzed to determine the minimum and maximum rate of changes of the Keplerian elements given the thrust vector and true anomaly of the spacecraft. These were then analytically incorporated into the Q-law feedback function. The complete mathematical derivations are presented. The extended Q-law is compared to the fully optimal control law, stemming from optimal control theory, for the same dynamical model. Two missions are used as test cases

Ray casting implicit fractal surfaces with reduced affine arithmetic

A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store

Optimal design for a NEO tracking spacecraft formation

The following paper presents the design and methodology for developing an optimal set of spacecraft orbits for a NEO tracking mission. The spacecraft is designed to fly in close formation with the asteroid, avoiding the nonlinear gravity field produced by the asteroid. A periodic orbit is developed, and the initial conditions are optimized by use of a global optimizer for constrained nonlinear problems. The asteroid Apophis (NEO 2004 MN4) was used as the case study due the potential impact with Earth in 2036, and the need for more accurate ephemerides

Design of optimal spacecraft-asteroid formations through a hybrid global optimization approach

Purpose – The purpose of this paper is to present a methodology and experimental results on using global optimization algorithms to determine the optimal orbit, based on the mission requirements, for a set of spacecraft flying in formation with an asteroid. Design/methodology/approach – A behavioral-based hybrid global optimization approach is used to first characterize the solution space and find families of orbits that are a fixed distance away from the asteroid. The same optimization approach is then used to find the set of Pareto optimal solutions that minimize both the distance from the asteroid and the variation of the Sun-spacecraft-asteroid angle. Two sample missions to asteroids, representing constrained single and multi-objective problems, were selected to test the applicability of using an in-house hybrid stochastic-deterministic global optimization algorithm (Evolutionary Programming and Interval Computation (EPIC)) to find optimal orbits for a spacecraft flying in formation with an orbit. The Near Earth Asteroid 99942 Apophis (2004 MN4) is used as the case study due to a fly-by of Earth in 2029 leading to two potential impacts in 2036 or 2037. Two black-box optimization problems that model the orbital dynamics of the spacecraft were developed. Findings – It was found for the two missions under test, that the optimized orbits fall into various distinct families, which can be used to design multi-spacecraft missions with similar orbital characteristics. Research limitations/implications – The global optimization software, EPIC, was very effective at finding sets of orbits which met the required mission objectives and constraints for a formation of spacecraft in proximity of an asteroid. The hybridization of the stochastic search with the deterministic domain decomposition can greatly improve the intrinsic stochastic nature of the multi-agent search process without the excessive computational cost of a full grid search. The stability of the discovered families of formation orbit is subject to the gravity perturbation of the asteroid and to the solar pressure. Their control, therefore, requires further investigation. Originality/value – This paper contributes to both the field of space mission design for close-proximity orbits and to the field of global optimization. In particular, suggests a common formulation for single and multi-objective problems and a robust and effective hybrid search method based on behaviorism. This approach provides an effective way to identify families of optimal formation orbits

Topological correction of hypertextured implicit surfaces for ray casting

Hypertextures are a useful modelling tool in that they can add three-dimensional detail to the surface of otherwise smooth objects. Hypertextures can be rendered as implicit surfaces, resulting in objects with a complex but well defined boundary. However, representing a hypertexture as an implicit surface often results in many small parts being detached from the main surface, turning an object into a disconnected set. Depending on the context, this can detract from the realism in a scene where one usually does not expect a solid object to have clouds of smaller objects floating around it. We present a topology correction technique, integrated in a ray casting algorithm for hypertextured implicit surfaces, that detects and removes all the surface components that have become disconnected from the main surface. Our method works with implicit surfaces that are C2 continuous and uses Morse theory to find the critical points of the surface. The method follows the separatrix lines joining the critical points to isolate disconnected components