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Near-Earth objects can be grouped into multiple orbit classifications, among them being the Aten group, whose members have orbits crossing Earth's with semi-major axes less than 1 astronomical unit. Atens comprise well under 10% of known near-Earth objects. This is in dramatic contrast to results from recent human space flight near-Earth object accessibility studies, where the most favorable known destinations are typically almost 50% Atens. Geocentric dynamics explain this enhanced Aten accessibility and lead to an understanding of where the most accessible near-Earth objects reside. Without a comprehensive space-based survey, however, highly accessible Atens will remain largely unknown.

Near-Earth Asteroids (NEAs) have been identified by the Administration as potential destinations for human explorers during the mid-2020s. Planning such ambitious missions requires selecting potentially accessible targets from the growing known population of 8,008 NEAs. NASA is therefore conducting the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Targets Study (NHATS), in which the trajectory opportunities to all known NEAs are being systematically evaluated with respect to a set of defined constraints. While the NHATS algorithms have identified hundreds of NEAs which satisfy purposely inclusive trajectory constraints, only a handful of them offer truly attractive mission opportunities in the time frame of greatest interest. In this paper we will describe the structure of the NHATS algorithms and the constraints utilized in the study, present current study results, and discuss various mission design considerations for future human space flight missions to NEAs.

In the context of human space flight (HSF), the concept of near-Earth object (NEO) accessibility is highly subjective. Whether or not a particular NEO is accessible critically depends on mass, performance, and reliability of interplanetary HSF systems yet to be designed. Such systems would certainly include propulsion and crew life support with adequate shielding from both solar flares and galactic cosmic radiation. Equally critical architecture options are relevant to NEO accessibility. These options are also far from being determined and include the number of launches supporting an HSF mission, together with whether or not consumables are to be pre-emplaced at the destination. Until the unknowns of HSF to NEOs come into clearer focus, the notion of relative accessibility is of great utility. Imagine a group of NEOs, each with nearly equal HSF merit determined from their individual characteristics relating to crew safety, scientific return, resource utilization, and planetary defense. The more accessible members of this group are more likely to be explored first. A highly accessible NEO could conceivably be deferred in favor of a less accessible HSF destination because the latter is more accessible during a programmatically desirable launch compliant mission trajectory solutions detected in association with a specific NEO. The known NEO population is then surveyed to illustrate in which regions of heliocentric semi-major axis, eccentricity, and inclination (a, e, i) space NEOs with large n values are mapped. The (a, e, i) mapping is also formatted such that membership in each of four NEO orbit classifications, as defined below, is evident. Amors have orbits everywhere superior to (outside of) Earth's. An Amor is therefore defined to have perihelion between 1.017 astronomical units (AU) and the maximum NEO value of 1.3 AU. As of 0 hrs Universal Time on 1 January 2011 (UT epoch 2011.0), Amors numbered 2855 in the Jet Propulsion Laboratory (JPL) Small-Body Database (SBDB), comprising 37.7% of known NEOs. Apollos have orbits crossing Earth's with periods greater than Earth's. An Apollo is therefore defined to have perihelion less than 1.017 AU and a greater than 1.0 AU. As of 2011.0 UT, Apollos numbered 4080 in the SBDB, comprising 53.9% of known NEOs. Atens have orbits crossing Earth's with periods less than Earth's. An Aten is therefore defined to have aphelion greater than 0.983 AU and a less than 1.0 AU. As of 2011.0 UT, Atens numbered 618 in the SBDB, comprising 8.2% of known NEOs. Atiras have orbits everywhere inferior to (inside of) Earth's. An Atira is therefore defined to have aphelion less than 0.983 AU. As of 2011.0 UT, Atiras numbered 11 in the SBDB, comprising 0.1% of known NEOs. It is no surprise that the largest n values are chiefly associated with Apollos and Atens. Because these orbits cross Earth's, distance to be covered in a given round trip mission time delta-t can be far less than is possible for Amors or Atiras . This delta-t or the sum of mission propulsive impulse magnitudes delta-v can more frequently be minimized to enhance NHATS compliance for Apollos and Atens than is generally the case for Amors and Atiras. A less intuitive trend in NHATS results is that Atens nearly outnumber the more numerous Apollos among the most compliant NEOs as measured by n. This trend is completely out of proportion to the degree Atens are represented among the known NEO population. A theory based on geocentric NEO dynamics is presented by this paper to explain why Atens enjoy inherently greater accessibility than do Apollos. Another trend evident from mapping into (a, e, i) space is the dearth of known NEOs at low e when a < 1 AU. Underrepresentation of Atens and Atiras in the NEO catalog is at least in part attributable to observing exclusively from a perspective near Earth. Generally inferior Aten and Atira orbits are rarely, if ever, in Earth's night sky. Until a comprehensive NEO survey is conducted from an appropriateegion remote from Earth, the theory developed in this paper indicates a substantial fraction of the most accessible NEOs will remain unknown. season. Such a season is really yet another undetermined HSF architecture option. A launch season's duration will likely be measured in weeks, and it will be utilized at an indeterminate point almost certainly more than a decade in the future when HSF programmatic maturity is sufficient. Furthermore, current knowledge of the NEO population relevant to HSF is far from complete. In the 100-m-diameter class of greatest interest, only a few percent of the estimated NEO population is known [2, Figure 2.4]. Therefore, any known, lost, or fictitious NEO in a highly accessible orbit is a potential HSF destination of merit. Even if lost, fictitious, small, or hazardous, such a potential target (or another in a similar orbit) may ultimately prove to be an early HSF destination when the pertinent NEO population is more thoroughly catalogued and NEO orbits are more thoroughly maintained at high accuracy. This paper first reviews methodology and pertinent results from NASA-sponsored research performed in late 2010 and dubbed NEO HSF Accessible Targets Study (NHATS, pronounced as "gnats"). A useful accessibility metric developed during this study is n, the tally of NHATS

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

A combination of methods is proposed of predicting spacecraft trajectories that possibly include multiple maneuvers and/or perturbing accelerations, with greater speed, accuracy, and repeatability than were heretofore achievable. The combination is denoted the WeavEncke method because it is based on unpublished studies by Jonathan Weaver of the orbit-prediction formulation of the noted astronomer Johann Franz Encke. Weaver evaluated a number of alternatives that arise within that formulation, arriving at an orbit-predicting algorithm optimized for complex trajectory operations. In the WeavEncke method, Encke's method of prediction of perturbed orbits is enhanced by application of modern numerical methods. Among these methods are efficient Kepler s-equation time-of-flight solutions and self-starting numerical integration with time as the independent variable. Self-starting numerical integration satisfies the requirements for accuracy, reproducibility, and efficiency (and, hence, speed). Self-starting numerical integration also supports fully analytic regulation of integration step sizes, thereby further increasing speed while maintaining accuracy.

Near-Earth Asteroids (NEAs) have been identified by the current administration as potential destinations for human explorers during the mid-2020s. While the close proximity of these objects' orbits to Earth's orbit creates a risk of highly damaging or catastrophic impacts, it also makes some of these objects particularly accessible to spacecraft departing Earth, and this presents unique opportunities for solar system science and humanity's first ventures beyond cislunar space. Planning such ambitious missions first requires the selection of potentially accessible targets from the growing population of nearly 7,800 NEAs. To accomplish this, NASA is conducting the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Targets Study (NHATS). Phase I of the NHATS was executed during September of 2010, and Phase II was completed by early March of 2011. The study is ongoing because previously undetected NEAs are being discovered constantly, which has motivated an effort to automate the analysis algorithms in order to provide continuous monitoring of NEA accessibility. The NHATS analysis process consists of a trajectory filter and a minimum maximum estimated size criterion. The trajectory filter employs the method of embedded trajectory grids to compute all possible ballistic round-trip mission trajectories to every NEA in the Jet Propulsion Laboratory (JPL) Small-Body Database (SBDB) and stores all solutions that satisfy the trajectory filter criteria. An NEA must offer at least one qualifying trajectory solution to pass the trajectory filter. The Phase II NHATS filter criteria were purposely chosen to be highly inclusive, requiring Earth departure date between January 1st, 2015 and December 31st, 2040, total round-trip flight time <= 450 days, stay time at the NEA >= 8 days, Earth departure C(sub 3) energy <= 60 km(exp 2)/s(exp 2), total mission delta-v <= 12 km/s (including an Earth departure maneuver from a 400 km altitude circular parking orbit), and a maximum atmospheric re-entry speed of 12 km/s. After determining which NEAs offer at least one trajectory solution meeting the criteria, the estimated size constraint is then imposed whereby those NEAs may only be considered NHATS- qualifying NEAs if their maximum estimated size is >= 30 m. This corresponds to an absolute magnitude H <= 26.5 with an assumed albedo p = 0:05. The following is a brief high-level summary of the Phase II study results. Of the 7,665 NEAs in the SBDB as of February 3rd, 2011, 765 NEAs passed the trajectory filter and yielded a total of 79,157,604 trajectory solutions. The trajectory solutions for each NEA are post-processed into Pork Chop Contour (PCC) plots which show total mission delta-v as a function of Earth departure date and total mission duration. Although the PCC plots necessarily compress a very multi-dimensional design space into a two-dimensional plot, they permit rapid assessment of the breadth and quality of an NEA's available Earth departure season and clearly indicate the regions of the trajectory design space which warrant further analysis and optimization. The PCC plot for the NEA with the greatest number of NHATS-qualifying trajectory solutions, 2000 SG-344, is shown. Of the 765 NEAs which passed the Phase II trajectory filter, a total of 590 NEAs also satisfied the further constraint of maximum estimated size >= 30 m. The distributions of osculating heliocentric orbital semi-major axis (a), eccentricity (e), and inclination (i), for those 590 NEAs are shown. Note that the semi-latus rectum used is equal to alpha (1-e(exp 2)). To further our understanding of round-trip trajectory accessibility dynamics, it is instructive to examine the distribution of the NHATS-Qualifying NEAs according to orbit classification. NEAs are grouped into four orbit families: Atiras (aphelion < 0.983 AU), Atens (aphelion > 0.983 AU, alpha < 1.0 AU), Apollos (perihelion < 1.017 AU, alpha > 1.0 AU), and Amors (1.017 < perihelion < 1.3 AU). Of the 765 NEAhich satisfied the NHATS trajectory criteria, none are Atiras, 193 are Atens (31% of known Atens), 456 are Apollos (11% of known Apollos), and 116 are Amors (4% of known Amors). While Apollos comprise 60% of the NEAs which pass the NHATS trajectory filter and Atens comprise only 25%, the percentages according to orbit family are perhaps more relevant. Note that only 11% of known Apollos passed the trajectory filter while 31% of known Atens passed. These simple statistics alone strongly suggest that Aten orbits possess features which tend to enhance their round-trip trajectory accessibility as compared to Apollos or Amors. This is significant because Atens' orbits cause them to spend considerable time in Earth's daytime sky, making them difficult to discover and track using ground-based observing assets. In this paper we will detail the NHATS analysis algorithms, present and analyze all NHATS results to date, and discuss aspects of HSF mission architecture design for future NEA missions.

Measurement of the jettisoned object departure trajectory and velocity vector in the International Space Station (ISS) reference frame is vitally important for prompt evaluation of the object s imminent orbit. We report on the first successful application of photogrammetric analysis of the ISS imagery for the prompt computation of the jettisoned object s position and velocity vectors. As post-EVA analyses examples, we present the Floating Potential Probe (FPP) and the Russian "Orlan" Space Suit jettisons, as well as the near-real-time (provided in several hours after the separation) computations of the Video Stanchion Support Assembly Flight Support Assembly (VSSA-FSA) and Early Ammonia Servicer (EAS) jettisons during the US astronauts space-walk. Standard close-range photogrammetry analysis was used during this EVA to analyze two on-board camera image sequences down-linked from the ISS. In this approach the ISS camera orientations were computed from known coordinates of several reference points on the ISS hardware. Then the position of the jettisoned object for each time-frame was computed from its image in each frame of the video-clips. In another, "quick-look" approach used in near-real time, orientation of the cameras was computed from their position (from the ISS CAD model) and operational data (pan and tilt) then location of the jettisoned object was calculated only for several frames of the two synchronized movies. Keywords: Photogrammetry, International Space Station, jettisons, image analysis.