A comprehensive astrodynamic exposition and classification of earth-moon transits
Three-body problem for development of geometrical and topological taxonomy of earth-moon transits
EARTH-MOON TRAJECTORY↗
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Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane
This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).
TRAJECTORY MEASURING SYSTEM↗
Lowest super 1 S and super 3 P scattering resonances in the e-H system.
Position and width of lowest elastic scattering resonances in three-body atomic system, showing resonance shape dependence upon observation angle and angular resolution
RESONANCE SCATTERING↗
Trilogy, A Planetary Geodesy Mission Concept for Measuring the Expansion of the Solar System
The scale of the solar system is slowly changing, likely increasing as a result of solar mass loss, with additional change possible if there is a secular variation of the gravitational constant, G. The measurement of the change of scale could provide insight into the past and the future of the solar system, and in addition a better understanding of planetary motion and fundamental physics. Estimates for the expansion of the scale of the solar system are of order 1.5 cm year(exp -1) AU(exp -1), which over several years is an observable quantity with present-day laser ranging systems. This estimate suggests that laser measurements between planets could provide an accurate estimate of the solar system expansion rate. We examine distance measurements between three bodies in the inner solar system -- Earth's Moon, Mars and Venus -- and outline a mission concept for making the measurements. The concept involves placing spacecraft that carry laser ranging transponders in orbit around each body and measuring the distances between the three spacecraft over a period of several years. The analysis of these range measurements would allow the co-estimation of the spacecraft orbit, planetary ephemerides, other geophysical parameters related to the constitution and dynamics of the central bodies, and key geodetic parameters related to the solar system expansion, the Sun, and theoretical physics.
David E Smith↗
A trajectory generation and system characterization model for cislunar low-thrust spacecraft. Volume 2: Technical manual
The documentation of the Trajectory Generation and System Characterization Model for the Cislunar Low-Thrust Spacecraft is presented in Technical and User's Manuals. The system characteristics and trajectories of low thrust nuclear electric propulsion spacecraft can be generated through the use of multiple system technology models coupled with a high fidelity trajectory generation routine. The Earth to Moon trajectories utilize near Earth orbital plane alignment, midcourse control dependent upon the spacecraft's Jacobian constant, and capture to target orbit utilizing velocity matching algorithms. The trajectory generation is performed in a perturbed two-body equinoctial formulation and the restricted three-body formulation. A single control is determined by the user for the interactive midcourse portion of the trajectory. The full spacecraft system characteristics and trajectory are provided as output.
Korsmeyer, David J.↗
Abort Trajectory Design Strategies for the Artemis Missions
NASA's Artemis campaign plans to send astronauts to the lunar surface for the first time since 1972. The campaign relies on the Orion crew capsule to ferry the crew from Earth to an L2 9:2 lunar synodic resonant Near-Rectlinear Halo Orbit (NRHO) before descent to the lunar surface. This investigation examines a process to construct various abort families during transit from Earth to the NRHO using the Earth-Moon Circular Restricted Three-Body Problem (CR3BP). The initial trajectories are constructed using the CR3BP and categorized in families. A process is then summarized to transcribe and converge trajectories from the CR3BP into a higher-fidelity model. Ultimately, an effective methodology to develop, classify and converge these aborts in higher-fidelity is critical to the Artemis program in the event of an anomaly during the crew transit.
Trajectory Design↗
Dynamic Optimization of Multi-Spacecraft Relative Navigation Configurations in the Earth-Moon System
In this paper, the notion of relative navigation introduced by Hill, Lo and Born is analyzed for a large class of periodic orbits in the Earth-Moon three-body problem, due to its potential in supporting Moon exploration efforts. In particular, a navigation metric is introduced and used as a cost function to optimize over a class of periodic orbits. While the problem could be solve locally as an optimal control problem, a dynamical based approach that allows for a global/systematic view of the problem is proposed. First, the simpler problem of multiple spacecraft placement on a given periodic orbit is solved before the notion of continuation and bifurcation analysis is used to expand the range of solutions thus obtained.
Three Body Problem↗
Simulation studies for surfaces and materials strength
From intermolecular force studies, it is now known that the overall non-additive contribution to the lattice enegy is positive so that analysis based on only pairwise additivity suggests a shallower intermolecular potential than the true value. Two body contributions alone are also known to be categorically unable to even qualitatively describe some configurations of molecular clusters in the gas phase or the general relaxation and reconstruction of fcc crystal surfaces. In addition, the many-body contribution was shown to play a key role in the stability of certain crystal structures. In these recent analyses, a relatively simple potential energy function (PEF), comprising only a two-body Mie-type potential plus a three-body Axilrod-Teller-type potential, was found to be extremely effective. This same parametric PEF is applied to describe the bulk stability and surface energy for the diamond cubic structure. To test the stability condition, the FCC, BCC, diamond cubic, graphite and beta-tin structures were considered.
Halicioglu, T.↗
Ab initio Quantum Chemical Studies of Reactions in Astrophysical Ices. Reactions Involving CH3OH, CO2, CO, HNCO in H2CO/NH3/H2O Ices
While reactions between closed shell molecules generally involve prohibitive barriers in the gas phase, prior experimental and theoretical studies have demonstrated that some of these reactions are significantly enhanced when confined within an icy grain mantle and can occur efficiently at temperatures below 100 K with no additional energy processing. The archetypal case is the reaction of formaldehyde (H2CO) and ammonia (NH3) to yield hydroxymethylamine (NH2CH2OH). In the present work we have characterized reactions involving methanol (CH3OH), carbon dioxide (CO2), carbon monoxide (CO), and isocyanic acid (HNCO) in search of other favorable cases. Most of the emphasis is on CH3OH, which was investigated in the two-body reaction with one H2CO and the three-body reaction with two H2CO molecules. The addition of a second H2CO to the product of the reaction between CH3OH and H2CO was also considered as an alternative route to longer polyoxymethylene polymers of the -CH2O- form. The reaction between HNCO and NH3 was studied to determine if it can compete against the barrierless charge transfer process that yields OCN(-) and NH4(+). Finally, the H2CO + NH3 reaction was revisited with additional benchmark calculations that confirm that little or no barrier is present when it occurs in ice.
Woon, David E.↗
Separable expansion for off-shell two-body t matrix with Coulomb potential.
Separable expansion for off shell two body t matrix with Coulomb potential to solve nonrelativistic three body problem with two body interactions
Chen, J. C. Y.↗
Direct Multiple Shooting Optimization with Variable Problem Parameters
Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.
Whitley, Ryan J.↗
Computation on collisionless steady-state plasma flow past a charged disk
A computer method is presented using the 'inside-out' approach, for predicting the structure of the disturbed zone near a moving body in space. The approach uses fewer simplifying assumptions than other available methods, and is applicable to large ranges of the values of body and plasma parameters. Two major advances concerning 3-dimensional bodies are that thermal motions of ions as well as of electrons are treated realistically by following their trajectories in the electric field, and the technique for achieving self-consistency is promising for very large bodies. Three sample solutions were obtained for a disk-shaped body, charged negatively to a potential 4kT/e. With ion Mach number 4, and equal ion and electron temperatures, the wakes of a relatively small body (radius 5 Debye lengths) and a relatively large body (radius 100 Debye lengths) both begin to fill up between 2 and 3 body radii downstream. For the large body there is in addition a potential well (about 6kT/e deep) behind the body. Increasing the ion Mach number to 8 for the large body causes the potential well to become wider and longer but not deeper. For the large body, the quasineutrality assumption is validated outside of a cone-shaped region in the very near wake. For the large as well as the small body, the disturbed zone behind the body extends transversely no more than 2 or 3 body radii, a result of significance for the design of spacecraft boom instrumentation.
Parker, L. W.↗
Outcomes of planetary close encounters - A systematic comparison of methodologies
Several methods for estimating the outcomes of close planetary encounters are compared on the basis of the numerical integration of a range of encounter types. An attempt is made to lay the foundation for the development of predictive rules concerning the encounter outcomes applicable to the refinement of the statistical mechanics that apply to planet-formation and similar problems concerning planetary swarms. Attention is given to Oepik's (1976) formulation of the two-body approximation, whose predicted motion differs from the correct three-body behavior.
Greenberg, Richard↗
Research in the Restricted Problems of Three and Four Bodies Final Scientific Report
Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.
Richards, Paul B.↗
Lunar transfer trajectory design and the four body problem
This paper presents a review of lunar transfer trajectories that go beyond three-body theory and the Jacobi integral.
lunar↗
The Galilean satellite geological mapping program, 1986
The Galilean Satellite Geological Mapping Program was established to illuminate detailed geologic relations on the four large satellites of Jupiter. The program involves some 40 investigators from various universities, research institutes, and government offices in the United States, U.K., West Germany, and Italy. A total of 24 researchers was assigned to map 15 quadrangles on Ganymede, 15 to map 6 quadrangles on Io, and 3 to map 2 quadrangles on Europa. Maps of these three bodies are at a scale of 1:5 M except for three on Io that cover selected areas where high-resolution pictures permit compilation at 1:2 and 1:1 M scales. A 1:15,000,000 scale map of Callisto has been assigned; from it, quadrangles containing useful geologic information will be extracted later for mapping at a scale of 1:5,000,000.
Lucchitta, B. K.↗
Hypersonic shock wave interaction and impingement
An experimental investigation was conducted on space shuttle type, body-wing configurations. The purpose of the investigation was to determine the effects of body and wing geometry on the hypersonic shock structure about these vehicles and on the resulting surface impingement of interior flow field shock and expansion waves. Schlieren photographs and thermographic phosphor paint data were obtained on three body cross sections with three wing planforms at 40, 50 and 60 degree angles of attack. Specific configuration data were obtained at 0 and 30 degree angles of attack to develop trends. These data were obtained at a nominal Mach number of 13.5 and a freestream unit Reynolds number of 0.7 million per foot. For comparison with these straight wing configurations, data were also obtained on a model of a point design, high cross-range, delta wing orbiter at 40, 50 and 60 degree angles of attack. As expected, the data on this delta wing orbiter indicated that the shock intersection/impingement phenomena associated with straight wing vehicles are considerably more complex than, and result in both windward and leeward surface heating regions not present on, the delta configuration.
Kessler, W. C.↗
Global stability and the restricted 3-body problem.
Global stability regions are found for class i orbits of the circular restricted three-body problem for primary masses equal and Jacobi constant K greater than 15.5. It is found that, this constant decreases, the stability region shrinks extremely rapidly.
Mullins, L. D.↗