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All sources NASA NTRS DOE OSTI

DOE OSTI2016

Full particle orbit effects in regular and stochastic magnetic fields

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

INTERACTING BINARIES WITH ECCENTRIC ORBITS. III. ORBITAL EVOLUTION DUE TO DIRECT IMPACT AND SELF-ACCRETION

The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow is a fundamental assumption common to all binary stellar evolution and population synthesis codes, even though the validity of this assumption is questionable both theoretically and observationally. Here we calculate the evolution of the orbital elements of an eccentric binary through the direct three-body integration of a massive particle ejected through the inner Lagrangian point of the donor star at periastron. The trajectory of this particle leads to three possible outcomes: direct accretion onto the companion star within a single orbit, self-accretion back onto the donor star within a single orbit, or a quasi-periodic orbit around the companion star, possibly leading to the formation of a disk. We calculate the secular evolution of the binary orbit in the first two cases and conclude that direct impact accretion can increase as well as decrease the orbital semimajor axis and eccentricity, while self-accretion always decreases the orbital semimajor axis and eccentricity. In cases where mass overflow contributes to circularizing the orbit, circularization can set in on timescales as short as a few percent of the mass-transfer timescale. In cases where mass overflow increases the eccentricity, the orbital evolution is governed by competition between mass overflow and tidal torques. In the absence of tidal torques, mass overflow results in direct impact can lead to substantially subsynchronously rotating donor stars. Contrary to assumptions common in the literature, direct impact accretion furthermore does not always provide a strong sink of orbital angular momentum in close mass-transferring binaries; in fact, we instead find that a significant part can be returned to the orbit during the particle orbit. The formulation presented in this paper together with our previous work can be combined with stellar and binary evolution codes to generate a better picture of the evolution of eccentric, Roche lobe overflowing binary star systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Spin-orbital correlations from complex orbital order in MgV 2⁢ O 4

MgV 2 ⁢O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 ⁢O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹⁡𝑑⁢$\overline{3}$⁢𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ ⁢60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ ⁢40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2⁢ O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2⁢ O 4 displays a high-temperature orbital memory of the low-temperature spin order.

Frustrated magnetism↗

NASA NTRS2014

Three Orbital Burns to Molniya Orbit via Shuttle Centaur G Upper Stage

An unclassified analytical trajectory design, performance, and mission study was done for the 1982-86 joint NASA-USAF Shuttle/Centaur G upper stage development program to send performance-demanding payloads to high orbits such as Molniya using an unconventional orbit transfer. This optimized three orbital burn transfer to Molniya orbit was compared to the then-baselined two burn transfer. The results of the three dimensional trajectory optimization performed include powered phase steering data and coast phase orbital element data. Time derivatives of the orbital elements as functions of thrust components were evaluated and used to explain the optimization's solution. Vehicle performance as a function of parking orbit inclination was given. Performance and orbital element data was provided for launch windows as functions of launch time. Ground track data was given for all burns and coasts including variation within the launch window. It was found that a Centaur with fully loaded propellant tanks could be flown from a 37deg inclination low Earth parking orbit and achieve Molniya orbit with comparable performance to the baselined transfer which started from a 57deg inclined orbit: 9,545 lb vs. 9,552 lb of separated spacecraft weight respectively. There was a significant reduction in the need for propellant launch time reserve for a one hour window: only 78 lb for the three burn transfer vs. 320 lb for the two burn transfer. Conversely, this also meant that longer launch windows over more orbital revolutions could be done for the same amount of propellant reserve. There was no practical difference in ground tracking station or airborne assets needed to secure telemetric data, even though the geometric locations of the burns varied considerably. There was a significant adverse increase in total mission elapsed time for the three vs. two burn transfer (12 vs. 11/4 hrs), but could be accommodated by modest modifications to Centaur systems. Future applications were discussed. The three burn transfer was found to be a viable, arguably preferable, alternative to the two burn transfer.

Orbital trajectory design↗

NASA NTRS2015

Three Orbital Burns to Molniya Orbit Via Shuttle_Centaur G Upper Stage

An unclassified analytical trajectory design, performance, and mission study was done for the 1982 to 1986 joint National Aeronautics and Space Administration (NASA)-United States Air Force (USAF) Shuttle/Centaur G upper stage development program to send performance-demanding payloads to high orbits such as Molniya using an unconventional orbit transfer. This optimized three orbital burn transfer to Molniya orbit was compared to the then-baselined two burn transfer. The results of the three dimensional trajectory optimization performed include powered phase steering data and coast phase orbital element data. Time derivatives of the orbital elements as functions of thrust components were evaluated and used to explain the optimization's solution. Vehicle performance as a function of parking orbit inclination was given. Performance and orbital element data was provided for launch windows as functions of launch time. Ground track data was given for all burns and coasts including variation within the launch window. It was found that a Centaur with fully loaded propellant tanks could be flown from a 37 deg inclination low Earth parking orbit and achieve Molniya orbit with comparable performance to the baselined transfer which started from a 57 deg inclined orbit: 9,545 versus 9,552 lb of separated spacecraft weight, respectively. There was a significant reduction in the need for propellant launch time reserve for a 1 hr window: only 78 lb for the three burn transfer versus 320 lb for the two burn transfer. Conversely, this also meant that longer launch windows over more orbital revolutions could be done for the same amount of propellant reserve. There was no practical difference in ground tracking station or airborne assets needed to secure telemetric data, even though the geometric locations of the burns varied considerably. There was a significant adverse increase in total mission elapsed time for the three versus two burn transfer (12 vs. 1-1/4 hr), but could be accommodated by modest modifications to Centaur systems. Future applications were discussed. The three burn transfer was found to be a viable, arguably preferable, alternative to the two burn transfer.

Orbital trajectory design↗

DOE OSTI2025

The balance of orbital overlap and orbital energy in the activation of methane by actinide cations: insights from inductively coupled plasma tandem mass spectrometry

The actinides present a unique challenge to chemical theory. The classical view of covalent bonding is driven by the extent of spatial overlap of valence orbitals. Modern theory has expanded assessments of covalency to include considerations of orbital energy degeneracy to assess orbital energy mixing between metal and ligand valence orbitals. Actinide–ligand (An–L) bonding has more recently been described as a balance between orbital overlap and orbital energy mixing, where 5f and L valence orbital overlap decreases while energy mixing between An 5f and L valence orbitals increases across the series. To test these existing views, we employed inductively coupled plasma tandem mass spectrometry to examine the kinetic energy dependences of reactions of actinide cations, Th + –Am + , with methane. Further, this is the first experimental report of the energy dependences of methane activation reactions involving the cations of Pa, Np, Pu, and Am and the first experimental determination of transuranic An + –D, An + –CD 2 , An + –CD 3 , and An + –CD bond dissociation energies. The correlation of the measured An + –CD 2 bond energies with E p (6d 2 ) indicates that An + 6d orbitals are the dominant contributors in the An + –CD 2 bonds. Close examination of the relative reactivities of An + offers additional support that the balance of classical and modern views of molecular bonding may lie between Np + and Pu + and that the increased reactivity of Th + –Np + may be attributed to the increased spatial extension of the 5f orbitals whereas covalent An + bond formation may be more driven by the decreasing energies of the 5f orbitals across the actinide series.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2018

Drag De-Orbit Device (D3): A Retractable Device for CubeSat Attitude and Orbit Control using Aerodynamic Forces

The increasing number of CubeSats being launched has raised concerns about orbital debris since most of these satellites have no means of active orbit control. Some technologies exist to increase the surface area of a CubeSat and expedite de-orbit due to aerodynamic drag in low Earth orbit, but most of these devices cannot be retracted and hence cannot be used for orbital maneuvering. This paper discusses the De-Orbit Drag Device (D3) module that is capable of de-orbiting a 12U, 15kg CubeSat from a 700 km circular orbit in under 25 years and can be deployed and retracted to modulate the aerodynamic drag force experienced by the satellite. This facilitates orbital maneuvering using aerodynamic drag and the active targeting of a de-orbit location. In addition, the geometry of this drag device provides 3-axis attitude stabilization of the host CubeSat using aerodynamic and gravity gradient torques which is useful for many missions and provides a predictable aerodynamic profile for use in orbital maneuvering algorithms.

algorithm↗

NASA NTRS2006

Real-time Sub-cm Differential Orbit Determination of two Low-Earth Orbiters with GPS Bias Fixing

An effective technique for real-time differential orbit determination with GPS bias fixing is formulated. With this technique, only real-time GPS orbits and clocks are needed (available from the NASA Global Differential GPS System with 10-20 cm accuracy). The onboard, realtime orbital states of user satellites (few meters in accuracy) are used for orbit initialization and integration. An extended Kalman filter is constructed for the estimation of the differential orbit between the two satellites as well as a reference orbit, together with their associating dynamics parameters. Due to close proximity of the two satellites and of similar body shapes, the differential dynamics are highly common and can be tightly constrained which, in turn, strengthens the orbit estimation. Without explicit differencing of GPS data, double-differenced phase biases are formed by a transformation matrix. Integer-valued fixing of these biases are then performed which greatly strengthens the orbit estimation. A 9-day demonstration between GRACE orbits with baselines of approx.200 km indicates that approx.80% of the double-differenced phase biases can successfully be fixed and the differential orbit can be determined to approx.7 mm as compared to the results of onboard K-band ranging.

global positioning system (GPS)↗

DOE OSTI2018

Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis

It is common to introduce electron-donating or electron-withdrawing substituent groups into functional conjugated molecules (such as dyes) to tune their electronic structure properties (such as frontier orbital energy levels) and photophysical properties (such as absorption and emission wavelengths). However, there lacks a generally applicable tool that can unravel the underlying interactions between orbitals from a substrate molecule and those from its substituents in modern electronic structure calculations, despite the long history of qualitative molecular orbital theory. In this work, the absolutely localized molecular orbitals (ALMO) based analysis is extended to analyze the effects of substituent groups on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a given system. This provides a bottom-up avenue towards quantification of effects from distinct physical origins (e.g. permanent electrostatics/Pauli repulsion, mutual polarization, inter-fragment orbital mixing). For the example case of prodan (a typical dye molecule), it is found that inter-fragment orbital mixing plays a key role in narrowing the HOMO–LUMO gap of the naphthalene core. Specifically, an out-of-phase mixing of high-lying occupied orbitals on the naphthalene core and the dimethylamino group leads to an elevated HOMO, whereas an in-phase combination of LUMOs on the naphthalene core and the propionyl group lowers the LUMO energy of the entire molecule. We expect this ALMO-based analysis to bridge the gap between concepts from qualitative orbital interaction analysis and quantitative electronic structure calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2006

Calculating Statistical Orbit Distributions Using GEO Optical Observations with the Michigan Orbital Debris Survey Telescope (MODEST)

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit suitable for tracking purposes. Telescopes operating in survey mode, however, randomly observe objects that pass through their field of view. Typically, these short-arc observation are inadequate to obtain detailed orbits, but can be used to estimate approximate circular orbit elements (semimajor axis, inclination, and ascending node). From this information, it should be possible to make statistical inferences about the orbital distributions of the GEO population bright enough to be observed by the system. The Michigan Orbital Debris Survey Telescope (MODEST) has been making such statistical surveys of the GEO region for four years. During that time, the telescope has made enough observations in enough areas of the GEO belt to have had nearly complete coverage. That means that almost all objects in all possible orbits in the GEO and near- GEO region had a non-zero chance of being observed. Some regions (such as those near zero inclination) have had good coverage, while others are poorly covered. Nevertheless, it is possible to remove these statistical biases and reconstruct the orbit populations within the limits of sampling error. In this paper, these statistical techniques and assumptions are described, and the techniques are applied to the current MODEST data set to arrive at our best estimate of the GEO orbit population distribution.

Matney, M.↗

NASA NTRS2006

Comparison of Orbital Parameters for GEO Debris Predicted by LEGEND and Observed by MODEST: Can Sources of Orbital Debris be Identified?

Since 2002 the National Aeronautics and Space Administration (NASA) has carried out an optical survey of the debris environment in the geosynchronous Earth-orbit (GEO) region with the Michigan Orbital Debris Survey Telescope (MODEST) in Chile. The survey coverage has been similar for 4 of the 5 years allowing us to follow the orbital evolution of Correlated Targets (CTs), both controlled and un-controlled objects, and Un-Correlated Targets (UCTs). Under gravitational perturbations the distributions of uncontrolled objects, both CTs and UCTs, in GEO orbits will evolve in predictable patterns, particularly evident in the inclination and right ascension of the ascending node (RAAN) distributions. There are several clusters (others have used a "cloud" nomenclature) in observed distributions that show evolution from year to year in their inclination and ascending node elements. However, when MODEST is in survey mode (field-of-view approx.1.3deg) it provides only short 5-8 minute orbital arcs which can only be fit under the assumption of a circular orbit approximation (ACO) to determine the orbital parameters. These ACO elements are useful only in a statistical sense as dedicated observing runs would be required to obtain sufficient orbital coverage to determine a set of accurate orbital elements and then to follow their evolution. Identification of the source(s) for these "clusters of UCTs" would be advantageous to the overall definition of the GEO orbital debris environment. This paper will set out to determine if the ACO elements can be used to in a statistical sense to identify the source of the "clustering of UCTs" roughly centered on an inclination of 12deg and a RAAN of 345deg. The breakup of the Titan 3C-4 transtage on February 21, 1992 has been modeled using NASA s LEGEND (LEO-to-GEO Environment Debris) code to generate a GEO debris cloud. Breakup fragments are created based on the NASA Standard Breakup Model (including fragment size, area-to-mass (A/M), and delta-V distributions). Once fragments are created, they are propagated forward in time with a subroutine GEOPROP. Perturbations included in GEOPROP are those due to solar/lunar gravity, radiation pressure, and major geopotential terms. The question to be addressed: are the UCTs detected by MODEST in this inclination/RAAN region related to the Titan 3C-4 breakup? Discussion will include the observational biases in attempting to detect a specific, uncontrolled target during given observing session. These restrictions include: (1) the length of the observing session which is 8 hours or less at any given date or declination; (2) the assumption of ACO elements for detected object when the breakup model predicts debris with non-zero eccentricities; (3) the size and illumination or brightness of the debris predicted by the model and the telescope/sky limiting magnitude.

Barker, Edwin S.↗

NASA NTRS2007

A Study into the Method of Precise Orbit Determination of a HEO Orbiter by GPS and Accelerometer

In the present day, orbit determination by Global Positioning System (GPS) is not unusual. Especially for low-cost small satellites, position determination by an on-board GPS receiver provides a cheap, reliable and precise method. However, the original purpose of GPS is for ground users, so the transmissions from all of the GPS satellites are directed toward the Earth s surface. Hence there are some restrictions for users above the GPS constellation to detect those signals. On the other hand, a desire for precise orbit determination for users in orbits higher than GPS constellation exists. For example, the next Japanese Very Long Baseline Interferometry (VLBI) mission "ASTRO-G" is trying to determine its orbit in an accuracy of a few centimeters at apogee. The use of GPS is essential for such ultra accurate orbit determination. This study aims to construct a method for precise orbit determination for such high orbit users, especially in High Elliptical Orbits (HEOs). There are several approaches for this objective. In this study, a hybrid method with GPS and an accelerometer is chosen. Basically, while the position cannot be determined by an on-board GPS receiver or other Range and Range Rate (RARR) method, all we can do to estimate the user satellite s position is to propagate the orbit along with the force model, which is not perfectly correct. However if it has an accelerometer (ACC), the coefficients of the air drag and the solar radiation pressure applied to the user satellite can be updated and then the propagation along with the "updated" force model can improve the fitting accuracy of the user satellite s orbit. In this study, it is assumed to use an accelerometer available in the present market. The effects by a bias error of an accelerometer will also be discussed in this paper.

Ikenaga, Toshinori↗

NASA NTRS1961

Flight Performance Handbook for Orbital Operations: Orbital Mechanics and Astrodynamics Formulae, Theorems, Techniques, and Applications

This handbook provides parametric data useful both to the space vehicle designer and mission analyst. It provides numerical and analytical relationships between missions and gross vehicle characteristics as a function of performance parameters. The effects of missile constraints and gross guidance limitations plus operational constraints such as launch site location, tracking net location, orbit visibility and mission on trajectory and orbit design parameters are exhibited. The influence of state-of- the-art applications of solar power as compared to future applications of nuclear power on orbit design parameters, such as eclipse time, are among the parameters included in the study. The principal aim, however, is in providing the analyst with useful parametric design information to cover the general area of earth satellite missions in the region of near-earth to cislunar space and beyond and from injection to atmospheric entry and controlled descent. The chapters are organized around the central idea of orbital operations in the 1961-1969 era with emphasis on parametric flight mechanics studies for ascent phase and parking orbits, transfer maneuvers, rendezvous maneuver, operational orbit considerations, and operational orbit control. The results are based almost entirely on the principles of flight and celestial mechanics. Numerous practical examples have been worked out in detail. This is especially important where it has been difficult or impossible to represent all possible variations of the parameters. The handbook contains analytical formulae and sufficient textual material to permit their proper use. The analytic methods consist of both exact and rapid, approximate methods. Scores of tables, working graphs and illustrations amplify the mathematical models which, together with important facts and data, cover the engineering and scientific applications of orbital mechanics. Each of the five major chapters are arranged to provide a rapid review of an entire astrodynamic subject. By the use of compact graphical and tabular presentation the full scope of the material is made available in an easy-to-use style. Throughout the volume the analyst is shown, by means of suitable introductions, notes, authoritative examples, and cross-references the vital interrelation of the various orbital mechanics topics in the general field of earth satellites and satellite rendezvous. The handbook is designed to give the analyst rapid, reliable access to the mathematics of orbital mechanics needed for virtually any working requirements.

Ambrosio, Alphonso↗

NASA NTRS2014

Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis

Results from operational OD produced by the NASA Goddard Flight Dynamics Facility for the LRO nominal and extended mission are presented. During the LRO nominal mission, when LRO flew in a low circular orbit, orbit determination requirements were met nearly 100% of the time. When the extended mission began, LRO returned to a more elliptical frozen orbit where gravity and other modeling errors caused numerous violations of mission accuracy requirements. Prediction accuracy is particularly challenged during periods when LRO is in full-Sun. A series of improvements to LRO orbit determination are presented, including implementation of new lunar gravity models, improved spacecraft solar radiation pressure modeling using a dynamic multi-plate area model, a shorter orbit determination arc length, and a constrained plane method for estimation. The analysis presented in this paper shows that updated lunar gravity models improved accuracy in the frozen orbit, and a multiplate dynamic area model improves prediction accuracy during full-Sun orbit periods. Implementation of a 36-hour tracking data arc and plane constraints during edge-on orbit geometry also provide benefits. A comparison of the operational solutions to precision orbit determination solutions shows agreement on a 100- to 250-meter level in definitive accuracy.

Gravitation↗

DOE OSTI2016

Orbital-differentiated coherence-incoherence crossover identified by photoemission spectroscopy in LiFeAs

In the iron-based superconductors (FeSCs), orbital differentiation is an important phenomenon, whereby correlations stronger on the d xy orbital than on the d xz /d yz orbital yield quasi-particles with d xy orbital character having larger mass renormalization and abnormal temperature evolution. However, the physical origin of this orbital di erentiation is debated between the Hund's coupling induced unbinding of spin and orbital degrees of freedom and the Hubbard interaction instigated orbital selective Mott transition. Here we use angle-resolved photoemission spectroscopy to identify an orbital-dependent correlation-induced quasi-particle (QP) anomaly in LiFeAs. Lastly, the excellent agreement between our photoemission measurements and first-principles many-body theory calculations shows that the orbital-differentiated QP lifetime anomalies in LiFeAs are controlled by the Hund's coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Spin-Orbit Coupling Controlled J = 3 / 2 Electronic Ground State in 5 d 3 Oxides

Spin-orbit entanglement in 5d-based transition metal oxides (TMOs) has been identified as a route to a host of unconventional physical states including quantum spin liquids, Weyl semimetals, and axion insulators. Yet despite intense interest, no clear rules have emerged for the treatment of spin-orbit coupling (SOC) in 5d TMOs outside of idealised LS or jj coupling paradigms. This is exemplified in 5d 3 oxides in which an orbitally-quenched singlet ground state is anticipated, yet SOC is manifest in the observed magnetic properties. Here we solve this long-outstanding puzzle by revealing that the electronic ground state of Os5+ 5d 3 ions is an unquenched J = 3/2 state. Resonant inelastic x-ray scattering (RIXS) in Ca3LiOsO6 and Ba 2 YOsO 6 exposes a SOC-controlled splitting of the t 2g manifold. The results are successfully described using an intermediate-coupling framework in which oxygen hybridisation promotes the breakdown of the orbital singlet. This framework opens the door to realistic treatment of SOC across a range of 5d TMOs beyond the 5d 3 case.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1988

LLOFX earth orbit to lunar orbit delta V estimation program user and technical documentation

The LLOFX computer program calculates in-plane trajectories from an Earth-orbiting space station to Lunar orbit in such a way that the journey requires only two delta V burns (one to leave Earth circular orbit and one to circularize into Lunar orbit). The program requires the user to supply the Space Station altitude and Lunar orbit altitude (in km above the surface), and the desired time of flight for the transfer (in hours). It then determines and displays the trans-Lunar injection (TLI) delta V required to achieve the transfer, the Lunar orbit insertion (LOI) delta V required to circularize the orbit around the Moon, the actual time of flight, and whether the transfer orbit is elliptical or hyperbolic. Return information is also displayed. Finally, a plot of the transfer orbit is displayed.

Source record↗

NASA NTRS1992

Orbit maintenance for low altitude near-circular lunar orbits

The behavior of low altitude near-circular lunar orbits is a key design issue for some missions in the proposed Space Exploration Initiative. The lunar gravity field strongly perturbs low altitude orbits, so an effective orbit maintenance strategy is needed. This strategy must contend with the long term orbit evolution due to the zonal gravity field. Two possible orbit control scenarios are passive control using a frozen orbit and active orbit control using maneuvers. A maneuver strategy can be designed which optimizes the propellant required for long term orbit sustenance. The long term requirements dominate the total propellant required for orbit control. Additional propellant may be required to offset the impact of medium period gravity field effects. Careful selection of maneuver times and directions, however, can eliminate any medium period penalty.

Cook, Richard A.↗