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NASA NTRS2004

Libration Point Navigation Concepts Supporting Exploration Vision

Farquhar described several libration point navigation concepts that would appear to support NASA s current exploration vision. One concept is a Lunar Relay Satellite operating in the vicinity of Earth-Moon L2, providing Earth-to-lunar far-side and long- range surface-to-surface navigation and communications capability. Reference [ 1] lists several advantages of such a system in comparison to a lunar orbiting relay satellite constellation. Among these are one or two vs. many satellites for coverage, simplified acquisition and tracking due to very low relative motion, much longer contact times, and simpler antenna pointing. An obvious additional advantage of such a system is that uninterrupted links to Earth avoid performing critical maneuvers "in the blind." Another concept described is the use of Earth-Moon L1 for lunar orbit rendezvous, rather than low lunar orbit as was done for Apollo. This rendezvous technique would avoid large plane change and high fuel cost associated with high latitude landing sites and long stay times. Earth-Moon L1 also offers unconstrained launch windows from the lunar surface. Farquhar claims this technique requires only slightly higher fuel cost than low lunar orbit rendezvous for short-stay equatorial landings. Farquhar also describes an Interplanetary Transportation System that would use libration points as terminals for an interplanetary shuttle. This approach would offer increased operational flexibility in terms of launch windows, rendezvous, aborts, etc. in comparison to elliptical orbit transfers. More recently, other works including Folta[3] and Howell[4] have shown that patching together unstable trajectories departing Earth-Moon libration points with stable trajectories approaching planetary libration points may also offer lower overall fuel costs than elliptical orbit transfers. Another concept Farquhar described was a Deep Space Relay at Earth-Moon IA and/or L5 that would serve as a high data rate optical navigation and communications relay satellite. The advantages in comparison to a geosynchronous relay are minimal Earth occultation, distance from large noise sources on Earth, easier pointing due to smaller relative velocity, and a large baseline for interferometry if both L4 and L5 are used.

Carpenter, J. Russell↗

NASA NTRS2004

Formation Flying in Earth, Libration, and Distant Retrograde Orbits

This slide presentation examines the current and future state of formation flying, LEO formations, control strategies for flight in the vicinity of the libration points, and distant retrograde orbit formations. This discussion of LEO formations includes background on perturbation theory/accelerations and LEO formation flying. The discussion of strategies for formation flight in the vicinity of the libration points includes libration missions and natural and controlled libration orbit formations. A reference list is included.

Folta, David C.↗

NASA NTRS2014

Access to Mars from Earth-Moon Libration Point Orbits:

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.

Dynamical Systems↗

NASA NTRS2022

Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point Orbits

The purpose and direction of this document is to provide U.S. government agencies, specifically National Aeronautics and Space Administration (NASA) and Department of Defense (DoD) space related centers, with a foundational summary of astrodynamics concepts for trajectory design, navigation, and operations in the cislunar, lunar, and libration point regions. This document is provided in response to an Interagency Agreement (IAA) between NASA and the National Geospatial-Intelligence Agency (NGA). With applications to these regions of the Earth-Moon system, this document summarizes: the definitions of standard and unique coordinate systems for Positioning, Navigation, Timing and targeting (PNT), transformations between those coordinate frames, definitions of common time systems, a description of numerical integration, description of a widely-used and approximate dynamical model of a three-body system for preliminary analysis and nomenclature definition, description of higher-fidelity models of cislunar space, and the application of these concepts to sample scenarios with a focus on common steps in trajectory and maneuver design for a spacecraft in cislunar space. This information is critical to mission design and navigation far above the geosynchronous orbit region, where lunar perturbations are required to be modeled accurately and consistently but render trajectory design and analysis a complex procedure. Software tools such as the Goddard Space Flight Center (GSFC) open source General Mission Analysis Tool (GMAT) is used as a reference, along with a wide variety of resources constructed by NASA and other government agencies, academia, and industry, for mathematical specifications and practical considerations. This document has been prepared by and under the auspices of NASA. The GSFC Mission Engineering and Systems Analysis (MESA) Division (Code 590) and the Navigation and Mission Design Branch (Code 595) are part of NASA. Their engineers and scientists have expertise in lunar, cislunar, and libration point region trajectory guidance and navigation and timing. NASA GSFC has supported many successful lunar and cislunar missions over the past several decades. These missions include the Lunar Reconnaissance Orbiter (LRO), the two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) spacecraft, Transiting Exoplanet Survey Satellite (TESS), Lunar Prospector, Lunar Crater Observation and Sensing Satellite (LCROSS), Clementine, and several Sun-Earth libration point missions such as WIND and Deep Space Climate Observatory (DSCOVR), dating back four decades. NASA GSFC also supports the upcoming Gateway lunar mission, the Artemis Lunar Program and Human Landing Systems, and leads both the Lunar IceCube low thrust mission and concept design for the Lunar Communication Relay and Navigation System (LCRNS).

Lunar, CisLunar, Libration, trajectory dynamics, p↗

NASA NTRS1973

Resonances and librations of some Apollo and Amor asteroids with the Earth.

The orbital evolution of the Apollo asteroids 1620 Geographos and 1685 Toro and Amor asteroids 433 Eros, 1221 Amor, and 1627 Ivar are investigated by numerical integration. All these asteroids, with the exception of Geographos, exhibit systematic orbital couplings with the Earth during the time interval studied (1600-2350 A.D.). 1685 Toro is captured into libration once with Venus due to the 13.5 resonance, and once with the Earth due to the 8:5 resonance. Both librations are unstable because of the effect of the 13:8 near commensurability of the Venus-Earth system. 433 Eros exhibits no libration pattern; the regular variation of its orbital period is due to the beat-effect of the 4:7 resonance with the Earth.

Ip, W.-H.↗

NASA NTRS1973

Effects of physical librations of the moon on the orbital elements of a lunar satellite.

Physical librations of the moon are small cyclic perturbations with periods of one month and longer, and amplitudes of 100 arc seconds or less. This paper gives data on the magnitude of the physical librations, the geometrical effects on the orbital elements, and the equivalent changes in the coefficients in the gravitational potential. It is shown that geometrical effects can be accommodated either by using an inertial axes system or by compensating for the lunar librations and precession when the selenographic axes are used. Further, it is shown that physical effects are small and negligible for all but the most exacting endeavors.

Ferrari, A. J.↗

NASA NTRS1973

Lunar physical librations and laser ranging

The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured by laser ranging to the moon. Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.-

Williams, J. G.↗

NASA NTRS1983

Stochastic analysis of the control of the movement of the spacecraft in the vicinity of the colinear libration point by means of the forces of luminous pressure

This paper is dedicated to the possible investigation of the utilization of the solar radiation pressure for the spacecraft motion control in the vicinity of collinear libration point of planar restricted ring problem of three bodies. The control is realized by changing the solar sail area at its permanent orientation. In this problem the influence of the trajectory errors and the errors of the execution control is accounted. It is worked out, the estimation method of the solar sail sizes, which are necessary for spacecraft keeping in the vicinity of collinear libration point during the certain time with given probability. The main control parameters were calculated for some examples in case of libration points of the Sun-Earth and Earth-Moon systems.

Lukyanov, S. S.↗

NASA NTRS1986

On the use of a sunward libration-point-orbiting spacecraft as an interplanetary magnetic field monitor for magnetospheric studies

In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point to determine the orientation of the interplanetary magnetic field (IMF), the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting the earth, has been calculated for a data set of 1-hour periods covering four months. For each period, a 10-minute average of ISEE 1 data is compared with 10-minute averages of ISEE 3 data at successively lagged intervals. It is concluded that the IMF orientation at a libration-point-orbiting spacecraft, lagged by the time required for the solar wind to convect to the earth, is a convenient predictor of IMF orientation near the earth, to within about 20-degree accuracy.

Kelly, T. J.↗

NASA NTRS1986

Libration-point staging concepts for Earth-Mars transportation

The use of libration points as transfer nodes for an Earth-Mars transportation system is briefly described. It is assumed that a reusable Interplanetary Shuttle Vehicle (ISV) operates between the libration point and Mars orbit. Propellant for the round-trip journey to Mars and other supplies would be carried from low Earth orbit (LEO) to the ISV by additional shuttle vehicles. Different types of trajectories between LEO and libration points are presented, and approximate delta-V estimates for these transfers are given. The possible use of lunar gravity-assist maneuvers is also discussed.

Robert Farquhar↗

NASA NTRS1990

A station-keeping method for libration point trajectories

Three-dimensional orbits in the vicinity of the interior libration point of the sun-earth/moon barycenter system are currently being considered for use with a number of missions planned for the 1990s. Since such libration-point trajectories are generally unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. The primary goal of this effort is the development of a stationkeeping strategy applicable to such trajectories. A method is presented that uses maneuvers executed impulsively at discrete time intervals. The analysis includes some investigation of a number of the problem parameters that affect the overall maneuver costs. Simulations are designed to provide representative stationkeeping costs for a spacecraft moving in a libration-point trajectory, and preliminary results are summarized.

Howell, K. C.↗

NASA NTRS1999

Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits

The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimize the cost associated with insertion onto a specified libration point orbit.

Howell, K. C.↗

NASA NTRS2000

Formation Flying With Decentralized Control in Libration Point Orbits

A decentralized control framework is investigated for applicability of formation flying control in libration orbits. The decentralized approach, being non-hierarchical, processes only direct measurement data, in parallel with the other spacecraft. Control is accomplished via linearization about a reference libration orbit with standard control using a Linear Quadratic Regulator (LQR) or the GSFC control algorithm. Both are linearized about the current state estimate as with the extended Kalman filter. Based on this preliminary work, the decentralized approach appears to be feasible for upcoming libration missions using distributed spacecraft.

Folta, David↗

NASA NTRS2001

Human Exploration Missions Study: Space Surveillance Telescope Transfer to and Station at a Halo Orbit at the Earth-Sun Libration Point L2

This study was undertaken to determine mission profile and delta velocity requirements to place a telescope at the Earth-Sun libration point L2. The program, Integrated Mission Program (IMP), was selected to be used in the investigation. A description of IMP and its capabilities may be found in the Addenda. The Addenda also contains the libration halo equations, constants and other parameters. Comments regarding the chaotic nature of numerical integration near the libration points are also attached in the Addenda. A basic two stage S/C with a simple mission profile was selected. This profile is shown.

Dauro, Vincent A., Sr.↗

NASA NTRS2001

A Non-Linear Approach to Spacecraft Trajectory Control in the Vicinity of a Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, station-keeping, control algorithm for trajectories in the vicinity of a libration point. The control law guarantees exponential convergence, based on a Lyaponov analysis. Controller performance is evaluated using FreeFlyer(R) and MATLAB(R) for a spacecraft stationed near the L2 libration point in the Earth-Moon system, tracking a pre-defined reference trajectory. Evaluation metrics are fuel usage and tracking accuracy. Simulation results are compared with a linear-based controller for a spacecraft tracking the same reference trajectory. Although the analysis is framed in the context of station-keeping, the control algorithm is equally applicable to a formation flying problem with an appropriate definition of the reference trajectory.

Luquette, Richard J.↗

NASA NTRS2001

A Non-Linear Approach to Spacecraft Formation Control in the Vicinity of a Collinear Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, formation maintenance, control algorithm for trajectories in the vicinity of a libration point. However, the formulation holds for any trajectory governed by the equations of motion for the restricted three body problem. The control law guarantees exponential convergence, based on a Lyaponov analysis. FreeFlyer and MATLAB provide the simulation environment for controller performance evaluation. The simulation, modeled after the MAXIM Pathfinder mission, maintains the relative position of a "follower" spacecraft with respect to a "leader" spacecraft, stationed near the L2 libration point in the Sun-Earth system. Evaluation metrics are fuel usage and tracking accuracy.

Luquette, Richard J.↗

NASA NTRS2002

Orbit Determination Issues for Libration Point Orbits

Libration point mission designers require knowledge of orbital accuracy for a variety of analyses including station keeping control strategies, transfer trajectory design, and formation and constellation control. Past publications have detailed orbit determination (OD) results from individual libration point missions. This paper collects both published and unpublished results from four previous libration point missions (ISEE (International Sun-Earth Explorer) -3, SOHO (Solar and Heliospheric Observatory), ACE (Advanced Composition Explorer) and MAP (Microwave Anisotropy Probe)) supported by Goddard Space Flight Center's Guidance, Navigation & Control Center. The results of those missions are presented along with OD issues specific to each mission. All past missions have been limited to ground based tracking through NASA ground sites using standard range and Doppler measurement types. Advanced technology is enabling other OD options including onboard navigation using seaboard attitude sensors and the use of the Very Long Baseline Interferometry (VLBI) measurement Delta Differenced One-Way Range (DDOR). Both options potentially enable missions to reduce coherent dedicated tracking passes while maintaining orbital accuracy. With the increased projected loading of the DSN (Deep Space Network), missions must find alternatives to the standard OD scenario.

Beckman, Mark↗

NASA NTRS2003

Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission

Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.

Marr, G.↗