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NASA NTRS1995

Sun-Earth Libration Point Trajectory Analysis

Due to the constant observation environment and low energy access of Sun-Earth libration point orbits, they have become extremely popular for many NASA science missions. The nonlinearity and instability of the orbits have made mission analysis more difficult as traditional approximations are no longer applicable. But the sensitivity of the orbits also provides greater flexibility in orbit design. Some typical mission trajectories are examined.

Sun-Earth Libration↗
NASA NTRSDate not supplied

Low SWaP Onboard Satellite Navigation, Guidance, and Control Technology

Onboard autonomy is a necessity for responsive space operations. Autonomous navigation, guidance, and control (NGC) enables space missions to reduce their dependence on high demand ground assets and costly ground personnel. It also allows for in-situ decision making and higher return on mission data. A flight software and hardware system providing this capability, called “autoNGC,” is currently being developed at NASA Goddard Space Flight Center for infusion into multiple future missions. The first build of autoNGC, providing autonomous navigation for lunar orbiting spacecraft, is targeted for completion by Fall 2024. It provides sensor fusion of multiple measurement types including pseudo-range from a weak signal Global Navigation Satellite Service (GNSS) receiver, 1-way and 2-way direct to Earth (DTE) range and Doppler, bearing and range from optical camera sensed images, and an accelerometer. AutoNGC is also being targeted for future missions that involve small body proximity operations, Sun Earth Libration point orbits, and distributed systems missions (DSMs) including those at outer planets. AutoNGC flight software is being built upon the plug-and-play architecture of the core Flight System (cFS) [Ref. 1]. Figure (Slide 7) shows the message-based software bus layout of various software applications (“apps”) consisting of the standard cFS apps and autoNGC interface apps and libraries. Accurate onboard navigation and timing is obtained through the Goddard Enhanced Onboard Navigation System (GEONS) software library [Ref. 2], which fuses different measurement types through an extended Kalman filter (EKF) framework. Optical measurements that are ingested in GEONS are provided by the cFS Goddard Image Analysis and Navigation Tool (cGIANT) app [Ref. 3]. This app processes optical images to extract the bearing angles of the centroid of the imaged body (near or far), the range to the imaged body, and/or of the features on the surface of a body to perform terrain relative navigation (TRN). Measurement of range to the body’s center of mass can also be derived from the detection of the limb. The first build of autoNGC for a lunar orbiting spacecraft is a minimal size, weight, and power (SWaP) hardware design allowing for inclusion into CubeSats and SmallSat-size class buses. Advancements in miniaturized space processors, such as the SpaceCube 3.0 Mini and the SpaceCube Mini-Z [Ref. 4] are utilized for low SWaP while maintaining a high level of performance. Figure (Slide 11) shows the composition of the first autoNGC build. The current enclosure design has dimensions 12 cm x 17 cm x 13.5 cm. The box mass is expected to be less than 2 kg, and the nominal power is 21 W. The hardware interfaces are designed for flexibility with a variety of sensor inputs. The achievable navigation performance depends on the sensors utilized, including the onboard clock for 1-way pseudo-range measurements. Analysis using a configuration that consists of weak signal GPS, TRN, and 1-way DTE has shown position and velocity accuracies of 10 meters and 2 cm/s (3-σ ) RSS, respectively, with onboard time knowledge estimated to better than 13 ns (3-σ ), for a spacecraft in a representative 12-hour eccentric lunar orbit. Other measurement types such as x-rays from known pulsars (called XNAV) and cross-links can also be processed in GEONS. With the plug-and-play architecture of autoNGC, cFS apps can easily be added and replaced, even after launch. Goddard is actively seeking partners to collaborate in the development of additional capabilities for autoNGC, including industry, academia, and others across the US Government. Plans are being formulated to make the autoNGC software platform available for use by any US government organization to leverage the non-recurring engineering associated with the development of onboard autonomous NGC 3 capabilities. As advancements in space qualified sensors, microprocessors, and algorithms are made, the autoNGC platform provides a ready starting point for inclusion of these technologies.

C. J. Gramling↗
NASA NTRS2018

Mission analysis for the EM-1 CubeSats EQUULEUS and OMOTENASHI

EQUULEUS is a Lunar L2 orbiter and a 6-Unit CubeSat by JAXA and the University of Tokyo. OMOTENASHI is a 6-Unit CubeSat by JAXA, the world’s smallest Lunar lander. EQUULEUS and OMOTENASHI are among the 13 secondary payloads selected by NASA to be launched with Exploration Mission-1 in 2019. Despite their limited size and cost, EQUULEUS and OMOTENASHI are challenging missions, especially in terms of trajectory design and control. EQUULEUS exploits the Earth-Sun-Moon chaotic dynamics and enter a libration point orbit around the L2 of the Earth-Moon system, using a new water propulsion system with low thrust and little propellant. This “Orbit Control Experiment” is one of the main objectives of the mission. OMOTENASHI executes a semi-hard landing that requires breaking the spacecraft to a stop just a few-hundred meters above the Moon’s surface. Both missions present new and unique challenges, where the design of the nominal trajectory is mainly driven by the constrains on orbital control capabilities, and operational and robustness considerations. This paper presents the current baselines, and give an overview of the new techniques developed for their design.

Oshima, Kenta↗
NASA NTRS2010

Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS

In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.

Folta, D. C.↗
NASA NTRS1980

Utilization of multi-body trajectories in the Sun-Earth-Moon system

An overview of three uncommon trajectory concepts for space missions in the Sun-Earth-Moon System is presented. One concept uses a special class of libration-point orbits called 'halo orbits.' It is shown that members of this orbit family are advantageous for monitoring the solar wind input to the Earth's magnetosphere, and could also be used to establish a continuous communications link between the Earth and the far side of the Moon. The second concept employs pretzel-like trajectories to explore the Earth's geomagnetic tail. These trajectories are formed by using the Moon to carry out a prescribed sequence of gravity-assist maneuvers. Finally, there is the 'boomerang' trajectory technique for multiple-encounter missions to comets and asteroids. In this plan, Earth-swingby maneuvers are used to retarget the original spacecraft trajectory. The boomerang method could be used to produce a triple-encounter sequence which includes flybys of comets Halley and Tempel-2 as well as the asteroid Geographos.

Farquhar, R. W.↗
NASA NTRS1986

Solar wind parameters and magnetospheric coupling studies

This paper presents distributions, means, and standard deviations of the fluxes of solar wind protons, momentum, and energy as observed near earth during the solar quiet and active years 1976 and 1979. Distributions of ratios of energies (Alfven Mach number, plasma beta) and distributions of interplanetary magnetic field orientations are also given. Finally, the uncertainties associated with the use of the libration point orbiting ISEE-3 spacecraft as a solar wind monitor are discussed.

King, Joseph H.↗
NASA NTRS1998

Trajectory design strategies that incorporate invariant manifolds and swingby

Libration point orbits serve as excellent platforms for scientific investigations involving the Sun as well as planetary environments. Trajectory design in support of such missions is increasingly challenging as more complex missions are envisioned in the next few decades. Software tools for trajectory design in this regime must be further developed to incorporate better understanding of the solution space and, thus, improve the efficiency and expand the capabilities of current approaches. Only recently applied to trajectory design, dynamical systems theory now offers new insights into the natural dynamics associated with the multi-body problem. The goal of this effort is the blending of analysis from dynamical systems theory with the well established NASA Goddard software program SWINGBY to enhance and expand the capabilities for mission design. Basic knowledge concerning the solution space is improved as well.

Guzman, J. J.↗
NASA NTRS2002

Relative Navigation of Formation Flying Satellites

The Guidance, Navigation, and Control Center (GNCC) at Goddard Space Flight Center (GSFC) has successfully developed high-accuracy autonomous satellite navigation systems using the National Aeronautics and Space Administration's (NASA's) space and ground communications systems and the Global Positioning System (GPS). In addition, an autonomous navigation system that uses celestial object sensor measurements is currently under development and has been successfully tested using real Sun and Earth horizon measurements.The GNCC has developed advanced spacecraft systems that provide autonomous navigation and control of formation flyers in near-Earth, high-Earth, and libration point orbits. To support this effort, the GNCC is assessing the relative navigation accuracy achievable for proposed formations using GPS, intersatellite crosslink, ground-to-satellite Doppler, and celestial object sensor measurements. This paper evaluates the performance of these relative navigation approaches for three proposed missions with two or more vehicles maintaining relatively tight formations. High-fidelity simulations were performed to quantify the absolute and relative navigation accuracy as a function of navigation algorithm and measurement type. Realistically-simulated measurements were processed using the extended Kalman filter implemented in the GPS Enhanced Inboard Navigation System (GEONS) flight software developed by GSFC GNCC. Solutions obtained by simultaneously estimating all satellites in the formation were compared with the results obtained using a simpler approach based on differencing independently estimated state vectors.

Long, Anne↗
NASA NTRS2004

Autonomous NanoTechnology Swarm (ANTS) Prospecting Asteroid Mission (PAM), Asteroid Proximity Operations

The Autonomous NanoTechnology Swarm (ANTS) is a generic mission architecture based on spatially distributed spacecraft, autonomous and redundant components, and hierarchical organization. The ANTS Prospecting Asteroid Mission (PAM) is an ANTS application which will nominally use a swarm of 1000 spacecraft. There would be 10 types of "specialists" with common spacecraft buses. There would be 10 subswarms of approximately 100 spacecraft each or approximately 10 of each specialist in each swarm. The ANTS PAM primary objective is the exploration of the asteroid belt in search of resources and material with astrobiologically relevant origins and signatures. The ANTS PAM spacecraft will nominally be released from a station in an Earth-Moon L1 libration point orbit, and they will use Solar sails for propulsion. The sail structure would be highly flexible, capable of changing morphology to change cross-section for capture of sunlight or to form effective "tip vanes" for attitude control. ANTS PAM sails would be capable of full to partial deployment, to change effective sail area and center of pressure, and thus allow attitude control. Results of analysis of a transfer trajectory from Earth to a sample target asteroid will be presented. ANTS PAM will require continuous coverage of different asteroid locations as close as one to two asteroid "diameters" from the surface of the asteroid for periods of science data collection during asteroid proximity operations. Hovering spacecraft could meet the science data collection objectives. The results of hovering analysis will be presented. There are locations for which hovering is not possible, for example on the illuminated side of the asteroid. For cases where hovering is not possible, the results of utilizing asteroid formations to orbit the asteroid and achieve the desired asteroid viewing will be presented for sample asteroids. The ability of ANTS PAM to reduce the area of the solar sail during asteroid proximity operations is critical to the maintenance of orbiting formations for a period of time. Results of analysis of potential "traffic" problems during asteroid proximity operations will be presented.

Marr, Greg↗
NASA NTRS2001

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

three body problem↗
NASA NTRS1997

Trajectory Design Using a Dynamical Systems Approach With Application to Genesis

A number of missions have recently been proposed that aim to take advantage of the growing scientific interest in the region of space near libration points in the Sun-Earth system. In support of missions that include increasingly complex trajectories and incorporate libration point orbits, more efficient techniques and new philosophies for design must be considered.

Genesis↗
NASA NTRS2011

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗
NASA NTRS2005

Investigations of Spacecraft Orbits Around the L(2) Sun-Earth Libration Point

Space agencies are planning missions to the vicinity of the Sun-Earth L sub 2 point, some involving a distributed system of telescope spacecraft, configured in a plane about a hub. An improved understanding is developed of their relative motion. First, the telescope equations of motion are written relative to L sub 2 in the context of the classical circular restricted three-body problem, and expanded in terms of the distance from L sub 2. A basic examination is presented of the spacecraft configuration requirements and effects of small orbit insertion errors. Next, the telescope equations of motion relative to the hub are written and further expanded in terms of the hub-L sub 2 and hub-telescope distances. An analytical solution is developed and a halo telescope orbit investigated, with appropriate initial conditions. Then, the force model is extended to include perturbations to an accuracy of 10 to 20 m, east as additive contributions to the circular restricted problem. Perturbations include Earth's orbital eccentricity, lunar motion, solar radiation pressure, and small thrusting forces. Simulations are presented, along with solution sensitivity to errors in hub position knowledge.

RELATIVE MOTION↗
NASA NTRS1983

Accelerometer-enhanced orbit control near the sun-earth L1 libration point

Because the halo-orbit about the sun-earth L(1) libration point in which the satellite ISEE-3 was maintained for nearly four years is unstable, a loose control scheme about a precomputed nominal path was implemented which required orbit maneuvers approximately every three months. Execution errors were minimized by processing on-board accelerometer telemetry data in real time, and adjusting the maneuvers. Because spacecraft vibrations caused oscillations in the accelerometer data, smoothing techniques were applied to provide accurate estimates of the performance of pulse mode thrusters employed in the spin stabilization of the spacecraft. It has been found that the processed accelerometer data has an average error of only + or - 1.3 per cent.

Muhonen, D. P.↗
NASA NTRS1996

LIbration Point Trajectory Design

Orbits about the Sun-Earth L1 and L2 libration points hve become very popular for space physics and astrophysics missions.

trajectory design mathematical methods libration l↗
NASA NTRS1993

An approach for finding long period elliptical orbits for precursor SEI missions

Precursors for Solar System Exploration Initiative (SEI) missions may require long period elliptical orbits about a planet. These orbits will typically have periods on the order of tens to hundreds of days. Some potential uses for these orbits may include the following: studying the effects of galactic cosmic radiation, parking orbits for engineering and operational test of systems, and ferrying orbits between libration points and low altitude orbits. This report presents an approach that can be used to find these orbits. The approach consists of three major steps. First, it uses a restricted three-body targeting algorithm to determine the initial conditions which satisfy certain desired final conditions in a system of two massive primaries. Then the initial conditions are transformed to an inertial coordinate system for use by a special perturbation method. Finally, using the special perturbation method, other perturbations (e.g., sun third body and solar radiation pressure) can be easily incorporated to determine their effects on the nominal trajectory. An algorithm potentially suitable for on-board guidance will also be discussed. This algorithm uses an analytic method relying on Chebyshev polynomials to compute the desired position and velocity of the satellite as a function of time. Together with navigation updates, this algorithm can be implemented to predict the size and timing for AV corrections.

Fraietta, Michael F.↗
NASA NTRS2003

Orbit Determination (OD) Error Analysis Results for the Triana Sun-Earth L1 Libration Point Mission and for the Fourier Kelvin Stellar Interferometer (FKSI) Sun-Earth L2 Libration Point Mission Concept

The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.

Marr, Greg C.↗
NASA NTRS2007

Analysis of Capture Trajectories to the Vicinity of Libration Points

Spacecraft capture trajectories to the periodic orbits of the L1 and L2 points in the restricted Hill three-body problem are studied. The specific focus is on transfer to these vicinities from interplanetary trajectories. This application is motivated by future proposals to place "Deep Space ports" at the Earth and Mars L1 or L2 points. These spaceports are considered as candidate gateways for interplanetary transfers in the future. We utilize stable manifolds for capture trajectories to periodic orbits around the libration points. As a result, the cost of capture into a periodic orbit is also reduced relative to direct capture into a parabolic orbit. The way of linking between interplanetary transfer trajectories and the stable manifold is also discussed.

Nakamiya, M.↗