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NASA NTRS1989

Design of a Lunar Farside Observatory

The design of a mantendable lunar farside observatory and science base is presented. A farside observatory will allow high accuracy astronomical observations, as well as the opportunity to perform geological and low gravity studies on the Moon. The requirements of the observatory and its support facilities are determined, and a preliminary timeline for the project development is presented. The primary areas of investigation include observatory equipment, communications, habitation, and surface operations. Each area was investigated to determine the available options, and each option was evaluated to determine the advantages and disadvantages. The options selected for incorporation into the design of the farside base are presented. The observatory equipment deemed most suitable for placement on the lunar farside consist of large optical and radio arrays and seismic equipment. A communications system consisting of a temporary satellite about the L sub 2 libration point and followed by a satellite at the stable L sub 5 libration point was selected. A space station common module was found to be the most practical option for housing the astronauts at the base. Finally, a support system based upon robotic construction vehicles and the use of lunar materials was determined to be a necessary component of the base.

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NASA NTRS1989

Dynamics of Pluto

The present study of the Pluto orbit yielded by the LONGSTOP 1B, 100-Myr numerical integration of the outer planets has given attention to the 3:2 resonance in mean motion with Neptune up to degree 2 in eccentricities and inclinations. Confirmations are obtained for both the 19,900-year period longitudinal libration and the 3.78-Myr period libration of the Pluto pericenter argument. Because chaos originates with small divisors, possible resonances have been searched for among the frequencies associated with the critical arguments. The macroscopic stability of the orbit of Pluto is explainable in terms of the association of high-order resonances with small chaotic regions.

Milani, A.↗

NASA NTRS1990

Halo-orbit and lunar-swingby missions of the 1990's

A significant number of spacecraft are planning to use halo orbits and lunar-swingby trajectories in the next decade. Four spacecraft will be placed into halo orbits around the earth's sunward libration point, while two others will be stationed near the sun-earth L2 libration point in the distant geomagnetic tail. Six spacecraft, including two of the aforementioned halo orbiters, will make use of lunar-swingby maneuvers to fulfill their mission objectives. Thus, a total of ten spacecraft, five from the Soviet Union, two from Japan, two from the United States, and one from the European Space Agency, will employ halo orbits and/or lunar-swingby trajectories in the 1990's. Pertinent facts are presented for each of these missions.

Farquhar, Robert W.↗

NASA NTRS1991

Mapping the stability field of Jupiter Trojans

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme.

Levison, H. F.↗

NASA NTRS1992

Stochasticity of comet P/Slaughter-Burnham

Three comets are now known to be at or near the 1/1 resonance with Jupiter: P/Slaughter-Burnham, P/Boethin and the newly discovered P/Ge-Wang. Although details of the individual orbits differ, the three comets have very similar dynamical behavior: their orbits show many transitions between the different types of resonant motion (satellite libration, anti-satellite libration, and circulating motion). The stochastic character of such cometary orbits, mainly due to encounters with Jupiter is investigated using Lyapunov Characteristic Indicators. For each comet of the group, we study the influences on the stochasticity of initial eccentricity, inclination, longitude of node, and l-l(sub J) (mean longitude of comet minus mean longitude of Jupiter). We present here our first results for P/Slaughter-Burnham.

Benest, Daniel↗

NASA NTRS1999

Autonomous Navigation Using Celestial Objects

In the twenty-first century, National Aeronautics and Space Administration (NASA) Enterprises envision frequent low-cost missions to explore the solar system, observe the universe, and study our planet. Satellite autonomy is a key technology required to reduce satellite operating costs. The Guidance, Navigation, and Control Center (GNCC) at the Goddard Space Flight Center (GSFC) currently sponsors several initiatives associated with the development of advanced spacecraft systems to provide autonomous navigation and control. Autonomous navigation has the potential both to increase spacecraft navigation system performance and to reduce total mission cost. By eliminating the need for routine ground-based orbit determination and special tracking services, autonomous navigation can streamline spacecraft ground systems. Autonomous navigation products can be included in the science telemetry and forwarded directly to the scientific investigators. In addition, autonomous navigation products are available onboard to enable other autonomous capabilities, such as attitude control, maneuver planning and orbit control, and communications signal acquisition. Autonomous navigation is required to support advanced mission concepts such as satellite formation flying. GNCC has successfully developed high-accuracy autonomous navigation systems for near-Earth spacecraft using NASA's space and ground communications systems and the Global Positioning System (GPS). Recently, GNCC has expanded its autonomous navigation initiative to include satellite orbits that are beyond the regime in which use of GPS is possible. Currently, GNCC is assessing the feasibility of using standard spacecraft attitude sensors and communication components to provide autonomous navigation for missions including: libration point, gravity assist, high-Earth, and interplanetary orbits. The concept being evaluated uses a combination of star, Sun, and Earth sensor measurements along with forward-link Doppler measurements from the command link carrier to autonomously estimate the spacecraft's orbit and reference oscillator's frequency. To support autonomous attitude determination and control and maneuver planning and control, the orbit determination accuracy should be on the order of kilometers in position and centimeters per second in velocity. A less accurate solution (one hundred kilometers in position) could be used for acquisition purposes for command and science downloads. This paper provides performance results for both libration point orbiting and high Earth orbiting satellites as a function of sensor measurement accuracy, measurement types, measurement frequency, initial state errors, and dynamic modeling errors.

Folta, David↗

NASA NTRS2000

Jet Propulsion Laboratory

Analyses of laser ranges to the Moon are utilized for a broad range of investigations: lunar science, gravitational physics, geodesy, geodynamics and astronomy. Unique contributions from LLR include: detection of a molten lunar core; measurement of tidal dissipation in the Moon; an accurate test of the principle of equivalence for massive bodies (strong equivalence principle); and detection of lunar free librations. LLR analysis has provided tests of relativity, measurements of the Moon's tidal acceleration and the Earth s precession, and has provided orders-of-magnitude improvements in the accuracies of the lunar ephemeris and three-dimensional rotation. JPL has been active in all of these various LLR applications and supplies lunar and planetary ephemerides and lunar physical librations to the community.

Williams, Jim↗

NASA NTRS2001

Repeat-Orbit Interferometric Precision Measurement of Mercury Obliquity

Repeat-orbit or time-delayed interferometry has been widely used for SAR (Synthetic Aperture Radar)-based observations of such terrestrial phenomena as flow of glaciers and post-seismic displacements from radar on Earth-orbiting satellites and spacecraft. Repeat-orbit interferometry has also obtained fringes while investigating the measurement of topography of the Moon from Arecibo radar observations. Because of the unique spin-orbit resonance of Mercury, the locus of the sub-radar point on Mercury crosses over itself many times per year. Moreover, the locus of the sub-radar track repeats these crossings from year to year over many years. Given the proper geometry, these subradar point crossings offer the opportunity for interplanetary repeat-orbit interferometry via Earth-based radar observations. The ephemerides of Mercury and Earth, and the orientation of the Earth, are all known to sufficiently high-precision with respect to 'inertial space' to enable this kind of interferometry. This capability would merely be a curiosity, since Earth-based radar lacks the signal-to-noise to measure planetary-scale topography, except that the technique can be used to measure Mercury's obliquity (and possibly the forced libration in longitude). Combining very accurate measurements of the obliquity and the forced libration in longitude with Mercury-orbiter-based measurements of the low-order and degree Mercury gravity field can place constraints on the size and state of Mercury's fluid core. Additional information is contained in the original extended abstract.

Slade, M. A.↗

NASA NTRS2002

Applying Strategic Visualization(Registered Trademark) to Lunar and Planetary Mission Design

NASA teams, such as the NASA Exploration Team (NEXT), utilize advanced computational visualization processes to develop mission designs and architectures for lunar and planetary missions. One such process, Strategic Visualization (trademark), is a tool used extensively to help mission designers visualize various design alternatives and present them to other participants of their team. The participants, which may include NASA, industry, and the academic community, are distributed within a virtual network. Consequently, computer animation and other digital techniques provide an efficient means to communicate top-level technical information among team members. Today,Strategic Visualization(trademark) is used extensively both in the mission design process within the technical community, and to communicate the value of space exploration to the general public. Movies and digital images have been generated and shown on nationally broadcast television and the Internet, as well as in magazines and digital media. In our presentation will show excerpts of a computer-generated animation depicting the reference Earth/Moon L1 Libration Point Gateway architecture. The Gateway serves as a staging corridor for human expeditions to the lunar poles and other surface locations. Also shown are crew transfer systems and current reference lunar excursion vehicles as well as the Human and robotic construction of an inflatable telescope array for deployment to the Sun/Earth Libration Point.

Frassanito, John R.↗

NASA NTRS2002

Stationkeeping Approach for the Microwave Anisotropy Probe (MAP)

The Microwave Anisotropy Probe was successfully launched on June 30, 2001 and placed into a Lissajous orbit about the L2 Sun-Earth-Moon libration point. However, the L2 libration point is unstable which necessitates occasional stationkeeping maneuvers in order to maintain the spacecraft s Lissajous orbit. Analyses were performed in order to develop a feasible L2 stationkeeping strategy for the MAP mission. The resulting strategy meets the allotted fuel budget, allowing for enough fuel to handle additional he1 taxes, while meeting the attitude requirements for the maneuvers. Results from the first two stationkeeping maneuvers are included.

Rohrbaugh, Dave↗

NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗

NASA NTRS2005

Proof-of-Concept Trajectory Designs for a Multi-Spacecraft, Low-Thrust Heliocentric Solar Weather Buoy Mission

A new solar weather mission has been proposed, involving a dozen or more small spacecraft spaced at regular, constant intervals in a mutual heliocentric circular orbit between the orbits of Earth and Venus. These solar weather buoys (SWBs) would carry instrumentation to detect and measure the material in solar flares, solar energetic particle events, and coronal mass ejections as they flowed past the buoys, serving both as science probes and as a radiation early warning system for the Earth and interplanetary travelers to Mars. The baseline concept involves placing a mothercraft carrying the SWBs into a staging orbit at the Sun-Earth L1 libration point. The mothercraft departs the L1 orbit at the proper time to execute a trailing-edge lunar flyby near New Moon, injecting it into a heliocentric orbit with its perihelion interior to Earth s orbit. An alternative approach would involve the use of a Double Lunar Swingby (DLS) orbit, rather than the L1 orbit, for staging prior to this flyby. After injection into heliocentric orbit, the mothercraft releases the SWBs-all equipped with low-thrust pulsed plasma thrusters (PPTs)-whereupon each SWB executes a multi-day low-thrust finite bum around perihelion, lowering aphelion such that each achieves an elliptical phasing orbit of different orbital period from its companions. The resulting differences in angular rates of motion cause the spacecraft to separate. While the lead SWB achieves the mission orbit following an insertion burn at its second perihelion passage, the remaining SWBs must complete several revolutions in their respective phasing orbits to establish them in the mission orbit with the desired longitudinal spacing. The complete configuration for a 14 SWB scenario using a single mothercraft is achieved in about 8 years, and the spacing remains stable for at least a further 6 years. Flight operations can be simplified, and mission risk reduced, by employing two mothercraft instead of one. In this scenario: the second mothercraft stays in a libration-point or DLS staging orbit until the first mothercraft has achieved nearly 180 separation from the Earth. The timing of the second mothercraft's subsequent lunar flyby is planned such that this spacecraft will be located 180 from the first mothercraft upon completion of its heliocentric circularization maneuvers. Both groups of satellites then only have to spread out over 180 to obtain full 360 coverage around the Sun.

Muller, Ronald↗

NASA NTRS2004

Proceedings from the 2nd International Symposium on Formation Flying Missions and Technologies

Topics discussed include: The Stellar Imager (SI) "Vision Mission"; First Formation Flying Demonstration Mission Including on Flight Nulling; Formation Flying X-ray Telescope in L2 Orbit; SPECS: The Kilometer-baseline Far-IR Interferometer in NASA's Space Science Roadmap Presentation; A Tight Formation for Along-track SAR Interferometry; Realization of the Solar Power Satellite using the Formation Flying Solar Reflector; SIMBOL-X : Formation Flying for High-Energy Astrophysics; High Precision Optical Metrology for DARWIN; Close Formation Flight of Micro-Satellites for SAR Interferometry; Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors; Closed-Loop Control of Formation Flying Satellites; Formation Control for the MAXIM Mission; Precision Formation Keeping at L2 Using the Autonomous Formation Flying Sensor; Robust Control of Multiple Spacecraft Formation Flying; Virtual Rigid Body (VRB) Satellite Formation Control: Stable Mode-Switching and Cross-Coupling; Electromagnetic Formation Flight (EMFF) System Design, Mission Capabilities, and Testbed Development; Navigation Algorithms for Formation Flying Missions; Use of Formation Flying Small Satellites Incorporating OISL's in a Tandem Cluster Mission; Semimajor Axis Estimation Strategies; Relative Attitude Determination of Earth Orbiting Formations Using GPS Receivers; Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion; Conservative Analytical Collision Probabilities for Orbital Formation Flying; Equations of Motion and Stability of Two Spacecraft in Formation at the Earth/Moon Triangular Libration Points; Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Ares; An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer; GVE-Based Dynamics and Control for Formation Flying Spacecraft; GNC System Design for a New Concept of X-Ray Distributed Telescope; GNC System for the Deployment and Fine Control of the DARWIN Free-Flying Interferometer; Formation Algorithm and Simulation Testbed; and PLATFORM: A Formation Flying, RvD and Robotic Validation Test-bench.

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NASA NTRS2006

Geodesy at Mercury with MESSENGER

In 2011 the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft will enter Mercury orbit and begin the mapping phase of the mission. As part of its science objectives the MESSENGER mission will determine the shape and gravity field of Mercury. These observations will enable the topography and the crustal thickness to be derived for the planet and will determine the small libration of the planet about its axis, the latter critical to constraining the state of the core. These measurements require very precise positioning of the MESSENGER spacecraft in its eccentric orbit, which has a periapsis altitude as low as 200 km, an apoapsis altitude near 15,000 km, and a closest approach to the surface varying from latitude 60 to about 70 N. The X-band tracking of MESSENGER and the laser altimetry are the primary data that will be used to measure the planetary shape and gravity field. The laser altimeter, which has an expected range of 1000 to 1200 km, is expected to provide significant data only over the northern hemisphere because of MESSENGER's eccentric orbit. For the southern hemisphere, radio occultation measurements obtained as the spacecraft passes behind the planet as seen from Earth and images obtained with the imaging system will be used to provide the long-wavelength shape of the planet. Gravity, derived from the tracking data, will also have greater resolution in the northern hemisphere, but full global models for both topography and gravity will be obtained at low harmonic order and degree. The limiting factor for both gravity and topography is expected to be knowledge of the spacecraft location. Present estimations are that in a combined tracking, altimetry, and occultation solution the spacecraft position uncertainty is likely to be of order 10 m. This accuracy should be adequate for establishing an initial geodetic coordinate system for Mercury that will enable positioning of imaged features on the surface, determination of the planet's obliquity, and detection of the librational motion of the planet about its axis.

Smith, David E.↗

NASA NTRS2007

NASA's Decadal Planning Team Mars Mission Analysis Summary

In June 1999 the NASA Administrator chartered an internal NASA task force, termed the Decadal Planning Team, to create new integrated vision and strategy for space exploration. The efforts of the Decadal Planning Team evolved into the Agency-wide team known as the NASA Exploration Team (NEXT). This team was also instructed to identify technology roadmaps to enable the science-driven exploration vision, established a cross-Enterprise, cross-Center systems engineering team with emphasis focused on revolutionary not evolutionary approaches. The strategy of the DPT and NEXT teams was to "Go Anywhere, Anytime" by conquering key exploration hurdles of space transportation, crew health and safety, human/robotic partnerships, affordable abundant power, and advanced space systems performance. Early emphasis was placed on revolutionary exploration concepts such as rail gun and electromagnetic launchers, propellant depots, retrograde trajectories, nano structures, and gas core nuclear rockets to name a few. Many of these revolutionary concepts turned out to be either not feasible for human exploration missions or well beyond expected technology readiness for near-term implementation. During the DPT and NEXT study cycles, several architectures were analyzed including missions to the Earth-Sun Libration Point (L2), the Earth-Moon Gateway and L1, the lunar surface, Mars (both short and long stays), one-year round trip Mars, and near-Earth asteroids. Common emphasis of these studies included utilization of the Earth-Moon Libration Point (L1) as a staging point for exploration activities, current (Shuttle) and near-term launch capabilities (EELV), advanced propulsion, and robust space power. Although there was much emphasis placed on utilization of existing launch capabilities, the team concluded that missions in near-Earth space are only marginally feasible and human missions to Mars were not feasible without a heavy lift launch capability. In addition, the team concluded that missions in Earth s neighborhood, such as to the Moon, can serve as stepping-stones toward further deep-space missions in terms of proving systems, technologies, and operational concepts. The material contained in this presentation was compiled to capture the work performed by the Mars Sub-Team of the DPT NEXT efforts in the late 1999-2001 timeframe.

Drake, Bret G.↗

NASA NTRS2008

New Worlds Observer Formation Control Design Based on the Dynamics of Relative Motion

The New Worlds Observer (NWO) mission is designed for the direct detection and characterization of extrasolar planets. The NWO mission concept employs a two spacecraft leader-follower formation on a trajectory around the Earth/Moon-Sun L(sub 2) Libration Point. The leader spacecraft is baselined as a 4 meter optical telescope. The follower, Starshade spacecraft, is designed to suppress light from a central body star permitting direct detection of a surrounding exoplanetary system. The current design requires a nominal leader-follower separation range of 72 Megameters. NWO poses many challenges including formation control. NWO cycles between three principal control modes during the nominal mission timeline: science (fine pointing), realignment and transition. This paper examines formation control strategies in the context of dynamics of relative motion for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2)libration point. The paper presents an overview of the equations of relative motion followed by a discussion of each of the control modes. Discussion and analysis characterize control strategies for each of the mission control modes, including requirements, implementation challenges and project fuel budgets.

Luquette, Richard J.↗

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 NTRS2011

The Space Review

Human space flight in the US and other space-faring countries is faced with a twin challenge that is likely to persist for many years: flat or declining budgets along with an expectation of continuing, significant achievements. A partial solution may involve increased participation by multiple commercial competitors with the promise - albeit yet to be fully demonstrated - of much-reduced costs. That said, most commercial goals are concentrated on low-Earth orbit (LEO) for the time being, leaving human trips beyond Earth orbit (BED) as governmental initiatives. The past decade, beginning with the 1999/2000 Decadal Planning Team (DPT)/NASA Exploration Team (NExT) human space flight studies for the White House Office of Management and Budget (http://history.nasa.gov/DPT/DPT.htm), can arguably be described as a Golden Age of engineering design, strategic planning, technology capability prioritization, and development programs on the International Space Station (ISS). However, cynics have criticized the same period as little more than PowerPoint presentations, and unfocused technology investments with only limited progress toward a goal of human space flight beyond the immediate vicinity of the Earth. We disagree with the cynics. Experience with the ISS on increasingly sophisticated capabilities have prepared international partners to deploy a major "stepping stone" for human space flight: a habitation system in free space beyond low-Earth orbit. Such an achievement would be a major milestone in human space flight and, very likely, an essential demonstration site for subsequent, very ambitious exploration missions such as to Mars. Developing critical capabilities for human voyages beyond LEO, such as Earth-Moon libration points, offers, as just one example, easy return to Earth within days (see, e.g., Farquhar 1971 (Aeronautics & Astronautics, July, p. 59ff), Thronson, Lester, and Talay 2011 (http://www.thespacereview.com/article/1756/1), and Lester 2012 (http://www.thespacereview.com/article/1650/1). Use of Earth-Moon libration points as sites for early demonstrations of capabilities necessary for human missions to Mars, for example, contrasts sharply with using missions to near-Earth asteroids (NEAs) for that purpose.

Thronson, Harley↗