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NASA NTRS2000

Nozomi Cis-Lunar Phase Orbit Determination

Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998. Scientific objectives of the mission are to study the structure and dynamics of the Martian upper atmosphere and its interaction with the solar wind. Nozomi is a cooperative mission between ISAS and the National Aeronautics and Space Administration (NASA). The NASA contribution includes navigation and tracking services provided by the Jet Propulsion Laboratory (JPL). The spacecraft also serves as an engineering demonstration of basic technology for planetary exploration. One of the new technologies was a unique trajectory, developed by ISAS, which used solar gravitational perturbations at the weak stability boundary as an aid to achieve an Earth-Mars transfer orbit. This trajectory saves approximately 120 m/s of Delta V compared to direct hyperbolic insertion and is considered an enabling technology for the mission. Nozomi was the first spacecraft to employ this trajectory and provided on-orbit validation of the technique. The trajectory was achieved by initially placing the spacecraft in a highly elliptical cis-lunar phasing orbit. Six maneuvers were performed during this period to correct injection errors and target an outbound lunar swingby in September 1998. The gravity assist from the lunar swingby raised apogee to the vicinity of the weak stability boundary. After three more targeting maneuvers, Nozomi performed an inbound lunar swingby followed immediately by a powered Earth swingby in late December 1998. A 420 m/s Trans Mars Insertion (TMI) burn at the final Earth periapsis was intended to place the spacecraft on a heliocentric trajectory leading to Mars orbit insertion in October 1999. Orbit determination for Nozomi is performed in parallel by both ISAS and the Multi-Mission Navigation (MMNAV) group at JPL. This was an advantage for the mission because each group would generate solutions based on data collected from their respective tracking networks. Spacecraft events, such as sequence uplinks and maneuvers, were generally scheduled during passes at the Usuda tracking station in Japan. As a result, maneuver design and reconstruction was derived from MMNAV solutions based on JPL tracking data obtained immediately prior to or following maneuvers. Data was also exchanged between ISAS and MMNAV so orbit determination could be performed on joint data sets in support of critical targeting late in the cis-lunar phase. In this paper, information regarding the MMNAV orbit determination effort for the first six months of the mission is presented. The spacecraft trajectory is characterized first, followed by a discussion of the orbit determination estimation procedure and models. Results from selected orbit solutions are presented and compared against reconstructed trajectories. One area of emphasis in this paper is orbit determination in the vicinity of the weak stability boundary. Precise navigation was necessary to target the second lunar swingby and the powered Earth swingby. Delivery accuracy of 150 m was required for these critical encounters, but a number of factors contributed to the general degradation of orbit determination accuracy. This included the fact that the spacecraft was at apogee, at a range of 1.7 million km and moving at less than I km/sec perpendicular to the line of sight. Nozomi was also close to zero degrees declination where there are known limitations on orbit determination performance. Finally, S-band tracking data was acquired through the Nozomi backup low gain antenna. This antenna is offset from the axis of this spin stabilized spacecraft and superimposed large signatures in the Doppler and range data. These difficulties were overcome by combining long data arcs, spanning several maneuvers, with a high fidelity solar pressure model. The model included a physically accurate representation of the spacecraft structure and a high time resolution orientation model. Observation modeling included the removal of the spin induced Doppler bias, spin signature and per pass correction of range calibration errors applied for data leading up to critical events. As a result, all orbit determination goals were met. A second area of emphasis in this paper is the JPL tracking and orbit determination effort in support of the TMI maneuver. TMI occurred out of contact with ground stations and the JPL Goldstone tracking complex had the first pass following the bum. As a result, MMNAV had the responsibility to make a rapid assessment of the maneuver performance. MMNAV made the determination that a 100 m/s under bum had occurred and promptly informed ISAS via voice lines. ISAS immediately began preparations for a correction maneuver (TMIc), which had to be performed during the next Usuda pass. The near real time assessment by MMNAV provided accurate antenna frequency and pointing updates for the spacecraft acquisition at Usuda and the close coordination between the two agencies enabled the design and successful execution of the TMc maneuver. Propellant consumption during the correction burn dictated that the mission be redesigned. ISAS developed a new plan which adds 3 full solar orbits, two Earth swingbys and one lunar swingby with arrival at Mars in January 2004. The final Mars orbit will still enable the mission to achieve all of its science objectives.

Ryne, Mark↗

NASA NTRS1987

A scaling law for accretion zone sizes

Current theories of runaway planetary accretion require small random velocities of the accreted particles. Two body gravitational accretion cross sections which ignore tidal perturbations of the Sun are not valid for the slow encounters which occur at low relative velocities. Wetherill and Cox have studied accretion cross sections for rocky protoplanets orbiting at 1 AU. Using analytic methods based on Hill's lunar theory, one can scale these results for protoplanets that occupy the same fraction of their Hill sphere as does a rocky body at 1 AU. Generalization to bodies of different sizes is achieved here by numerical integrations of the three-body problem. Starting at initial positions far from the accreting body, test particles are allowed to encounter the body once, and the cross section is computed. A power law is found relating the cross section to the radius of the accreting body (of fixed mass).

Greenzweig, Yuval↗

NASA NTRS1974

In-situ measurements of lunar heat flow

During the Apollo program two successful heat flow measurements were made in situ on the lunar surface. At the Apollo 15 site a value of 0.0000031 watts/sqcm was measured and at the Apollo 17 site a value of 0.0000022 watts/sqcm was determined. Both measurements have uncertainty limits of + or - 20% and have been corrected for perturbing topographic effects. The apparent difference between the observations may correlate with observed variations in the surface abundance of thorium. Comparison with earlier determinations of heat flow, using the microwave emission spectrum from the moon, gives support to the high gradients and heat flows observed in situ.

Langseth, M. G.↗

NASA NTRS2011

A Minimum Delta V Orbit Maintenance Strategy for Low-Altitude Missions Using Burn Parameter Optimization

Orbit maintenance is the series of burns performed during a mission to ensure the orbit satisfies mission constraints. Low-altitude missions often require non-trivial orbit maintenance Delta V due to sizable orbital perturbations and minimum altitude thresholds. A strategy is presented for minimizing this Delta V using impulsive burn parameter optimization. An initial estimate for the burn parameters is generated by considering a feasible solution to the orbit maintenance problem. An low-lunar orbit example demonstrates the Delta V savings from the feasible solution to the optimal solution. The strategy s extensibility to more complex missions is discussed, as well as the limitations of its use.

Brown, Aaron J.↗

NASA NTRS1977

In-situ measurements of lunar heat flow

During the Apollo program two successful heat flow measurements were made in situ on the lunar surface. At the Apollo 15 site a value of .0000031 W/sq cm was measured, and at the Apollo 17 site a value of .0000022 W/sq cm was determined. Both measurements have uncertainty limits of + or - 20 percent and have been corrected for perturbing topographic effects. The apparent difference between the observations may correlate with observed variations in the surface abundance of thorium. Comparison with earlier determinations of heat flow, using the microwave emission spectrum from the moon, gives support to the high gradients and heat flows observed in situ.

Langseth, M. B.↗

NASA NTRS2026

High Temperature Dielectric Properties and Differential Scanning Calorimetry of Lunar Simulants

To guide development of microwave process technology that could be used during in situ construction on the Moon, we measured the high-temperature basic dielectric properties (εʹ and εʺ) of 17 lunar simulants and related materials. In order to confidently use these data one needs to understand the data’s strengths and weaknesses. Therefore, a goal of this publication is to provide insights into the comparative effects of sample composition, pre-treatments, experimental variables, high temperatures, and other factors on the measured response. The dielectric measurements were performed using the cavity perturbation method over a temperature range between room temperature to 1000 °C, or higher, and provided the real and imaginary components of permittivity at six frequencies. The utility of the original values was limited by the varying density of the pellets used in the measurement. Therefore, all of the εʹ and εʺ measurements at the frequency of 2466 MHz have been scaled to a constant density, 1.75 g/cm 3 . Here the data are presented as graphs chosen to aid analysis within and across simulant groups. To gain additional insight into the processes happening at the elevated temperatures in the dielectric measurements, heat capacity data was obtained using differential scanning calorimetry (DSC) on several of the simulant materials. Our data show that over the frequency range 397 MHz – 2985 MHz a material’s behavior does not greatly change, as compared to the scale of differences observed between lunar mare and highland simulants at high temperatures. For example at 1000 °C, the mare simulant JSC-1A absorbs 10 times more power than the highland simulant NUW-LHT-5M. We observe that as melting temperatures are reached both permittivity and dielectric loss rise non-linearly, helping to explain thermal runaway during microware heating. Our data show that even less than a few weight % of many non-lunar minerals, and the use of mixtures in simulants can affect the dielectric behavior at higher temperatures. A comparison of our results with published dielectric data for Apollo samples and with remote sensing of the Moon supports the conclusion the simulants and lunar material at room temperature have very similar dielectric values.

Differential Scanning Calorimetry↗

NASA NTRS2016

Monte Carlo Analysis as a Trajectory Design Driver for the TESS Mission

The Transiting Exoplanet Survey Satellite (TESS) will be injected into a highly eccentric Earth orbit and fly 3.5 phasing loops followed by a lunar flyby to enter a mission orbit with lunar 2:1 resonance. Through the phasing loops and mission orbit, the trajectory is significantly affected by lunar and solar gravity. We have developed a trajectory design to achieve the mission orbit and meet mission constraints, including eclipse avoidance and a 30-year geostationary orbit avoidance requirement. A parallelized Monte Carlo simulation was performed to validate the trajectory after injecting common perturbations, including launch dispersions, orbit determination errors, and maneuver execution errors. The Monte Carlo analysis helped identify mission risks and is used in the trajectory selection process.

trajectory↗

NASA NTRS2016

Monte Carlo Analysis as a Trajectory Design Driver for the Transiting Exoplanet Survey Satellite (TESS) Mission

monte carlo↗

NASA NTRS2007

Predicting the Earth encounters of (99942) Apophis

Arecibo delay-Doppler measurements of (99942) Apophis in 2005 and 2006 resulted in a five standard-deviation trajectory correction to the optically predicted close approach distance to Earth in 2029. The radar measurements reduced the volume of the statistical uncertainty region entering the encounter to 7.3% of the pre-radar solution, but increased the trajectory uncertainty growth rate across the encounter by 800% due to the closer predicted approach to the Earth. A small estimated Earth impact probability remained for 2036. With standard-deviation plane-of-sky position uncertainties for 2007-2010 already less than 0.2 arcsec, the best near-term ground-based optical astrometry can only weakly affect the trajectory estimate. While the potential for impact in 2036 will likely be excluded in 2013 (if not 2011) using ground-based optical measurements, approximations within the Standard Dynamical Model (SDM) used to estimate and predict the trajectory from the current era are sufficient to obscure the difference between a predicted impact and a miss in 2036 by altering the dynamics leading into the 2029 encounter. Normal impact probability assessments based on the SDM become problematic without knowledge of the object's physical properties; impact could be excluded while the actual dynamics still permit it. Calibrated position uncertainty intervals are developed to compensate for this by characterizing the minimum and maximum effect of physical parameters on the trajectory. Uncertainty in accelerations related to solar radiation can cause between 82 and 4720 Earth-radii of trajectory change relative to the SDM by 2036. If an actionable hazard exists, alteration by 2-10% of Apophis' total absorption of solar radiation in 2018 could be sufficient to produce a six standard-deviation trajectory change by 2036 given physical characterization; even a 0.5% change could produce a trajectory shift of one Earth-radius by 2036 for all possible spin-poles and likely masses. Planetary ephemeris uncertainties are the next greatest source of systematic error, causing up to 23 Earth-radii of uncertainty. The SDM Earth point-mass assumption introduces an additional 2.9 Earth-radii of prediction error by 2036. Unmodeled asteroid perturbations produce as much as 2.3 Earth-radii of error. We find no future small-body encounters likely to yield an Apophis mass determination prior to 2029. However, asteroid (144898) 2004 VD17, itself having a statistical Earth impact in 2102, will probably encounter Apophis at 6.7 lunar distances in 2034, their uncertainty regions coming as close as 1.6 lunar distances near the center of both SDM probability distributions.

Orbit determination↗

NASA NTRSDate not supplied

Mission Design Strategies for Rendezvous and Servicing of Sun-Earth Libration Point Missions

With the launch of the James Webb Space Telescope (JWST) and future launches of the Roman Space Telescope (RST) and larger telescopes such as the proposed Habitable Worlds Observatory (HWO), the questions of where and how to rendezvous to enable servicing of these telescope missions arise. To aid in determining the allowable locations to rendezvous for servicing from a trajectory design approach, our previous research and analysis has shown feasible transfer trajectories between the Sun-Earth Libration L2 region (Quasi-Halo orbit) and the Earth Moon vicinity (Distant Retrograde Orbit (DRO), Quasi-Halo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit (NRHO)), along with the related transfer constraints and the corresponding total fuel mass costs. We now focus on operational-like optimal scenarios for these transfers to complete a rendezvous to permit servicing at various Libration orbit locations. In this paper, we address how operational navigation and maneuver execution uncertainties impact the rendezvous timing and fuel mass (via ΔV). While optimization techniques are applied to ensure minimal ΔVs, we also analyze various transfer trajectory durations and rendezvous arrival geometries. The analysis presented includes dynamical system approaches and applies optimization through several tools including the Adaptive Trajectory Design (ATD) module as an initial guess, numerical computation using the General Mission Analysis Tool (GMAT) and Systems Tool Kit (STK) with higher fidelity perturbation modeling, and recently developed optimization tools that incorporate dynamical systems directly into the optimization process. Transfer trajectory options examined include a direct transfer from Earth versus departures from the previously examined Earth-Moon regime orbits, e.g. NRHOs and DROs. A return from Sun-Earth to lunar vicinity for a complete servicing after a rendezvous in Sun-Earth orbit is also considered. The resultant ΔV’s for each scenario is provided with discussions on various transfer trades, rendezvous considerations, and orbital limitations from the dynamical systems. A Poincare-like mapping of trajectory and rendezvous conditions categorize feasible and optimum transfer approaches, dependent on Sun-Earth orbit mission parameters. The focus of this research addresses questions for upcoming trades regarding servicing options for current and future Sun-Earth L1 and L2 missions. By doing a comprehensive analysis approach (dynamical systems + high fidelity optimization with true operational constraints), this paper will serve as a guide for mission architecture and operational trade considerations.

Maneuver Design↗

NASA NTRS1994

Measuring temporal gravitational variations using SLR data

Redistribution of mass within the Earth system changes its gravitational field, and thus changes the orbits of Earth satellites. While these variations are small, Satellite Laser Ranging (SLR) to precise geodetic satellites such as Lageos-1, Lageos-2, Starlette, Ajisai, and Stella can detect these changes at their broadest spatial scales (currently greater than 10,000 km). The satellites sense only the combined variation in the solid Earth-ocean-atmosphere system; however, modeling of these different components has led to detection of long-wavelength variations in the distribution of atmospheric mass, changes in the amplitudes of atmospheric and oceanic tides, and secular variations caused by the post-glacial adjustment of the Earth's crust. The unambiguous detection of ocean mass redistribution by SLR has not been verified due largely to inadequacies in current ocean models. Great progress has been made in recent years in the determination of luni-solar tides and the braking they induce in the Earth-Moon-Sun system (leading to secular changes in the length-to-day and lengthening of the lunar orbit period) using a wide variety of techniques including ocean tide gauges, satellite altimetry, Lunar Laser Ranging, and near-Earth satellite orbit modeling. Recent investigations of the more complex and less predictable non-tidal temporal variations in the gravity field have generally proceeded along two fronts: 1) the determination of long-wavelength variations in the gravity field through the changing perturbations seen in the orbits of near-Earth satellites, and 2) the prediction of temporal variations in gravity using geophysical, atmospheric, and oceanic models. A convergence of these efforts is sought to better understand the source of observed changes in the Earth's gravitational field.

Nerem, Robert S.↗

NASA NTRSDate not supplied

Lunar Regolith Trajectories as a Result of Plume Surface Interactions

Lunar regolith is ejected from the impingement points of descent engine plumes. Such particles pose potential risks to surface operations, sites of scientific and historical interest, and orbiting spacecraft. Consequently, determining the resultant trajectories of these particles is necessary in order to estimate and mitigate risk. Here we present the ranges, impact latitudes, times of flight, and maximum altitudes for particles accelerated by a plume surface interaction at the lunar south pole. Using launch angles determined from observations and simulations, and for velocities <1:6 km/s, particles pose little risk. However, above 1:6 km/s the risks increase, and the results become highly sensitive to the initial angle. In addition, gravitational and non-gravitational processes will introduce perturbations to high-velocity trajectories resulting in a reduction in precision. Therefore, while local topography or artificial berms may mitigate trajectories with low initial angles, it remains important to place tight constraints on the potential launch angles of particles accelerated by plume surface interactions through simulations and experimentation. If these angles are indeed constrained to within a few degrees of the horizon, the risks posed by accelerated regolith particles at any velocity will be minimal.

Daniel Batcheldor↗

NASA NTRSDate not supplied

Autonomous Burn Targeting for a Lunar Sortie Staged From a Near-Rectilinear Halo Orbit

NASA is planning manned lunar landings starting in the mid 2020s as part of its Artemis program. These lunar sortie missions will be staged from a Near-Rectilinear Halo Orbit (NRHO), with a requirement for the lander to autonomously determine the timing and targets for multiple burns so that it can navigate its way back to the staging vehicle in the NRHO. The lander mission profile transitions through multiple gravitational regimes, at times influenced equally by 3rd bodies (Earth and Sun) as much as by the Moon, while at other times the lander is primarily influenced by lunar gravitation. These different gravitational regimes pose challenges to guidance and targeting logic. The present work describes options for autonomous logic for each of several major maneuvers of the lunar sortie, including numerical techniques to incorporate the effect of 3rd bodies. Throughout the development there is an emphasis on simplicity and computational efficiency.

NRHO↗

NASA NTRS2019

Building Booster Separation Aerodynamic Databases for Artemis II

NASA’s Artemis II mission will mark the return of humans to near-lunar space for the first time since Apollo. Shortly after launch on the Space Launch System (SLS), a critical phase of ascent occurs when 16 small rockets fire to push the boosters away from the core. Minimizing the risk of failure during separation requires the construction of multiple 13-dimensional databases, including perturbations in position, flight conditions, and engine thrust. The SLS Computational Fluid Dynamics team used NASA’s FUN3D flow solver on the Pleiades and Electra supercomputers to run 5,780 simulations at nominal conditions and over 8,000 simulations with a core stage engine failure to generate the databases needed to verify the booster separation system for Artemis II.

Meeroff, Jamie G.↗

NASA NTRS2008

A Testbed for Evaluating Lunar Habitat Autonomy Architectures

A lunar outpost will involve a habitat with an integrated set of hardware and software that will maintain a safe environment for human activities. There is a desire for a paradigm shift whereby crew will be the primary mission operators, not ground controllers. There will also be significant periods when the outpost is uncrewed. This will require that significant automation software be resident in the habitat to maintain all system functions and respond to faults. JSC is developing a testbed to allow for early testing and evaluation of different autonomy architectures. This will allow evaluation of different software configurations in order to: 1) understand different operational concepts; 2) assess the impact of failures and perturbations on the system; and 3) mitigate software and hardware integration risks. The testbed will provide an environment in which habitat hardware simulations can interact with autonomous control software. Faults can be injected into the simulations and different mission scenarios can be scripted. The testbed allows for logging, replaying and re-initializing mission scenarios. An initial testbed configuration has been developed by combining an existing life support simulation and an existing simulation of the space station power distribution system. Results from this initial configuration will be presented along with suggested requirements and designs for the incremental development of a more sophisticated lunar habitat testbed.

Lawler, Dennis G.↗

NASA NTRS1999

Nozomi Cis-Lunar Phase Orbit Determination

Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998.

orbit↗

NASA NTRS1980

Development and implementation of Shuttle/IUS proximity operations flight design software

The High Fidelity Relative Motion Program (HFRMP), a trajectory/attitude numerical integration program, was developed and implemented on the MPAD HP-9825A desk top computer systems. A solar and a lunar ephemeris is included in the HFRMP along with models of the oblate Earth, a rotating atmosphere, the orbiter's OMS/RCS/DAP system, orbiter vents, rotor dynamics, and upper stage propulsion systems. Although designed primarily for the analysis of proximity operations, it is useful in other areas such as attitude/stability analysis, propulsive consumables estimation, and trajector perturbation studies. An unique identification was assigned to each of the various configurations of the HFRMP that were developed to test new techniques and algorithms are briefly described. These include the HFRMP Versions 03H, 03M, 03T, 03U, and 05D. Development of orbiter/upper stage separation techniques including flight design support for the TDRS-A and Galileo deployment flights and design of standard maneuver sequences is discussed. Also, the development and implementation of the Euler angle conversion program is briefly addressed.

Wilson, S. W.↗

NASA NTRS2006

Terrestrial Planet Growth in Circumbinary Disks

We examine the accu~ulation of terrestrial from circumbinary disks surrounding pairs of stars with masses of either 0.5 solar masses each or 0.8 and 0.2 solar masses and orbital separations of 0.05 AU to 0.4 AU by performing numerical simulations of the late stages of planetary growth. Initial disks contain about 2.6 Earth masses of lunar to Mars-sized bodies orbiting within 2 AU of the center of mass of the system, plus giant planets with masses and orbits analogous to those of Jupiter and Saturn. We also performed simulations using analogous disks orbiting single 1 solar mass stars. The dynamics of planetary growth is quite chaotic because the gravitational perturbations resulting from close approaches greatly amplify differences in orbits. Thus, several simulations of each configuration were run with very slightly different initial conditions to enable us to distinguish systematic effects resulting from differences in the binary orbit (or differences of the initial orbits of the bodies within the disk) from pseudo-random variability in outcomes resulting from chaos. Most runs simulated 200 million years of evolution. At least one terrestrial planet remained at the end of each run; one simulation produced 6 terrestrial planets in a configuration that appears to be quite stable. The systems that formed around stars with binary apastron separations of less than 0.2 AU contained on average slightly more planets than those that formed around single stars, with the outermost planet typically orbiting at a greater distance from the system barycenter. Greater stellar separations tended to result in fewer planets, with the inner planet orbiting farther from the stars. More eccentric binaries have a more pronounced effect for the same apastron distance. The statistical distribution of final systems is not sensitive to moderate differences in the initial eccentricities of the bodies in the disk.

Lissauer, J. J.↗