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NASA NTRSDate not supplied

Trajectory Optimization Methods and Applications at NASA Goddard

The process of spacecraft trajectory design frequently incorporates an optimization step in which one or more objectives, such as propellant consumption or time of flight, is minimized. Optimization is especially crucial for low-thrust mission design, due to the need to specify a thrust vector at every instant in time along a trajectory. At NASA's Goddard Space Flight Center (GSFC) a number of open-source tools have been developed for spacecraft trajectory optimization that utilize direct shooting and collocation methods. These tools have been effectively applied to cislunar, libration point, and interplanetary mission design for the Lunar IceCube, SWFO, and DAVINCI missions, among others. This presentation outlines the theory underlying these optimization tools along with the details of their application to several trajectory design problems, with a focus on the Lunar IceCube (LIC) mission. The LIC mission required a low-thrust trajectory from a high-energy deployment state to a lunar orbit, and its limited control authority necessitated the use of optimization tools and low-energy trajectory design techniques. The tools discussed demonstrate how the use of optimization methods expands mission capabilities and enables transformational science.

Robert Pritchett↗

NASA NTRS2018

NASA's Black Marble Nighttime Lights Product Suite

NASA's Black Marble nighttime lights product suite (VNP46) is available at 500 meters resolution since January 2012 with data from the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) onboard the Suomi National Polar-orbiting Platform (SNPP). The retrieval algorithm, developed and implemented for routine global processing at NASA's Land Science Investigator-led Processing System (SIPS), utilizes all high-quality, cloud-free, atmospheric-, terrain-, vegetation-, snow-, lunar-, and stray light-corrected radiances to estimate daily nighttime lights (NTL) and other intrinsic surface optical properties. Key algorithm enhancements include: (1) lunar irradiance modeling to resolve non-linear changes in phase and libration; (2) vector radiative transfer and lunar bidirectional surface anisotropic reflectance modeling to correct for atmospheric and BRDF (Bidirectional Reflectance Distribution Function) effects; (3) geometric-optical and canopy radiative transfer modeling to account for seasonal variations in NTL; and (4) temporal gap-filling to reduce persistent data gaps. Extensive benchmark tests at representative spatial and temporal scales were conducted on the VNP46 time series record to characterize the uncertainties stemming from upstream data sources. Initial validation results are presented together with example case studies illustrating the scientific utility of the products. This includes an evaluation of temporal patterns of NTL dynamics associated with urbanization, socioeconomic variability, cultural characteristics, and displaced populations affected by conflict. Current and planned activities under the Group on Earth Observations (GEO) Human Planet Initiative are aimed at evaluating the products at different geographic locations and time periods representing the full range of retrieval conditions.

Suomi-NPP↗

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 NTRS2001

The TPF Mission at L2

The Terrestrial Planet Finder (TPF) is one of the center pieces of NASA's Origins Program. The goal of TPF is to identify terrestrial planets around stars nearby the Sun. For this purpose, a space-based interferometer with a baseline of approximately 100 m is required. To achieve such a large baseline, a distributed system of five spacecraft flying in formation is an efficient approach. Since the TPF instruments need a cold and stable environment, a halo orbit about 4 is ideal. First, we describe formation flight near the Lagrange point is feasible for the TPF mission. Second, we propose a novel approach for human servicing of Lagrange point missions by placing a Lunar service station in an Lunar L1 orbit. The TPF spacecraft can be transferred to a Lunar L1 orbit in a few days and requires relatively little delta-V. This efficient transfer results from the system of low energy pathways connecting the entire Solar System generated by the Lagrange points. The halo orbits are the portals of this Interplanetary . A Lunar Station at the L,portal, in addition to servicing missions from the Sun-Earth Lagrange points, may play an even more important role in the future development of space.

human servicing↗

NASA NTRS2000

A Survey and Recent Development of Lunar Gravity Assist

Earth's moon is the largest in the solar system relative to its parent body, the Earth, and can have significant effect on the path of a spacecraft flying close by. This effect, when planned to benefit a specific mission, is called lunar gravity assist (LGA) , and assumes that one aims the spacecraft towards the Moon in such a way that the Moon's gravitational pull will alter the spacecraft's course in a favorable manner. The first application of LGA was in the Apollo program, where the command and lunar modules (and astronauts) were propelled to the Moon such that, if no additional course changes were made, they would swing around the backside of the Moon at a certain altitude and be flung back to Earth to enter the atmosphere at a specified location in the Pacific ocean. This LGA was an essential element saving the lives of the astronauts on Apollo 13. This paper will illustrate the basic mechanics of gravity assist, and list the many applications where it has been used effectively over the past 30 some years. These include missions to the sun and Earth libration points, redirecting a spacecraft from one of these point to a comet encounter, and enhancing payloads by providing an energy boost by the Moon. More recently, studies and actual missions have shown the benefits of LGA in: (1) assisting lunar capture, (2) repositioning geosynchronous communications satellites, (3) boosting spacecraft to Earth escape and departure to planets and other solar system bodies, and (4) allowing small spacecraft to be launched as secondary payloads and released into almost a random orbit from which each may depart and maneuver in space with gravity assists from the Earth and Moon to perform a specific planetary or other mission. This latter application is a recent development by the author and is being applied in 2002 and later years, with piggyback flights on the Ariane 5 which launches comsats to GEO.

Penzo, Paul A.↗

NASA NTRS2008

Precision Lunar Laser Ranging For Lunar and Gravitational Science

Laser ranging to retroreflector arrays placed on the lunar surface by the Apollo astronauts and the Soviet Lunar missions over the past 39 years have dramatically increased our understanding of gravitational physics along with Earth and Moon geophysics, geodesy, and dynamics. Significant advances in these areas will require placing modern retroreflectors and/or active laser ranging systems at new locations on the lunar surface. Ranging to new locations will enable better measurements of the lunar librations, aiding in our understanding of the interior structure of the moon. More precise range measurements will allow us to study effects that are too small to be observed by the current capabilities as well as enabling more stringent tests of Einstein's theory of General Relativity. Setting up retroreflectors was a key part of the Apollo missions so it is natural to ask if future lunar missions should include them as well. The Apollo retroreflectors are still being used today, and nearly 40 years of ranging data has been invaluable for scientific as well as other studies such as orbital dynamics. However, the available retroreflectors all lie within 26 degrees latitude of the equator, and the most useful ones within 24 degrees longitude of the sub-earth meridian. This clustering weakens their geometrical strength.

Merkowitz, S. M.↗

NASA NTRS2003

On-Orbit Cross-Calibration of AM Satellite Remote Sensing Instruments using the Moon

On April 14,2003, three Earth remote sensing spacecraft were maneuvered enabling six satellite instruments operating in the visible through shortwave infrared wavelength region to view the Moon for purposes of on-orbit cross-calibration. These instruments included the Moderate Resolution Imaging Spectroradiometer (MODIS), the Multi-angle Imaging SpectroRadiometer (MISR), the Advanced Spaceborne Thermal Emission and Reflection (ASTER) radiometer on the Earth Observing System (EOS) Terra spacecraft, the Advanced Land Imager (ALI) and Hyperion instrument on Earth Observing-1 (EO-1) spacecraft, and the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) on the SeaStar spacecraft. Observations of the Moon were compared using a spectral photometric mode for lunar irradiance developed by the Robotic Lunar Observatory (ROLO) project located at the United States Geological Survey in Flagstaff, Arizona. The ROLO model effectively accounts for variations in lunar irradiance corresponding to lunar phase and libration angles, allowing intercomparison of observations made by instruments on different spacecraft under different time and location conditions. The spacecraft maneuvers necessary to view the Moon are briefly described and results of using the lunar irradiance model in comparing the radiometric calibration scales of the six satellite instruments are presented here.

Butler, James J.↗

NASA NTRS2012

Exploration Platform in the Earth-Moon Libration System Based on ISS

International Space Station (ISS) industry partners have been working for the past two years on concepts using ISS development methods and residual assets to support a broad range of exploration missions. These concepts have matured along with planning details for NASA's Space Launch System (SLS) and Multi-Purpose Crew Vehicle (MPCV) to allow serious consideration for a platform located in the Earth-Moon Libration (EML) system. This platform would provide a flexible basis for future exploration missions and would significantly reduce costs because it will enable re-use of expensive spacecraft and reduce the total number of launches needed to accomplish these missions. ISS provides a robust set of methods which can be used to test systems and capabilities needed for missions to the Moon, Mars, asteroids and other potential destinations. We will show how ISS can be used to reduce risk and improve operational flexibility for missions beyond low earth orbit through the development of a new Exploration Platform based in the EML system. The benefits of using the EML system as a gateway will be presented along with additional details of a lunar exploration mission concept. International cooperation is a critical enabler and ISS has already demonstrated successful management of a large multi-national technical endeavor. We will show how technology developed for ISS can be evolved and adapted to the new exploration challenge. New technology, such as electric propulsion and advanced life support systems can be tested and proven at ISS as part of an incremental development program. Finally, we will describe how the EML Platform could be built and deployed and how International access for crew and cargo could be provided.

Raftery, Michael↗

NASA NTRS1999

A View of the Lunar Interior Through Lunar Laser Range Analysis

Laser ranges between observatories on the Earth and retroreflectors on the Moon started in 1969 and continue to the present. Recent range accuracies are 2 cm while earliest ranges are an C, order of magnitude less certain. Four retroreflectors are ranged: three located at the Apollo 11, 14, and 15 sites and one on the Lunakhod 2 rover. Accurate analysis of the range data determines a number of lunar science parameters. The lunar interior variables include a fluid core parameter. The Lunar Laser Ranging effort is reviewed elsewhere. Many parameters are detected through their influence on rotation. Also detected are solid-body tides and accurate selenocentric reflector locations. Determined through the rotation are moment-of-inertia differences, gravitational harmonics, potential Love number, and dissipation effects due to tides and molten core. The rotation of the Moon is not at its minimum energy state; some recently active process has caused free librations. The moment differences contributed to the recent improvement of the Moon's moment of inertia from the Lunar Prospector gravity field. The Love numbers provide bulk elastic properties. Future possibilities for measurement include oblateness of the core-mantle boundary and core moment. A study of dissipation signatures in the rotation determines tidal Q vs. frequency and concludes that the Moon has a molten core. At 1 month the tidal Q is 37 and at 1 yr it is 60. The core radius is < or = 352 km for Fe and < or = 374 km for the Fe-FeS eutectic. The core detection exceeds 3x its uncertainty. The spin of the core is not aligned with the spin of the mantle and torque arises from the velocity difference at the boundary. Yoder's turbulent boundary layer theory is used to compute the radii. The present heat generation from tides and core interaction is minor compared to radiogenic heating. The heating for ancient times is more interesting. Peale and Cassen investigated lunar tidal heating while the lunar orbit expanded due to tides on Earth. Their calculations predate the measurement of Q and should be multiplied by 3.45 to match the lunar-laser-determined Love number and monthly Q. Tidal-heating computations depend on how fast the lunar orbit evolved and whether the tidal dissipation is localized. Neither is known, but plausible assumptions lead to early central region temperature increases of several hundred degrees. Most of the energy is deposited early in the Moon's history. The turbulent boundary layer theory allows a prediction of energy dissipated at the core-mantle boundary during orbit evolution. Under the assumption that the properties of the early core are the same as at present, the energy dissipated by core-mantle interaction is about the same as for tidal dissipation, but it is deposited in a smaller volume. This source of energy is capable of promoting convection in an early fluid core and driving a dynamo. This is a transient phase with a duration depending on the rate of orbit evolution. Plausible assumptions lead to a duration of a few hundred million years. Thus, the remnant magnetization of many lunar rocks is compatible with a brief global magnetic field powered by dynamical energy dissipation. Analysis of the lunar laser ranges is providing information on lunar geophysics. Future data will improve accuracies of present solution parameters, and several more interior effects should be detectable.

Williams, J. G.↗

NASA NTRS2019

Predicted Performance of an X-Ray Navigation System for Future Deep Space and Lunar Missions

In November 2017, the NASA Goddard Space Flight Center (GSFC) Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) experiment successfully demonstrated the feasibility of X-ray Pulsar Navigation (XNAV) as part of the Neutron Star Interior Composition Explorer (NICER) mission, which is an X-ray Astrophysics Mission of Opportunity currently operating onboard the International Space Station (ISS). XNAV provides a GPS-like absolute autonomous navigation and timing capability available anywhere in the Solar System and beyond. While the most significant benefits of XNAV are expected to come in support of very deep-space missions, the absolute autonomous navigation and timing capability also has utility for inner Solar System missions where increased autonomy or backup navigation and timing services are required, e.g., address loss of communication scenarios.The NASA commitment to develop a Gateway to support exploration of the Moon and eventually Mars, as well as current and future robotic missions such as James Webb Space Telescope (JWST), New Horizons, and much more, certainly will tax the existing ground based infrastructure in terms of availability. There- fore, an extended look at the feasibility and potential performance of XNAV for comparable missions is warranted. In this paper, we briefly review the XNAV concept and present case studies of its utility and performance for a Gateway orbit, Sun-Earth libration orbit, and a deep space transit trajectory.

Getchius, Joel↗

NASA NTRS2014

Trajectory Design for the Transiting Exoplanet Survey Satellite (TESS)

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission launching in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the SWM76 launch window tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements.

Monte Carlo↗