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NASA NTRS2003

Solar System Test of Gravitational Theories

We are engaged in testing gravitational theory, mainly using observations of objects in the solar system and mainly on the interplanetary scale. Our goal is either to detect departures from the standard model (general relativity) - if any exist within the level of sensitivity of our data - or to place tighter bounds on such departures. For this project, we have analyzed a combination of observational data with our model of the solar system, including primarily planetary radar ranging, lunar laser ranging, and spacecraft tracking, but also including both pulsar timing and pulsar VLBI measurements. In the past year, we have included new data in the analysis, primarily tracking data from the Mars Pathfinder mission. Although these data are relatively few in number, they extend the time span of high-precision tracking on the surface of Mars from six years to over 20. As a result, the statistical standard deviation of our estimate of Mars precession rate has nearly halved, and the rest of the parameters in our solar-system model have experienced a corresponding, albeit smaller, improvement (about 20% for t,he relevant asteroid masses, 10% for the semimajor axis of Mars orbit, and smaller amounts for most other parameters). In the coming year, we plan to continue adding data to our set, as available. Ne 2 expect to use these data and improved models to obtain estimates of the gravitational- theory parameters and to publish these results.

Shapiro, Irwin I.↗

NASA NTRS1973

Asteroid and comet exploration

Exploration of Venus, Mars, and the Moon have had two major scientific objectives. One was to clarify the processes which control planetary evolution. The fulfillment of this purpose, although far from complete, was eminently successful in generating entirely new perspectives on the growth and differentiation of earth. The second objective, particularly prominent in the planning of the lunar exploration, was to augment the understanding of the virtually unknown preplanetary history of the solar system. This would include the fundamental questions of the origin, emplacement, and state of matter gathered around the sun and some planets. Preplanetary history also inquires into the problems of fractionation, condensation, and non-gravitation aggregation of circumsolar and circumplanetary matter.

Arrhenius, G.↗

NASA NTRS2019

Cloud Computing Methods for Near Rectilinear Halo Orbit Trajectory Design

Complicated mission design problems require innovative computational solutions. As spacecraft depart from a proposed Gateway in a Near Rectilinear Halo Orbit (NRHO), recontact analysis is required to avoid risk of collision and ensure safe operations. Escape dynamics from NRHOs are governed by multiple gravitational bodies, yielding a trajectory design space that is exhaustively large. This paper summarizes the recontact analysis for departure from the NRHO and describes how the Deep Space Trajectory Explorer (DSTE) trajectory design software incorporates high performance cloud computing to compute and visualize the orbit design space. Recent focus on exploration missions to cislunar space has kindled accelerated interest in multibody orbit solutions. Trajectory analysis in the presence of multiple gravity fields is complex, and innovative computational tools are needed to simplify complicated design spaces, to generate large quantities of data quickly, and to visualize the output for user accessibility. The Gateway mission is a prime example. The Gateway1 is proposed as a human outpost in deep space. The current baseline orbit for the Gateway is a Near Rectilinear Halo Orbit (NRHO) near the Moon.2 The NRHO exists in a regime that experiences the gravitational effects of the Earth and the Moon simultaneously, complicating orbit analysis. The mission design process benefits greatly from updated computational tools for multibody missions like the Gateway. As an example, consider the problem of assessing the risk of collision in an NRHO. As a staging location to missions to the lunar surface and beyond the Earth-Moon system, the Gateway will experience spacecraft and other objects regularly arriving and departing. Departing objects potentially include spent logistics modules, visiting crew vehicles, debris objects, wastewater particles, and cubesats. Each departure is governed by the dynamics of the Gateway orbit and the surrounding dynamical environment. Over time, any unmaintained object in such an orbit eventually departs due to the small instabilities associated with the NRHOs. A separation maneuver speeds the departure from the NRHO, but the effects of the maneuver on the spacecraft behavior depend on the location, magnitude, and direction of the burn. Escape dynamics from the NRHO with regard to these maneuver options open up an enormous potential trajectory design space where subtle changes in input can produce dramatically large changes in the results. Any departing object must avoid recontacting the Gateway as it leaves the lunar vicinity, and a recontact analysis thus involves a significant number of computations and extensive output data. To explore the dynamics of this extensive design space, the Deep Space Trajectory Explorer3 (DSTE) trajectory design software incorporates new High Performance Computing (HPC) services and novel interactive visualizations. This paper details the HPC and cloud infrastructure techniques that are implemented in the DSTE, applying the new capabilities to analysis of recontact risk with the Gateway in NRHO. NEAR RECTILINEAR HALO ORBITS The Gateway is planned to fly in a lunar NRHO as its baseline orbit. The NRHO families of orbits are subsets of the larger halo families, which originate from planar orbits near the L1 and L2 libration points; the Earth-Moon L2 halo family appears in Figure 1. Each halo orbit is perfectly periodic in the Circular Restricted 3-Body Problem (CR3BP) and becomes a quasi-periodic orbit in a higher fidelity ephemeris force model. The NRHOs are defined as those members of the halo family with bounded stability properties;2 they pass near the Moon at perilune and are nearly polar. Families exist with apolunes located both above the lunar north pole and above the lunar south pole; the Gateway is planned to reside in a southern L2 NRHO in a 9:2 resonance with the lunar synodic period. The 9:2 NRHO is characterized by a period of about 6.5 days, a perilune radius of about 3,500 km, and an apolune radius of about 71,000 km; it is strongly affected by the gravity of both the Earth and the Moon simultaneously. This NRHO offers extended communications with assets on the south pole of the Moon,4 as well as low-cost orbit maintenance and attitude control,5 favorable eclipse avoidance properties,6 and inexpensive transfers from Earth and to other destinations.5,7 The NRHO portion of the southern L2 halo family is highlighted in black in Figure 1, and the 9:2 NRHO appears in blue.

Phillips, Sean M.↗

NASA NTRS1992

Minimum impulse trajectories for Mars round trip missions

Data are presented for minimum-impulse earth-Mars round-trip trajectories for the 2010 to 2027 Mars launch opportunities. Round-trip mission times from 120 to 600 days, including a 30-day rendezvous at Mars, for direct trajectories and trajectories utilizing a Venus gravitational assist are considered. Optimal planetary launch and arrival dates and total impulse requirements are based on all maneuvers being performed propulsively with no finite burn or other losses. Direct trajectories have the lowest impulse requirements for shorter mission times and Venus gravitational assist trajectories have the lowest impulse requirements for longer mission times. It is shown that one can depart on trajectories to Mars, beginning with lower energy trajectories to the moon. The fuel savings varies, depending on the final energy level required and on the swingby procedure used. Procedures discussed include single lunar swingbys, double-powered or unpowered lunar swingbys, third lunar flybys a year later, and gravity assists by Venus and earth after the final lunar swingby.

Horvat, Glen M.↗

NASA NTRS2004

Gravitational Wave Detection on the Moon and the Moons of Mars

The Moon and the moons of Mars should be extremely quiet seismically and could therefore become sensitive gravitational wave detectors, if instrumented properly. Highly sensitive displacement sensors could be deployed on these planetary bodies to monitor the motion induced by gravitational waves. A superconducting displacement sensor with a 10-kg test mass cooled to 2 K will have an intrinsic instrument noise of 10(exp -16) m Hz(exp -1/2). These sensors could be tuned to the lowest two quadrupole modes of the body or operated as a wideband detector below its fundamental mode. An interesting frequency range is 0.1 to approx. 1 Hz, which will be missed by both the ground detectors on the Earth and LISA and would be the best window for searching for stochastic background gravitational waves. Phobos and Deimos have their lowest quadrupole modes at 0.2 to approx. 0.3 Hz and could offer a sensitivity h(sub min) = 10(exp -22) Hz(exp -1/2) within their resonance peaks, which is within two orders of magnitude from the goal of the Big Bang Observer (BBO). The lunar and Martian moon detectors would detect many interesting foreground sources in a new frequency window and could serve as a valuable precursor for BBO.

Paik, Ho Jung↗

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 NTRS2008

Science on the Moon: The Wailing Wall of Space Exploration

Science on and from the Moon has important implications for expanding human knowledge and understanding, a prospect for the 21st Century that has been under discussion for at least the past 25 years. That having been said, however, there remain many issues of international versus national priorities, strategy, economy, and politics that come into play. The result is a very complex form of human behavior where science and exploration take center stage, but many other important human options are sacrificed. To renew this dialogue about the Moon, it seems we are already rushing pell-mell into it as has been done in the past. The U.S., Japan, China, India, and Russia either have sent or plan to send satellites and robotic landers there at this time. What does a return to the Moon mean, why are we doing this now, who should pay for it, and how? The only semblance of such a human enterprise seems to be the LHC currently coming online at CERN. Can it be used as a model of international collaboration rather than a sports or military event focused on national competition? Who decides and what is the human sacrifice? There are compelling arguments for establishing science on the Moon as one of the primary goals for returning to the Moon and venturing beyond. A number of science endeavors will be summarized, beyond lunar and planetary science per se. These include fundamental physics experiments that are background-limited by the Earth's magnetic dipole moment and noise produced by its atmosphere and seismic interior. The Moon is an excellent platform for some forms of astronomy. Other candidate Moon-based experiments vary from neutrino and gravitational wave astronomy, particle astrophysics, and cosmic-ray calorimeters, to space physics and fundamental physics such as proton decay. The list goes on and includes placing humans in a hostile environment to study the long-term effects of space weather. The list is long, and even newer ideas will come from this COSPAR conference. However, whatever the list the issue of cooperation and binding collaboration remains. As observers of Moon and other space enterprises, we all know that a room full of 60 scientists will not agree on much of anything and there will probably be 60! please for more funding. People have special interests and little common sense (e.g., conflict between NSF- and NASA-funding roadmaps). Scientists are no exception. Nevertheless, CERN has done it on Earth! Can we do the same on the Moon? Some of the present generation of proposals for science from and on the Moon, plus new ones, will witness a place in space exploration's future. It is clear, however, that the world has not thought this through adequately, except for talk about an international space federation whatever that is. An outpost on the Moon with humans permanently living there much like Antarctica on Earth may be in our future. However, such planning is our collective international responsibility and not that of special-interest investigators from individual nations unless they intend to pay for it.

Wilson, Thomas↗

NASA NTRS2011

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.

Scott, James R.↗

NASA NTRS1972

An analytic guidance technique for planetary and lunar approach trajectories.

An explicit, analytic guidance technique is developed for the hyperbolic approach phases of interplanetary and lunar spacecraft trajectories. The guidance technique is based upon a first-order analytic solution for the perturbed planet-centered (or moon-centered) trajectory. This trajectory is represented as the sum of two components: (1) the unperturbed osculating hyperbola at pericenter, and (2) first-order position and velocity perturbations due to gravitational effects of the sun and other planets. A closed-form analytic approximation for these perturbations valid for the entire approach trajectory is derived, thereby eliminating the need for numerical integration of the equations of motion. By means of this analytic trajectory model, the approach guidance problem is reduced to an equivalent two-body problem. The guidance objectives are specified in terms of actual, attainable conditions at pericenter, and the required corrective velocity is determined explicitly for both fixed and variable times of arrival.

Carlson, N. A.↗

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.↗

NASA NTRS1976

The asymmetric distribution of lunar maria and the earth's gravity

The paper investigates the hypothesis that the asymmetry of the moon with respect to the distribution of maria, reflected in that the surface area of the moon covered by mare material is far greater on the earth-facing side than on the far side, is due to the action of the earth's gravity at a time when the moon was less distant from the earth than today. Such conditions would lead to gravitationally favored areas on the moon such that mare basalt magmas might erupt preferentially on the front side of the moon. Gravitational asymmetry is also discussed in terms of its effect on the shape of the moon, its center of mass, its moments of inertia, and the time scale for the evolution of its orbit.

Hartung, J. B.↗

NASA NTRS2020

Evidence for a Stratified Upper Mantle Preserved within the South Pole - Aitken Basin

The evolution and compositional structure of the lunar mantle has been extensively modeled but insufficiently constrained by observations. Here, we identify and characterize mantle materials exposed by the Moon's largest impact basin to better understand the composition, stratigraphy, and evolution of the upper mantle. The vast South Pole-Aitken Basin (SPA) exhibits a broad, crescent-shaped thorium and potassium distribution. These incompatible elements are predicted to be concentrated in the dregs of the lunar magma ocean during end-stage crystallization. Through consideration of basin formation models convolved with subsequent geologic evolution, we demonstrate that the distribution and implied stratigraphy of Th- and K-bearing materials across SPA are consistent with an upper mantle ejecta origin. The most pristine exposures of these materials are confined to northwest SPA and also exhibit elevated Ti and Fe (relative to the farside highlands) in association with a gabbronoritic mineralogy. This is consistent with latestage magma ocean assemblages predicted by petrologic models. In contrast, SPA impact melt derived from greater depths is associated with a low-Ca pyroxene-dominated assemblage. Together, these compositional patterns are evidence for a stratified ancient upper mantle. Importantly, the incompatible-element-enriched, ilmenite-bearing ferroan gabbronoritic cumulates evidently had not participated in gravitational overturn at the time of SPA formation. Contrary to recent hypotheses invoking nearside sequestration of incompatible elements to explain hemispherical differences in crustal building and volcanic resurfacing, it follows that incompatible elements were globally distributed in the magma ocean at the time of SPA formation.

Lunar dichotomy↗

NASA NTRSDate not supplied

Viability of Small Dimension Crew Quarters for Surface Habitation

It is possible that in the next twenty years NASA may fly crew quarters on twice as many spacecraft as it has in the past fifty years. In short, US experience with spacecraft crew quarters is limited and with few available standards to guide their design there is significant uncertainty facing spacecraft currently in development, several of which are also subject to substantial mass and volume challenges. Those spacecraft developments will face considerable pressure to minimize crew quarters size, including those intended for use on the lunar surface. Given that a crew quarters is the only space a crew member can call his or her own during missions that can last weeks to years in duration, providing an appropriate volume is especially important. This is even more critical when one considers the reality that all crew quarters flown to date have been smaller than minimum standards for US jail cells. This research will categorize functional capabilities of crew quarters and explore physical and virtual prototypes of small crew quarters that have attempted to include these capabilities. The Exploration Atmospheres Test at NASA Johnson Space Center represents the first opportunity to collect multi-day test data on crew quarters of this size in a gravitational environment. Intended to validate exploration prebreathe protocols, this test will house eight people inside a vacuum chamber that has been outfitted as a habitat prototype for twelve days. In addition to their other test activity, the crew will evaluate the acceptability of their crew quarters. This data will aid in establishing design guidelines for crew quarters in both short and long duration missions beyond low Earth orbit.

Crew Quarters↗

NASA NTRS2011

Method and Apparatus for the Quantification of Particulate Adhesion Forces on Various Substrates

Mitigation strategies for lunar dust adhesion have typically been limited to qualitative analysis. This technical memorandum describes the generation and operation of an adhesion testing device capable of quantitative assessment of adhesion forces between particulates and substrates. An aerosolization technique is described to coat a surface with a monolayer of particulates. Agitation of this surface, via sonication, causes particles to dislodge and be gravitationally fed into an optical particle counter. Experimentally determined adhesion force values are compared to forces calculated from van der Waals interactions and are used to calculate the work of adhesion using Johnson-Kendall-Roberts (JKR) theory. Preliminary results indicate that a reduction in surface energy and available surface area, through topographical modification, improve mitigation of particulate adhesion.

Wohl, Christopher J.↗

NASA NTRS2021

Marshall Space Flight Center Faculty Fellowship Program

The 2020 Marshall Aerospace Fellowship Program involved 11 faculty in the laboratories and departments at Marshall Space Flight Center and one faculty researcher working from Colorado. These faculty engineers and scientists worked with NASA collaborators on NASA projects, bringing new perspectives and solutions to bear. This Technical Memorandum is a compilation of nine research reports of the 2020 Marshall Aerospace Fellowship program, along with the Program Announcement (Appendix A) and the Program Description (Appendix B). The research affected the following five areas: (1) Materials (2) Spacecraft systems (3) Human-System Interactions (4) Vehicle systems (5) Space science Additive manufacturing was the single materials investigation during the summer of 2020. Spacecraft systems tasks dominated the fellows’ explorations: covering camera sensors for lunar surface mobility, a real-time system for navigation and mapping, flexible sensor modeling, and transmitter design for high data rate telemetry. One project concentrated on Human-System Interactions. Another fellow designed a model to predict heat leak into a cryogen tank, as in most vehicle systems. One of the scientists worked on a proposed space-based gravitational wave interferometer that will detect Galactic white dwarf binaries. Another space science fellow used a mature astrophysical code to synthesize galactic stellar populations. Our goal is to continue the Marshall Aerospace Program funded by Center project offices.

N. F. Six↗

NASA NTRS2023

Rapid transition from primary to secondary crust building on the Moon explained by mantle overturn

Geochronology indicates a rapid transition (tens of Myrs) from primary to secondary crust building on the Moon. The processes responsible for initiating secondary magmatism, however, remain in debate. Here we test the hypothesis that the earliest secondary crust (Mg-suite) formed as a direct consequence of density-driven mantle overturn, and advance 3D mantle convection models to quantify the resulting extent of lower mantle melting. Our modeling demonstrates that overturn of thin ilmenite-bearing cumulates ≤ 100 km triggers a rapid and short-lived episode of lower mantle melting which explains the key volume, geochronological, and spatial characteristics of early secondary crust building without contributions from other energy sources, namely KREEP (potassium, rare earth elements, phosphorus, radiogenic U, Th). Observations of globally distributed Mg-suite eliminate degree-1 overturn scenarios. We propose that gravitational instabilities in magma ocean cumulate piles are major driving forces for the onset of mantle convection and secondary crust building on differentiated bodies.

Moon↗

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 NTRS2015

Volcanism on Mars

Spacecraft exploration has revealed abundant evidence that Mars possesses some of the most dramatic volcanic landforms found anywhere within the solar system. How did a planet half the size of Earth produce volcanoes like Olympus Mons, which is several times the size of the largest volcanoes on Earth? This question is an example of the kinds of issues currently being investigated as part of the space-age scientific endeavor called "comparative planetology." This chapter summarizes the basic information currently known about volcanism on Mars. The volcanoes on Mars appear to be broadly similar in overall morphology (although, often quite different in scale) to volcanic features on Earth, which suggests that Martian eruptive processes are not significantly different from the volcanic styles and processes on Earth. Martian volcanoes are found on terrains of different age, and Martian volcanic rocks are estimated to comprise more than 50% of the Martian surface. This is in contrast to volcanism on smaller bodies such as Earth's Moon, where volcanic activity was mainly confined to the first half of lunar history (see "Volcanism on the Moon"). Comparative planetology supports the concept that volcanism is the primary mechanism for a planetary body to get rid of its internal heat; smaller bodies tend to lose their internal heat more rapidly than larger bodies (although, Jupiter's moon Io appears to contradict this trend; Io's intense volcanic activity is powered by unique gravitational tidal forces within the Jovian system; see "Volcanism on Io"), so that volcanic activity on Mars would be expected to differ considerably from that found on Earth and the Moon.

Mars↗