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NASA NTRS1993

Control of nonlinear systems with applications to constrained robots and spacecraft attitude stabilization

This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude cannot be asymptotically stabilized using continuous feedback, but a discontinuous stabilizing feedback control strategy is constructed. If the uncontrolled principal axis is an axis of symmetry, the complete spacecraft dynamics cannot be stabilized. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but again a discontinuous feedback control strategy is constructed.

Krishnan, Hariharan↗

NASA NTRS1993

Experimental apparatus for optimization of flap position for a three-element airfoil model

It is proposed to design and build a wind tunnel model comprising a Douglas Aircraft Company three-element high-lift airfoil with internal actuators to move the flap vertically and horizontally under computer control. The model will be used to find the optimum flap location for a fixed angle of attack, slat position and flap deflection angle. The model will span the full tunnel width and lift will be measured by integration of pressure readings taken from midspan taps. It is proposed to conduct experiments in the NASA Langley EFPB 2' x 3' low speed wind tunnel. This report serves as a project overview and a review of work completed to date through funding by the 1993 NASA/ASEE Summer Faculty Fellowship Program.

Landman, Drew↗

NASA NTRS1994

A Supersonic Tunnel for Laser and Flow-Seeding Techniques

A supersonic wind tunnel with flow conditions of 3 lbm/s (1.5 kg/s) at a free-stream Mach number of 2.5 was designed and tested to provide an arena for future development work on laser measurement and flow-seeding techniques. The hybrid supersonic nozzle design that was used incorporated the rapid expansion method of propulsive nozzles while it maintained the uniform, disturbance-free flow required in supersonic wind tunnels. A viscous analysis was performed on the tunnel to determine the boundary layer growth characteristics along the flowpath. Appropriate corrections were then made to the contour of the nozzle. Axial pressure distributions were measured and Mach number distributions were calculated based on three independent data reduction methods. A complete uncertainty analysis was performed on the precision error of each method. Complex shock-wave patterns were generated in the flow field by wedges mounted near the roof and floor of the tunnel. The most stable shock structure was determined experimentally by the use of a focusing schlieren system and a novel, laser based dynamic shock position sensor. Three potential measurement regions for future laser and flow-seeding studies were created in the shock structure: deceleration through an oblique shock wave of 50 degrees, strong deceleration through a normal shock wave, and acceleration through a supersonic expansion fan containing 25 degrees of flow turning.

Bruckner, Robert J.↗

NASA NTRS1992

A new model for estimating total body water from bioelectrical resistance

Estimation of total body water (T) from bioelectrical resistance (R) is commonly done by stepwise regression models with height squared over R, H(exp 2)/R, age, sex, and weight (W). Polynomials of H(exp 2)/R have not been included in these models. We examined the validity of a model with third order polynomials and W. Methods: T was measured with oxygen-18 labled water in 27 subjects. R at 50 kHz was obtained from electrodes placed on the hand and foot while subjects were in the supine position. A stepwise regression equation was developed with 13 subjects (age 31.5 plus or minus 6.2 years, T 38.2 plus or minus 6.6 L, W 65.2 plus or minus 12.0 kg). Correlations, standard error of estimates and mean differences were computed between T and estimated T's from the new (N) model and other models. Evaluations were completed with the remaining 14 subjects (age 32.4 plus or minus 6.3 years, T 40.3 plus or minus 8 L, W 70.2 plus or minus 12.3 kg) and two of its subgroups (high and low) Results: A regression equation was developed from the model. The only significant mean difference was between T and one of the earlier models. Conclusion: Third order polynomials in regression models may increase the accuracy of estimating total body water. Evaluating the model with a larger population is needed.

Siconolfi, S. F.↗

NASA NTRS2001

The Magnitude and Variability of Global and Regional Precipitation Based on the 22-Year GPCP (Global Precipitation Climatology Project) and Three-Year TRMM (Tropical Rainfall Measuring Mission) Data Sets

This paper gives an overview of the analysis of global precipitation over the last few decades and the impact of the new TRMM precipitation observations. The 20+ year, monthly, globally complete precipitation analysis of the World Climate Research Program's (WCRP/GEWEX) Global Precipitation Climatology Project (GPCP) is used to study global and regional variations and trends and is compared to the much shorter TRMM (Tropical Rainfall Measuring Mission) tropical data set. The GPCP data set shows no significant trend in precipitation over the twenty years, unlike the positive trend in global surface temperatures over the past century. The global trend analysis must be interpreted carefully, however, because the inhomogeneity of the data set makes detecting a small signal very difficult, especially over this relatively short period. Identifying regional trends in precipitation may be more practical. From 1979 to 1999 the northern mid-latitudes appear to be drying, the southern mid-latitudes have gotten wetter, and there is a mixed signal in the tropics. The relation between this field of trends and the relation to the frequency of El Nino events during this time period is explored. Monthly anomalies of precipitation are related to ENSO variations with clear signals extending into middle and high latitudes of both hemispheres. The El Nino and La Nina mean anomalies are near mirror images of each other and when combined produce an ENSO signal with significant spatial continuity over large distances. These El Nino minus La Nina composites of normalized precipitation show the usual positive, or wet, anomaly over the central and eastern Pacific Ocean with the negative, or dry, anomaly over the maritime continent along with an additional negative anomaly over Brazil and the Atlantic Ocean extending into Africa and a positive anomaly over the Horn of Africa and the western Indian Ocean. A number of the features are shown to extend into high latitudes. Positive anomalies extend in the Southern Hemisphere (S.H.) from the Pacific southeastward across Chile and Argentina into the south Atlantic Ocean. In the Northern Hemisphere (N.H.) the counterpart feature extends across the southern US and Atlantic Ocean into Europe. Further to the west a negative anomaly extends southeastward again from the Maritime Continent across the South Pacific and through the Drake Passage. The N.H. counterpart crosses the North Pacific and southern Canada. In the Southern Hemisphere an anomaly feature is shown to spiral into the Antarctica land mass. The extremes of ENSO-related anomalies are also examined and indicate that globally, during both El Nino and La Nina, more extremes of precipitation ( both wet and dry) occur than during the "neutral" regime, with the El Nino regime showing larger magnitudes. The distribution is different for the globe as a whole and when the area is restricted to just land. The recent (1998-present) TRMM observations are compared with the similar period of GPCP analyses with very good agreement in terms of pattern and generally good agreement with regard to magnitude. However, there still are differences among the individual TRMM products using passive and active microwave techniques and these need to be resolved before longer-term products such as the GPCP analyses can be validated.

Adler, Robert F.↗

NASA NTRS2002

Global Precipitation Analyses at Time Scales of Monthly to 3-Hourly

Global precipitation analysis covering the last few decades and the impact of the new TRMM precipitation observations are discussed. The 20+ year, monthly, globally complete precipitation analysis of the World Climate Research Program's (WCRP/GEWEX) Global Precipitation Climatology Project (GPCP) is used to explore global and regional variations and trends and is compared to the much shorter TRMM (Tropical Rainfall Measuring Mission) tropical data set. The GPCP data set shows no significant trend in precipitation over the twenty years, unlike the positive trend in global surface temperatures over the past century. Regional trends are also analyzed. A trend pattern that is a combination of both El Nino and La Nina precipitation features is evident in the Goodyear data set. This pattern is related to an increase with time in the number of combined months of El Nino and La Nina during the Goodyear period. Monthly anomalies of precipitation are related to ENRON variations with clear signals extending into middle and high latitudes of both hemispheres. The GPCP daily, 1 degree latitude-longitude analysis, which is available from January 1997 to the present is described and the evolution of precipitation patterns on this time scale related to El Nino and La Nina is described. Finally, a TRMM-based Based analysis is described that uses TRMM to calibrate polar-orbit microwave observations from SSM/I and geosynchronous OR observations and merges the various calibrated observations into a final, Baehr resolution map. This TRMM standard product will be available for the entire TRMM period (January Represent). A real-time version of this merged product is being produced and is available at 0.25 degree latitude-longitude resolution over the latitude range from 50 deg. N -50 deg. S. Examples will be shown, including its use in monitoring flood conditions.

Adler, Robert F.↗

NASA NTRS2002

Global Precipitation Analyses (3-Hourly to Monthly) Using TRMM, SSM/I and other Satellite Information

Global precipitation analysis covering the last few decades and the impact of the new TRMM precipitation observations are discussed. The 20+ year, monthly, globally complete precipitation analysis of the World Climate Research Program's (WCRP/GEWEX) Global Precipitation Climatology Project (GPCP) is used to explore global and regional variations and trends and is compared to the much shorter TRMM(Tropical Rainfall Measuring Mission) tropical data set. The GPCP data set shows no significant trend in precipitation over the twenty years, unlike the positive trend in global surface temperatures over the past century. Regional trends are also analyzed. A trend pattern that is a combination of both El Nino and La Nina precipitation features is evident in the 20-year data set. This pattern is related to an increase with time in the number of combined months of El Nino and La Nina during the 20 year period. Monthly anomalies of precipitation are related to ENS0 variations with clear signals extending into middle and high latitudes of both hemispheres. The GPCP daily, 1 deg. latitude-longitude analysis, which is available from January 1997 to the present is described and the evolution of precipitation patterns on this time scale related to El Nino and La Nina is discussed. Finally, a TRMM-based 3-hr analysis is described that uses TRMM to calibrate polar-orbit microwave observations from SSM/I and geosynchronous IR observations and merges the various calibrated observations into a final, 3-hr resolution map. This TRMM standard product will be available for the entire TRMM period (January 1998-present). A real-time version of this merged product is being produced and is available at 0.25 deg. latitude-longitude resolution over the latitude range from 5O deg. N-50 deg. S. Examples are shown, including its use in monitoring flood conditions.

Adler, Robert F.↗

NASA NTRS1954

Wind-Tunnel Investigation at Subsonic and Supersonic Speeds of a Fighter Model Employing a Low-aspect-ratio Unswept Wing and a Horizontal Tail Mounted Well above the Wing Plane - Lateral and Directional Stability

The static lateral- and directional-stability characteristics of a high-speed fighter-type airplane, obtained from wind-tunnel tests of a model, are presented. The model consisted of a thin, unswept wing of aspect ratio 2.3 and taper ratio 0.385, a body, and a horizontal tail mounted in a high position on a vertical tail. Rolling-moment, yawing moment, and cross-wind-force coefficients are presented for a range of sideslip angles of -5 deg. to +5 deg, for Mach numbers of 0.90, 1.45, and 1.90. Data are presented which show the effects on the lateral and directional stability of: (1) component parts of the complete model, (2) modification of the empennage so as to provide different heights of the horizontal tail above the wing plane, (3) angle of attack, and (4) dihedral of the wing.

Wetzel, Benton E.↗

NASA NTRS1976

The formation of Saturn's satellites and rings, as influenced by Saturn's contraction history

The paper investigates constraints imposed on the ice content of Saturn's satellites and rings by the planet's high luminosity during the early part of its quasi-equilibrium contraction phase. It is assumed that the addition of ices to the satellites was not completed until after the start of the quasi-equilibrium contraction and that the condensation of ices ceased at the same time within the primordial nebulae of Jupiter and Saturn. Using previously derived limits on the time of condensation cessation for Jupiter's system, the following tentative conclusions are made: (1) Titan is the innermost satellite at whose position a methane-containing ice could condense; (2) water ice could have condensed at the positions of all the satellites; (3) the systematic decrease in the mass of the regular satellites with decreasing distance from the planet may have been caused, in part, by the larger time intervals, for the closer satellites, between the start of contraction and the first condensation of ices at their positions; and (4) ammonia ices, primarily NH4SH, were able to condense at the positions of all but the innermost satellites. It is also shown that water ice could have condensed in the region of the rings near the end of the condensation period.

Pollack, J. B.↗

NASA NTRS1993

Seasonal variation of surface and atmospheric cloud radiative forcing over the globe derived from satellite data

Global distributions of surface and atmospheric cloud radiative forcing parameters have been derived using parameterized radiation models with satellite meteorological data from the International Satellite Cloud Climatology Project, and directly measured top-of-atmosphere radiative fluxes from the Earth Radiation Budget Experiment. Specifically, shortwave, longwave, and total cloud forcing at the surface, and column-averaged values of longwave cloud forcing of the atmosphere were derived for the midseasonal months of April, July, and October 1985 and January 1986, covering a complete annual cycle. Seasonal variability is illustrated by comparing the results for July 1985 and January 1986, which represent the seasonal extremes. Surface shortwave cloud forcing is always negative, representing a cooling of the surface, with strongest cooling (-120 to -180 W/sq m) occurring over midlatitude storm tracks of the summer hemisphere. Surface longwave cloud forcing is always positive, representing a warming of the surface, with strongest warming (60 to 75 W/sq m) occurring over storm tracks of the winter hemisphere. Zonal averages show the entire summer hemisphere dominated by shortwave cooling, the middle and high latitudes of the winter hemisphere dominated by longwave warming, and a broad zone of transition in between. The globally averaged total cloud forcing amounts to a cooling throughout the year, ranging from a low of about -12 W/sq m for July 1985 to a high of about -25 W/sq m for January 1986. The longwave cloud forcing of the atmosphere shows a strong warming over deep convective regions in the tropics and a moderate cooling outside the tropics, amounting to a weak cooling (-2 to -5 W/sq m) in the global average. Comparisons of the results with general circulation model simulations show broad qualitative agreement regarding the locations of prominent warming and cooling regions. Quantitative comparisons, on the other hand, show significant differences between the magnitudes of warming and cooling in these regions. Most of the larger differences can be attributed to known deficiences of the general circulation model simulations. Comparisons with satellite-derived results of other investigators show much better agreement.

Gupta, Shashi K.↗

NASA NTRS1996

Development of a Large Scale, High Speed Wheel Test Facility

Draper Laboratory, with its internal research and development budget, has for the past two years been funding a joint effort with the Massachusetts Institute of Technology (MIT) for the development of a large scale, high speed wheel test facility. This facility was developed to perform experiments and carry out evaluations on levitation and propulsion designs for MagLev systems currently under consideration. The facility was developed to rotate a large (2 meter) wheel which could operate with peripheral speeds of greater than 100 meters/second. The rim of the wheel was constructed of a non-magnetic, non-conductive composite material to avoid the generation of errors from spurious forces. A sensor package containing a multi-axis force and torque sensor mounted to the base of the station, provides a signal of the lift and drag forces on the package being tested. Position tables mounted on the station allow for the introduction of errors in real time. A computer controlled data acquisition system was developed around a Macintosh IIfx to record the test data and control the speed of the wheel. This paper describes the development of this test facility. A detailed description of the major components is presented. Recently completed tests carried out on a novel Electrodynamic (EDS) suspension system, developed by MIT as part of this joint effort are described and presented. Adaptation of this facility for linear motor and other propulsion and levitation testing is described.

Kondoleon, Anthony↗

NASA NTRS1999

Virtual Manufacturing Techniques Designed and Applied to Manufacturing Activities in the Manufacturing Integration and Technology Branch

One of the identified goals of EM3 is to implement virtual manufacturing by the time the year 2000 has ended. To realize this goal of a true virtual manufacturing enterprise the initial development of a machinability database and the infrastructure must be completed. This will consist of the containment of the existing EM-NET problems and developing machine, tooling, and common materials databases. To integrate the virtual manufacturing enterprise with normal day to day operations the development of a parallel virtual manufacturing machinability database, virtual manufacturing database, virtual manufacturing paradigm, implementation/integration procedure, and testable verification models must be constructed. Common and virtual machinability databases will include the four distinct areas of machine tools, available tooling, common machine tool loads, and a materials database. The machine tools database will include the machine envelope, special machine attachments, tooling capacity, location within NASA-JSC or with a contractor, and availability/scheduling. The tooling database will include available standard tooling, custom in-house tooling, tool properties, and availability. The common materials database will include materials thickness ranges, strengths, types, and their availability. The virtual manufacturing databases will consist of virtual machines and virtual tooling directly related to the common and machinability databases. The items to be completed are the design and construction of the machinability databases, virtual manufacturing paradigm for NASA-JSC, implementation timeline, VNC model of one bridge mill and troubleshoot existing software and hardware problems with EN4NET. The final step of this virtual manufacturing project will be to integrate other production sites into the databases bringing JSC's EM3 into a position of becoming a clearing house for NASA's digital manufacturing needs creating a true virtual manufacturing enterprise.

Shearrow, Charles A.↗

NASA NTRS2001

Variations and Trends in Global and Regional Precipitation Based on the 22-Year GPCP (Global Precipitation Climatology Project) and Three-Year TRMM (Tropical Rainfall Measuring Mission) Data Sets

This paper gives an overview of the analysis of global precipitation over the last few decades and the impact of the new TRMM precipitation observations. The 20+ year, monthly, globally complete precipitation analysis of the World Climate Research Program's (WCRP/GEWEX) Global Precipitation Climatology Project (GPCP) is used to study global and regional variations and trends and is compared to the much shorter TRMM(Tropical Rainfall Measuring Mission) tropical data set. The GPCP data set shows no significant trend in global precipitation over the twenty years, unlike the positive trend in global surface temperatures over the past century. The global trend analysis must be interpreted carefully, however, because the inhomogeneity of the data set makes detecting a small signal very difficult, especially over this relatively short period. The relation of global (and tropical) total precipitation and ENSO events is quantified with no significant signal when land and ocean are combined. Identifying regional trends in precipitation may be more practical. From 1979 to 2000 the tropics have pattern of regional rainfall trends that has an ENSO-like pattern with features of both the El Nino and La Nina. This feature is related to a possible trend in the frequency of ENSO events (either El Nino or La Nina) over the past 20 years. Monthly anomalies of precipitation are related to ENSO variations with clear signals extending into middle and high latitudes of both hemispheres. The El Nino and La Nina mean anomalies are near mirror images of each other and when combined produce an ENSO signal with significant spatial continuity over large distances. A number of the features are shown to extend into high latitudes. Positive anomalies extend in the Southern Hemisphere (S.H.) from the Pacific southeastward across Chile and Argentina into the south Atlantic Ocean. In the Northern Hemisphere (N.H.) the counterpart feature extends across the southern U.S. and Atlantic Ocean into Europe. Further to the west a negative anomaly extends southeastward again from the Maritime Continent across the South Pacific and through the Drake Passage. In the Southern Hemisphere an anomaly feature is shown to spiral into the Antarctica land mass. The extremes of ENSO-related anomalies are also examined and indicate that globally, during both El Nino and La Nina, more extremes of precipitation (both wet and dry) occur than during the "neutral" regime, with the El Nino regime showing larger magnitudes. The distribution is different for the globe as a whole and when the area is restricted to just land. The recent (1998-present) TRMM observations are compared with the similar period of GPCP analyses with very good agreement in terms of pattern and generally good agreement with regard to magnitude. However, there still are differences among the individual TRMM products using passive and active microwave techniques and these need to be resolved before longer-term products such as the GPCP analyses can be validated.

Adler, Robert F.↗

NASA NTRS1998

Segmentation and tracking in echocardiographic sequences: active contours guided by optical flow estimates

This paper presents a method for segmentation and tracking of cardiac structures in ultrasound image sequences. The developed algorithm is based on the active contour framework. This approach requires initial placement of the contour close to the desired position in the image, usually an object outline. Best contour shape and position are then calculated, assuming that at this configuration a global energy function, associated with a contour, attains its minimum. Active contours can be used for tracking by selecting a solution from a previous frame as an initial position in a present frame. Such an approach, however, fails for large displacements of the object of interest. This paper presents a technique that incorporates the information on pixel velocities (optical flow) into the estimate of initial contour to enable tracking of fast-moving objects. The algorithm was tested on several ultrasound image sequences, each covering one complete cardiac cycle. The contour successfully tracked boundaries of mitral valve leaflets, aortic root and endocardial borders of the left ventricle. The algorithm-generated outlines were compared against manual tracings by expert physicians. The automated method resulted in contours that were within the boundaries of intraobserver variability.

Non-NASA Center↗

NASA NTRS2007

NASA GRC and MSFC Space-Plasma Arc Testing Procedures

Tests of arcing and current collection in simulated space plasma conditions have been performed at the NASA Glenn Research Center (GRC) in Cleveland, Ohio, for over 30 years and at the Marshall Space Flight Center (MSFC) in Huntsville, Alabama, for almost as long. During this period, proper test conditions for accurate and meaningful space simulation have been worked out, comparisons with actual space performance in spaceflight tests and with real operational satellites have been made, and NASA has achieved our own internal standards for test protocols. It is the purpose of this paper to communicate the test conditions, test procedures, and types of analysis used at NASA GRC and MSFC to the space environmental testing community at large, to help with international space-plasma arcing-testing standardization. Discussed herein are neutral gas conditions, plasma densities and uniformity, vacuum chamber sizes, sample sizes and Debye lengths, biasing samples versus self-generated voltages, floating samples versus grounded samples, test electrical conditions, arc detection, preventing sustained discharges during testing, real samples versus idealized samples, validity of LEO tests for GEO samples, extracting arc threshold information from arc rate versus voltage tests, snapover, current collection, and glows at positive sample bias, Kapton pyrolysis, thresholds for trigger arcs, sustained arcs, dielectric breakdown and Paschen discharge, tether arcing and testing in very dense plasmas (i.e. thruster plumes), arc mitigation strategies, charging mitigation strategies, models, and analysis of test results. Finally, the necessity of testing will be emphasized, not to the exclusion of modeling, but as part of a complete strategy for determining when and if arcs will occur, and preventing them from occurring in space.

Ferguson, Dale C.↗

NASA NTRS2015

3-D Printed Ultem 9085 Testing and Analysis

The purpose of this document is to analyze the mechanical properties of 3-D printed Ultem 9085. This document will focus on the capabilities, limitations, and complexities of 3D printing in general, and explain the methods by which this material is tested. Because 3-D printing is a relatively new process that offers an innovative means to produce hardware, it is important that the aerospace community understands its current advantages and limitations, so that future endeavors involving 3-D printing may be completely safe. This document encompasses three main sections: a Slosh damage assessment, a destructive test of 3-D printed Ultem 9085 samples, and a test to verify simulation for the 3-D printed SDP (SPHERES Docking Port). Described below, 'Slosh' and 'SDP' refer to two experiments that are built using Ultem 9085 for use with the SPHERES (Synchronized Position Hold, Engage, Reorient, Experimental Satellites) program onboard the International Space Station (ISS) [16]. The SPHERES Facility is managed out of the National Aeronautics and Space Administration (NASA) Ames Research Center in California.

Aguilar, Daniel↗

NASA NTRS2004

Improved Estimate of Phobos Secular Acceleration from MOLA Observations

We report on new observations of the orbital position of Phobos, and use them to obtain a new and improved estimate of the rate of secular acceleration in longitude due to tidal dissipation within Mars. Phobos is the inner-most natural satellite of Mars, and one of the few natural satellites in the solar system with orbital period shorter than the rotation period of its primary. As a result, any departure from a perfect elastic response by Mars in the tides raised on it by Phobos will cause a transfer of angular momentum from the orbit of Phobos to the spin of Mars. Since its discovery in 1877, Phobos has completed over 145,500 orbits, and has one of the best studied orbits in the solar system, with over 6000 earth-based astrometric observations, and over 300 spacecraft observations. As early as 1945, Sharpless noted that there is a secular acceleration in mean longitude, with rate (1.88 + 0.25) 10(exp -3) degrees per square year. In preparation for the 1989 Russian spacecraft mission to Phobos, considerable work was done compiling past observations, and refining the orbital model. All of the published estimates from that era are in good agreement. A typical solution (Jacobson et al., 1989) yields (1.249 + 0.018) 10(exp -3) degrees per square year. The MOLA instrument on MGS is a laser altimeter, and was designed to measure the topography of Mars. However, it has also been used to make observations of the position of Phobos. In 1998, a direct range measurement was made, which indicated that Phobos was slightly ahead of the predicted position. The MOLA detector views the surface of Mars in a narrow field of view, at 1064 nanometer wavelength, and can detect shadows cast by Phobos on the surface of Mars. We have found 15 such serendipitous shadow transit events over the interval from xx to xx, and all of them show Phobos to be ahead of schedule, and getting progressively farther ahead of the predicted position. In contrast, the cross-track positions are quite close to the predicted values. Assuming that the along-track discrepancy is small enough that we can linearize the corrections, we model the mean orbital longitude as a quadratic function of time, and solve for corrections to the constant, linear, and quadratic terms. The time span of the recent observations is insufficient to properly resolve this issue alone, but when the 127 years of prior observations are added, we find a solution which reduces misfit to the new observations considerably, and makes no significant change to the fit to earlier observations. Our estimate for the secular acceleration term is (1.367 + 0.006) degrees per square year. The corresponding rate of energy dissipation is 3.34 MW. From a geophysical perspective, a more interesting parameter than the secular acceleration itself is the tidal lag angle, or tidal quality factor Q, for Mars. Unfortunately, the limiting error source in that determination is remaining uncertainty in the tidal Love numbers at harmonic degrees 2,3, and even 4. Until those parameters are better constrained, improvement in the orbital model of Phobos will not provide corresponding benefits for understanding the interior of Mars.

Bills, Bruce↗

DOE OSTI2026

Causal horizons, geodesic completeness and stability in slow contraction cosmology

We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, flat or open slow contraction admits a stable past attractor that asymptotes to Minkowski space and is past geodesically complete, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde–Guth–Vilenkin theorem. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗