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NASA NTRS2006

13 Years of TOPEX/POSEIDON Precision Orbit Determination and the 10-fold Improvement in Expected Orbit Accuracy

Launched in the summer of 1992, TOPEX/POSEIDON (T/P) was a joint mission between NASA and the Centre National d Etudes Spatiales (CNES), the French Space Agency, to make precise radar altimeter measurements of the ocean surface. After the remarkably successful 13-years of mapping the ocean surface T/P lost its ability to maneuver and was de-commissioned January 2006. T/P revolutionized the study of the Earth s oceans by vastly exceeding pre-launch estimates of surface height accuracy recoverable from radar altimeter measurements. The precision orbit lies at the heart of the altimeter measurement providing the reference frame from which the radar altimeter measurements are made. The expected quality of orbit knowledge had limited the measurement accuracy expectations of past altimeter missions, and still remains a major component in the error budget of all altimeter missions. This paper describes critical improvements made to the T/P orbit time series over the 13-years of precise orbit determination (POD) provided by the GSFC Space Geodesy Laboratory. The POD improvements from the pre-launch T/P expectation of radial orbit accuracy and Mission requirement of 13-cm to an expected accuracy of about 1.5-cm with today s latest orbits will be discussed. The latest orbits with 1.5 cm RMS radial accuracy represent a significant improvement to the 2.0-cm accuracy orbits currently available on the T/P Geophysical Data Record (GDR) altimeter product.

Lemoine, F. G.↗
NASA NTRS2007

Comparison Between Simulated and Experimentally Measured Performance of a Four Port Wave Rotor

Performance and operability testing has been completed on a laboratory-scale, four-port wave rotor, of the type suitable for use as a topping cycle on a gas turbine engine. Many design aspects, and performance estimates for the wave rotor were determined using a time-accurate, one-dimensional, computational fluid dynamics-based simulation code developed specifically for wave rotors. The code follows a single rotor passage as it moves past the various ports, which in this reference frame become boundary conditions. This paper compares wave rotor performance predicted with the code to that measured during laboratory testing. Both on and off-design operating conditions were examined. Overall, the match between code and rig was found to be quite good. At operating points where there were disparities, the assumption of larger than expected internal leakage rates successfully realigned code predictions and laboratory measurements. Possible mechanisms for such leakage rates are discussed.

Paxson, Daniel E.↗
NASA NTRS2007

Analytical Approach Validation for the Spin-Stabilized Satellite Attitude

An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques and the satellite in an elliptical orbit. Assuming a quadripole model for the Earth s magnetic field, an analytical averaging method is applied to obtain the mean residual torque in every orbital period. The orbit mean anomaly is used to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that the residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft. The theory developed has been applied to the Brazilian s spin stabilized satellites, which are quite appropriated for verification and comparison of the theory with the data generated and processed by the Satellite Control Center of Brazil National Research Institute. The results show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of Brazil National Research Institute.

Zanardi, Maria Cecilia F. P. S.↗
NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗
NASA NTRS2007

SIM Planetquest Science and Technology: A Status Report

Optical interferometry will open new vistas for astronomy over the next decade. The Space Interferometry Mission (SIM-PlanetQuest), operating unfettered by the Earth's atmosphere, will offer unprecedented astrometric precision that promises the discovery of Earth-analog extra-solar planets as well as a wealth of important astrophysics. Results from SIM will permit the determination of stellar masses to accuracies of 2% or better for objects ranging from brown dwarfs through main sequence stars to evolved white dwarfs, neutron stars, and black holes. Studies of star clusters will yield age determinations and internal dynamics. Microlensing measurements will present the mass spectrum of the Milky Way internal to the Sun while proper motion surveys will show the Sun's orbital radius and speed. Studies of the Galaxy's halo component and companion dwarf galaxies permit the determination of the Milky Way's mass distribution, including its Dark Matter component and the mass distribution and Dark Matter component of the Local Group. Cosmology benefits from precision (1-2%) determination of distances to Cepheid and RR Lyrae standard candles. The emission mechanism of supermassive black holes will be investigated. Finally, radio and optical celestial reference frames will be tied together by an improvement of two orders of magnitude. Optical interferometers present severe technological challenges. The Jet Propulsion Laboratory, with the support of Lockheed Martin Advanced Technology Center (LM ATC) and Northrop Grumman Space Technology (NGST), has addressed these challenges with a technology development program that is now complete. The requirements for SIM have been satisfied, based on outside peer review, using a series of laboratory tests and appropriate computer simulations: laser metrology systems perform with 10 picometer precision; mechanical vibrations have been controlled to nanometers, demonstrating orders of magnitude disturbance rejection; and knowledge of component positions throughout the whole test assembly has been demonstrated to the required picometer level. Technology transfer to the SIM flight team is now well along.

astrometry↗
NASA NTRS2006

Three Decades of Precision Orbit Determination Progress, Achievements, Future Challenges and its Vital Contribution to Oceanography and Climate Research

Although satellite altimetry has been around for thirty years, the last fifteen beginning with the launch of TOPEX/Poseidon (TP) have yielded an abundance of significant results including: monitoring of ENS0 events, detection of internal tides, determination of accurate global tides, unambiguous delineation of Rossby waves and their propagation characteristics, accurate determination of geostrophic currents, and a multi-decadal time series of mean sea level trend and dynamic ocean topography variability. While the high level of accuracy being achieved is a result of both instrument maturity and the quality of models and correction algorithms applied to the data, improving the quality of the Climate Data Records produced from altimetry is highly dependent on concurrent progress being made in fields such as orbit determination. The precision orbits form the reference frame from which the radar altimeter observations are made. Therefore, the accuracy of the altimetric mapping is limited to a great extent by the accuracy to which a satellite orbit can be computed. The TP mission represents the first time that the radial component of an altimeter orbit was routinely computed with an accuracy of 2-cm. Recently it has been demonstrated that it is possible to compute the radial component of Jason orbits with an accuracy of better than 1-cm. Additionally, still further improvements in TP orbits are being achieved with new techniques and algorithms largely developed from combined Jason and TP data analysis. While these recent POD achievements are impressive, the new accuracies are now revealing subtle systematic orbit error that manifest as both intra and inter annual ocean topography errors. Additionally the construction of inter-decadal time series of climate data records requires the removal of systematic differences across multiple missions. Current and future efforts must focus on the understanding and reduction of these errors in order to generate a complete and consistent time series of improved orbits across multiple missions and decades required for the most stringent climate-related research. This presentation discusses the POD progress and achievements made over nearly three decades, and presents the future challenges, goals and their impact on altimetric derived ocean sciences.

Luthcke, Scott↗
NASA NTRS2008

System for Measuring Flexing of a Large Spaceborne Structure

An optoelectronic metrology system is used for determining the attitude and flexing of a large spaceborne radar antenna or similar structure. The measurements are needed for accurate pointing of the antenna and correction and control of the phase of the radar signal wavefront. The system includes a dual-field-of-view star tracker; a laser ranging unit (LRU) and a position-sensitive-detector (PSD)-based camera mounted on an optical bench; and fiducial targets at various locations on the structure. The fiducial targets are illuminated in sequence by laser light coupled via optical fibers. The LRU and the PSD provide measurements of the position of each fiducial target in a reference frame attached to the optical bench. During routine operation, the star tracker utilizes one field of view and functions conventionally to determine the orientation of the optical bench. During operation in a calibration mode, the star tracker also utilizes its second field of view, which includes stars that are imaged alongside some of the fiducial targets in the PSD; in this mode, the PSD measurements are traceable to star measurements.

Scharf, Daniel↗
NASA NTRS2009

Recent Enhancements To The FUN3D Flow Solver For Moving-Mesh Applications

An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been extended to handle general mesh movement involving rigid, deforming, and overset meshes. Mesh deformation is achieved through analogy to elastic media by solving the linear elasticity equations. A general method for specifying the motion of moving bodies within the mesh has been implemented that allows for inherited motion through parent-child relationships, enabling simulations involving multiple moving bodies. Several example calculations are shown to illustrate the range of potential applications. For problems in which an isolated body is rotating with a fixed rate, a noninertial reference-frame formulation is available. An example calculation for a tilt-wing rotor is used to demonstrate that the time-dependent moving grid and noninertial formulations produce the same results in the limit of zero time-step size.

Biedron, Robert T,↗
NASA NTRS2008

Parallel-Processing Software for Creating Mosaic Images

A computer program implements parallel processing for nearly real-time creation of panoramic mosaics of images of terrain acquired by video cameras on an exploratory robotic vehicle (e.g., a Mars rover). Because the original images are typically acquired at various camera positions and orientations, it is necessary to warp the images into the reference frame of the mosaic before stitching them together to create the mosaic. [Also see "Parallel-Processing Software for Correlating Stereo Images," Software Supplement to NASA Tech Briefs, Vol. 31, No. 9 (September 2007) page 26.] The warping algorithm in this computer program reflects the considerations that (1) for every pixel in the desired final mosaic, a good corresponding point must be found in one or more of the original images and (2) for this purpose, one needs a good mathematical model of the cameras and a good correlation of individual pixels with respect to their positions in three dimensions. The desired mosaic is divided into slices, each of which is assigned to one of a number of central processing units (CPUs) operating simultaneously. The results from the CPUs are gathered and placed into the final mosaic. The time taken to create the mosaic depends upon the number of CPUs, the speed of each CPU, and whether a local or a remote data-staging mechanism is used.

Klimeck, Gerhard↗
NASA NTRS2009

Effect of Space Radiation Processing on Lunar Soil Surface Chemistry: X-Ray Photoelectron Spectroscopy Studies

Current understanding of the chemistry and microstructure of the surfaces of lunar soil grains is dominated by a reference frame derived mainly from electron microscopy observations [e.g. 1,2]. These studies have shown that the outermost 10-100 nm of grain surfaces in mature lunar soil finest fractions have been modified by the combined effects of solar wind exposure, surface deposition of vapors and accretion of impact melt products [1,2]. These processes produce surface-correlated nanophase Feo, host grain amorphization, formation of surface patinas and other complex changes [1,2]. What is less well understood is how these changes are reflected directly at the surface, defined as the outermost 1-5 atomic monolayers, a region not easily chemically characterized by TEM. We are currently employing X-ray Photoelectron Spectroscopy (XPS) to study the surface chemistry of lunar soil samples that have been previously studied by TEM. This work includes modification of the grain surfaces by in situ irradiation with ions at solar wind energies to better understand how irradiated surfaces in lunar grains change their chemistry once exposed to ambient conditions on earth.

Dukes, C.↗
NASA NTRS2009

Simulation of an Isolated Tiltrotor in Hover with an Unstructured Overset-Grid RANS Solver

An unstructured overset-grid Reynolds Averaged Navier-Stokes (RANS) solver, FUN3D, is used to simulate an isolated tiltrotor in hover. An overview of the computational method is presented as well as the details of the overset-grid systems. Steady-state computations within a noninertial reference frame define the performance trends of the rotor across a range of the experimental collective settings. Results are presented to show the effects of off-body grid refinement and blade grid refinement. The computed performance and blade loading trends show good agreement with experimental results and previously published structured overset-grid computations. Off-body flow features indicate a significant improvement in the resolution of the first perpendicular blade vortex interaction with background grid refinement across the collective range. Considering experimental data uncertainty and effects of transition, the prediction of figure of merit on the baseline and refined grid is reasonable at the higher collective range- within 3 percent of the measured values. At the lower collective settings, the computed figure of merit is approximately 6 percent lower than the experimental data. A comparison of steady and unsteady results show that with temporal refinement, the dynamic results closely match the steady-state noninertial results which gives confidence in the accuracy of the dynamic overset-grid approach.

Lee-Rausch, Elizabeth M.↗
NASA NTRS2009

Icing Simulation

A grid block transformation scheme which allows the input of grids in arbitrary reference frames, the use of mirror planes, and grids with relative velocities has been developed. A simple ice crystal and sand particle bouncing scheme has been included.. Added an SLD splashing model based on that developed by William Wright for the LEWICE 3.2.2 software. A new area based collection efficiency algorithm will be incorporated which calculates trajectories from inflow block boundaries to outflow block boundaries. This method will be used for calculating and passing collection efficiency data between blade rows for turbo-machinery calculations.

Bidwell, Colin↗
NASA NTRS2009

Icing Branch Current Research Activities in Icing Physics

Current development: A grid block transformation scheme which allows the input of grids in arbitrary reference frames, the use of mirror planes, and grids with relative velocities has been developed. A simple ice crystal and sand particle bouncing scheme has been included. Added an SLD splashing model based on that developed by William Wright for the LEWICE 3.2.2 software. A new area based collection efficiency algorithm will be incorporated which calculates trajectories from inflow block boundaries to outflow block boundaries. This method will be used for calculating and passing collection efficiency data between blade rows for turbo-machinery calculations.

Vargas, Mario↗
NASA NTRS2009

Simulation of Attitude and Trajectory Dynamics and Control of Multiple Spacecraft

Agora software is a simulation of spacecraft attitude and orbit dynamics. It supports spacecraft models composed of multiple rigid bodies or flexible structural models. Agora simulates multiple spacecraft simultaneously, supporting rendezvous, proximity operations, and precision formation flying studies. The Agora environment includes ephemerides for all planets and major moons in the solar system, supporting design studies for deep space as well as geocentric missions. The environment also contains standard models for gravity, atmospheric density, and magnetic fields. Disturbance force and torque models include aerodynamic, gravity-gradient, solar radiation pressure, and third-body gravitation. In addition to the dynamic and environmental models, Agora supports geometrical visualization through an OpenGL interface. Prototype models are provided for common sensors, actuators, and control laws. A clean interface accommodates linking in actual flight code in place of the prototype control laws. The same simulation may be used for rapid feasibility studies, and then used for flight software validation as the design matures. Agora is open-source and portable across computing platforms, making it customizable and extensible. It is written to support the entire GNC (guidance, navigation, and control) design cycle, from rapid prototyping and design analysis, to high-fidelity flight code verification. As a top-down design, Agora is intended to accommodate a large range of missions, anywhere in the solar system. Both two-body and three-body flight regimes are supported, as well as seamless transition between them. Multiple spacecraft may be simultaneously simulated, enabling simulation of rendezvous scenarios, as well as formation flying. Built-in reference frames and orbit perturbation dynamics provide accurate modeling of precision formation control.

Stoneking, Eric T.↗
NASA NTRS2007

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗
NASA NTRS2010

Cascade and Dissipation of Solar Wind Turbulence at Electron Scales: Whistlers or Kinetic Alfv\'en Waves?

Over the past few decades, large-scales solar wind (SW) turbulence has been studied extensively, both theoretically and observationally. Observed power spectra of the low frequency turbulence, which can be described in the magnetohydrodynamic (MHD) limit, are shown to obey the Kolmogorov scaling, $k"{ -5/3 }$, down the local proton gyrofrequency ($C{ci} \sim O.l$-Hz). Turbulence at frequencies above $C{ci}$ has not been thoroughly investigated and remains far less well understood. Above $C{ ci}$ the spectrum steepens to $\sim f"{ -2.5}$ and a debate exists as to whether the turbulence has become dominated by dispersive kinetic Alfven waves (KA W) or by whistler waves, before it is dissipated at small scales, In a case study Sahraoui et al., PRL (2009) have reported the first direct determination of the dissipation range of solar wind turbulence near the electron gyroscale using the high resolution Cluster magnetic and electric field data (up to $10"2$-Hz in the spacecraft reference frame). Above the Doppler-shifted proton scale $C{\rho i}$ a new inertial range with a scaling $\sim f"{ -2.3}$ has been evidenced and shown to remarkably agree with theoretical predictions of a quasi-two-dimensional cascade into KA W turbulence. Here, we use a wider sample of data sets of small scale SW turbulence under different plasma conditions, and investigate under which physical criteria the KA W (or the whistler) turbulence may be observed to carry out the cascade at small scales, These new observations/criteria are compared to the predictions on the cascade and the (kinetic) dissipation from the Vlasov theory. Implications of the results on the heating problem of the solar wind will be discussed.

Sahraoui, Fouad↗
NASA NTRS2010

A Transportable Gravity Gradiometer Based on Atom Interferometry

A transportable atom interferometer-based gravity gradiometer has been developed at JPL to carry out measurements of Earth's gravity field at ever finer spatial resolutions, and to facilitate high-resolution monitoring of temporal variations in the gravity field from ground- and flight-based platforms. Existing satellite-based gravity missions such as CHAMP and GRACE measure the gravity field via precise monitoring of the motion of the satellites; i.e. the satellites themselves function as test masses. JPL's quantum gravity gradiometer employs a quantum phase measurement technique, similar to that employed in atomic clocks, made possible by recent advances in laser cooling and manipulation of atoms. This measurement technique is based on atomwave interferometry, and individual laser-cooled atoms are used as drag-free test masses. The quantum gravity gradiometer employs two identical atom interferometers as precision accelerometers to measure the difference in gravitational acceleration between two points (Figure 1). By using the same lasers for the manipulation of atoms in both interferometers, the accelerometers have a common reference frame and non-inertial accelerations are effectively rejected as common mode noise in the differential measurement of the gravity gradient. As a result, the dual atom interferometer-based gravity gradiometer allows gravity measurements on a moving platform, while achieving the same long-term stability of the best atomic clocks. In the laboratory-based prototype (Figure 2), the cesium atoms used in each atom interferometer are initially collected and cooled in two separate magneto-optic traps (MOTs). Each MOT, consisting of three orthogonal pairs of counter-propagating laser beams centered on a quadrupole magnetic field, collects up to 10(exp 9) atoms. These atoms are then launched vertically as in an atom fountain by switching off the magnetic field and introducing a slight frequency shift between pairs of lasers to create a moving rest frame for the trapped atoms. While still in this moving-frame molasses, the laser frequencies are further detuned from the atomic resonance (while maintaining this relative frequency shift) to cool the atom cloud's temperature to 2 K or below, corresponding to an rms velocity of less than 2 cm/s. After launch, the cold atoms undergo further state and velocity selection to prepare for atom interferometry. The atom interferometers are then realized using laser-induced stimulated Raman transitions to perform the necessary manipulations of each atom, and the resulting interferometer phase is measured using laser-induced fluorescence for state-normalized detection. More than 20 laser beams with independent controls of frequency, phase, and intensity are required for this measurement sequence. This instrument can facilitate the study of Earth's gravitational field from surface and air vehicles, as well as from space by allowing gravity mapping from a low-cost, single spacecraft mission. In addition, the operation of atom interferometer-based instruments in space offers greater sensitivity than is possible in terrestrial instruments due to the much longer interrogation times available in the microgravity environment. A space-based quantum gravity gradiometer has the potential to achieve sensitivities similar to the GRACE mission at long spatial wavelengths, and will also have resolution similar to GOCE for measurement at shorter length scales.

Yu, Nan↗
NASA NTRS2010

Inertia and Double Bending of Light from Equivalence

Careful examination of light paths in an accelerated reference frame, with use of Special Relativity, can account fully for the observed bending of light in a gravitational field, not just half of it as reported in 1911. This analysis also leads to a Machian formulation of inertia similar to the one proposed by Einstein in 1912 and later derived from gravitational field equations in Minkowsky Space by Sciama in 1953. There is a clear inference from equivalence that there is some type of inertial mass increase in a gravitational field. It is the purpose of the current paper to suggest that equivalence provides a more complete picture of gravitational effects than previously thought, correctly predicting full light bending, and that since the theory of inertia is derivable from equivalence, any theory based on equivalence must take account of it. Einstein himself clearly was not satisfied with the status of inertia in GRT, as our quotes have shown. Many have tried to account for inertia and met with less than success, for example Davidson s integration of Sciama s inertia into GRT but only for a steady state cosmology [10], and the Machian gravity theory of Brans and Dicke [11]. Yet Mach s idea hasn t gone away, and now it seems that it cannot go away without also disposing of equivalence.

Shuler, Robert L., Jr.↗