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Querying databases of trajectories of differential equations 2: Index functions

Suppose that a large number of parameterized trajectories (gamma) of a dynamical system evolving in R sup N are stored in a database. Let eta is contained R sup N denote a parameterized path in Euclidean space, and let parallel to center dot parallel to denote a norm on the space of paths. A data structures and indices for trajectories are defined and algorithms are given to answer queries of the following forms: Query 1. Given a path eta, determine whether eta occurs as a subtrajectory of any trajectory gamma from the database. If so, return the trajectory; otherwise, return null. Query 2. Given a path eta, return the trajectory gamma from the database which minimizes the norm parallel to eta - gamma parallel.

Grossman, Robert↗

Space Studies Board Annual Report, 2009

The year 2009 was one of transition for the nation, for NASA, and for the Space Studies Board (SSB). The nation pulled back from 2008's economic precipice, but did not return to the path of economic growth that it had been on. The United States inaugurated a new president who set out to build his administration. By mid-year President Obama had announced the appointment of Charlie Bolden as NASA administrator, and Lori Garver as deputy administrator. The president and Charlie Bolden jointly appointed an independent commission, the now well-known Augustine Commission, to provide guidance on the future of NASA's human spaceflight program. Many had known for quite a while that NASA's human spaceflight program faced a profound change at the time of the retirement of the space shuttle. This year was also a year of transition for the SSB. In 2009, Marcia Smith stepped down as staff director for both SSB and ASEB, and Dick Rowberg had a very good turn at the plate as a pinch-hitter. We are deeply indebted to both of them. We are pleased that, after a successful run as study director for Astro2010, Michael Moloney is now director of SSB and ASEB. The profound work begun in 2009 on the decadal surveys will only see the light of day later as they are released and the scientific work begins. The SSB will have much to report for 2010.

National Aeronautics and Space Administration(NASA↗

Advanced Sine Wave Modulation of Continuous Wave Laser System for Atmospheric CO2 Differential Absorption Measurements

NASA Langley Research Center in collaboration with ITT Exelis have been experimenting with Continuous Wave (CW) laser absorption spectrometer (LAS) as a means of performing atmospheric CO2 column measurements from space to support the Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) mission.Because range resolving Intensity Modulated (IM) CW lidar techniques presented here rely on matched filter correlations, autocorrelation properties without side lobes or other artifacts are highly desirable since the autocorrelation function is critical for the measurements of lidar return powers, laser path lengths, and CO2 column amounts. In this paper modulation techniques are investigated that improve autocorrelation properties. The modulation techniques investigated in this paper include sine waves modulated by maximum length (ML) sequences in various hardware configurations. A CW lidar system using sine waves modulated by ML pseudo random noise codes is described, which uses a time shifting approach to separate channels and make multiple, simultaneous online/offline differential absorption measurements. Unlike the pure ML sequence, this technique is useful in hardware that is band pass filtered as the IM sine wave carrier shifts the main power band. Both amplitude and Phase Shift Keying (PSK) modulated IM carriers are investigated that exibit perfect autocorrelation properties down to one cycle per code bit. In addition, a method is presented to bandwidth limit the ML sequence based on a Gaussian filter implemented in terms of Jacobi theta functions that does not seriously degrade the resolution or introduce side lobes as a means of reducing aliasing and IM carrier bandwidth.

Campbell, Joel F.↗

Lessons Learned from the Investigation of an Anomalous Termination of BETTII

The Balloon Experimental Twin Telescope for Infrared Interferometry (BETTII) mission launched from Palestine, Texas in June 2017. After an exciting launch and successful cruise, the BETTII gondola suffered an anomalous event at termination. BETTII separated from its parachute and free-fell 136,000 feet into the west Texas desert. This event was classified as a "close-call" and investigated as such. We present here the recovery effort required to find the payload and extract the payload from its impact site. We also present lessons learned from the event and results from the investigation, the design for the next BETTII gondola, and a path forward for return to flight.

Veach, Todd J.↗

Multiple Smaller Missions as a Direct Pathway to Mars Sample Return

Recent discoveries by the Mars Exploration Rovers, Mars Express, Mars Odyssey, and Mars Reconnaissance Orbiter spacecraft include multiple, tantalizing astrobiological targets representing both past and present environments on Mars. The most desirable path to Mars Sample Return (MSR) would be to collect and return samples from that site which provides the clearest examples of the variety of rock types considered a high priority for sample return (pristine igneous, sedimentary, and hydrothermal). Here we propose an MSR architecture in which the next steps (potentially launched in 2018) would entail a series of smaller missions, including caching, to multiple landing sites to verify the presence of high priority sample return targets through in situ analyses. This alternative architecture to one flagship-class sample caching mission to a single site would preserve a direct path to MSR as stipulated by the Planetary Decadal Survey, while permitting investigation of diverse deposit types and providing comparison of the site of returned samples to other aqueous environments on early Mars

Niles, P. B.↗

Atmospheric Multiple Scattering Effects on GLAS Altimetry: Calculations of Single Pulse Bias - Part 1

Estimates of the effect of pulse stretching on satellite laser altimetry in particular the Geoscience Laser Altimeter System (GLAS), by cloud multiple scattering were made from an analytical method and from Monte Carlo calculations. The path delay of the return pulse was found to be largest for low-level clouds with particle radii (3-20 microns). The magnitude of the path delay was affected by several factors including cloud height, cloud optical depth, cloud particle size, particle shape, and receiver field of view. Polar aerosol and Rayleigh scattering usually added less than 1 cm to the overall path delay. Path delay estimates for all cloud conditions would be less if a simple Gaussian fit of the return pulse peak were used to measure the pulse's centroid. However, care must be taken in determining the centroid as factors such as pulse width, surface slope and the fitting method used will affect the estimate. A planned application for laser altimetry is high precision monitoring of the height change of polar ice sheets. In the absence of a correction algorithm, the required GLAS altimetry accuracies will not be achieved unless atmospheric channel information is used to remove profiles that are likely to be heavily contaminated by multiple scattering.

Duda, David P.↗

Method and apparatus for reducing microwave oscillator output noise

Microwave oscilltors incorporate r.f. feedback with carrier suppression to reduce phase noise. In a direct feedback oscillator arrngement a circulator is interposed between the r.f. amplifier and the high-Q resonator. The amplifier output is applied to the slightly over-coupled input port of the resonator so that the resultant net return signal is the vectorial difference between the signals emitted and reflected from the resonator. The gain of the r.f. amplifier is chosen to regenerate the forward signal from the net return signal. In a STALO-type arrangement, the resonator is critically coupled and an r.f. amplifier added to the path of the net return signal. The sensitivity of the STALO-type feedback loop is thereby enhanced while added amplifier noise is minimized by the superposition of the signals emitted by and reflected from the resonator.

Dick, G. John↗

Microwave Radar Sensor Modules

Systems and methods for detecting biometrics using microwave radar sensor modules are disclosed. Integrated microwave sensor modules can include a transmitter unit configured to generate at least one continuous wave transmit signal based upon at least one frequency control signal, a receiver unit configured to utilize a cancellation path to cancel contributions to a return signal based upon at least one cancellation path control signal, and a microcontroller unit that includes a processor, a memory containing a microcontroller application, where the microcontroller application configures the processor to generate at least one frequency control signal to generate least one CW transmit signal having a plurality of frequencies, generate at least one cancellation path control signal to automatically adjust the cancellation path in real time, receive at least one demodulated signal, digitize the at least one demodulated signal, and update the at least one frequency control and cancellation path control signals.

Lux, James Paul↗

Evaluation of glide paths for landing a VTOL airplane using linear regulator theory.

A method of evaluating certain characteristics of approach paths for VTOL airplanes is presented which is based on the solution of the matrix Riccati equation to obtain an optimal state variable feedback controller. The longitudinal equations of motion of the airplane are linearized about a preselected path and the resulting system of equations is treated as a linear, time-varying regulator. The controller which minimizes a quadratic cost function is applied to the linearized system to determine the airplane's ability to return to the prescribed path given a specified initial error in altitude. The procedure is applied to the XC-142A, tilt-wing, V/STOL airplane, under decelerating approach conditions with a glide path consisting of two segments, the first having a smaller angle of descent than the second.

Reid, G. F.↗

A Martian Telecommunications Network: UHF Relay Support of the Mars Exploration Rovers by the Mars Global Surveyor, Mars Odyssey, and Mars Express Orbiters

NASA and ESA have established an international network of Mars orbiters, outfitted with relay communications payloads, to support robotic exploration of the red planet. Starting in January, 2004, this network has provided the Mars Exploration Rovers with telecommunications relay services, significantly increasing rover engineering and science data return while enhancing mission robustness and operability. Augmenting the data return capabilities of their X-band direct-to-Earth links, the rovers are equipped with UHF transceivers allowing data to be relayed at high rate to the Mars Global Surveyor (MGS), Mars Odyssey, and Mars Express orbiters. As of 21 July, 2004, over 50 Gbits of MER data have been obtained, with nearly 95% of that data returned via the MGS and Odyssey UHF relay paths, allowing a large increase in science return from the Martian surface relative to the X-band direct-to-Earth link. The MGS spacecraft also supported high-rate UHF communications of MER engineering telemetry during the critical period of entry, descent, and landing (EDL), augmenting the very low-rate EDL data collected on the X-band direct-to-Earth link. Through adoption of the new CCSDS Proximity-1 Link Protocol, NASA and ESA have achieved interoperability among these Mars assets, as validated by a successful relay demonstration between Spirit and Mars Express, enabling future interagency cross-support and establishing a truly international relay network at Mars.

telecommunications↗

Near Rectilinear Halo Orbit Determination with Simulated DSN Observations

This paper presents the results of a high-fidelity simulation of spacecraft orbit determination in a near rectilinear halo orbit (NRHO). Others in the literature have examined this problem with linear covariance analysis, but the highly-nonlinear dynamics of this orbit challenge the assumptions underlying such analyses. The present work builds on similar analysis performed by other authors to contribute a fuller understanding of the operational requirements for NRHO navigation. The present work serves as a check to the assumptions of previous studies and an independent verification of those results. The results from the literature are extended by quantifying the space of orbital states from which a spacecraft with given control authority can safely return to the nominal path. Spacecraft state uncertainty estimates are evaluated as a function of time. Simulated range and range-rate measurements with the Deep Space Network (DSN) ground stations are used to model orbit determination accuracy. Orbit maintenance maneuvers are performed using both short-horizon and long-horizon stationkeeping targeting. Monte Carlo analysis of orbit determination and stationkeeping is performed. This paper quantifies the achievable state uncertainty with deep space network (DSN)-only range and range-rate observations. This paper also addresses requirements on the frequency of DSN observation periods and correlates ground contact frequency with navigation accuracy. The results of several related studies are presented and discussed: the effect of missing ground station passes, the effect of missing stationkeeping maneuvers, the sensitivity of the spacecraft state estimate to realistic error sources, and stationkeeping propellant budget.

Nathan L Parrish↗

Hayabusa Re-Entry: Trajectory Analysis and Observation Mission Design

On June 13th, 2010, the Hayabusa sample return capsule successfully re-entered Earth s atmosphere over the Woomera Prohibited Area in southern Australia in its quest to return fragments from the asteroid 1998 SF36 Itokawa . The sample return capsule entered at a super-orbital velocity of 12.04 km/sec (inertial), making it the second fastest human-made object to traverse the atmosphere. The NASA DC-8 airborne observatory was utilized as an instrument platform to record the luminous portion of the sample return capsule re-entry (~60 sec) with a variety of on-board spectroscopic imaging instruments. The predicted sample return capsule s entry state information at ~200 km altitude was propagated through the atmosphere to generate aerothermodynamic and trajectory data used for initial observation flight path design and planning. The DC- 8 flight path was designed by considering safety, optimal sample return capsule viewing geometry and aircraft capabilities in concert with key aerothermodynamic events along the predicted trajectory. Subsequent entry state vector updates provided by the Deep Space Network team at NASA s Jet Propulsion Laboratory were analyzed after the planned trajectory correction maneuvers to further refine the DC-8 observation flight path. Primary and alternate observation flight paths were generated during the mission planning phase which required coordination with Australian authorities for pre-mission approval. The final observation flight path was chosen based upon trade-offs between optimal viewing requirements, ground based observer locations (to facilitate post-flight trajectory reconstruction), predicted weather in the Woomera Prohibited Area and constraints imposed by flight path filing deadlines. To facilitate sample return capsule tracking by the instrument operators, a series of two racetrack flight path patterns were performed prior to the observation leg so the instruments could be pointed towards the region in the star background where the sample return capsule was expected to become visible. An overview of the design methodologies and trade-offs used in the Hayabusa re-entry observation campaign are presented.

Cassell, Alan M.↗

Mars rover sample return missions

An important intermediate step in the path to human exploration of Mars is the accomplishment of a mission which lands an unmanned rover on the Martian surface, selects and collects various samples of the terrain and atmosphere, and returns them to earth for analysis. Such a mission is being developed under the management of NASA's JPL and the Johnson Space Center. The concepts for a wide range of rover capabilities are studied and an assessment of the driving technological developments required to implement these capabilities is made.

Cunningham, Glenn E.↗

Airborne radar and radiometer experiment for quantitative remote measurements of rain

An aircraft experiment has been conducted with a dual-frequency (10 GHz and 35 GHz) radar/radiometer system and an 18-GHz radiometer to test various rain-rate retrieval algorithms from space. In the experiment, which took place in the fall of 1988 at the NASA Wallops Flight Facility, VA, both stratiform and convective storms were observed. A ground-based radar and rain gauges were also used to obtain truth data. An external radar calibration is made with rain gauge data, thereby enabling quantitative reflectivity measurements. Comparisons between path attenuations derived from the surface return and from the radar reflectivity profile are made to test the feasibility of a technique to estimate the raindrop size distribution from simultaneous radar and path-attenuation measurements.

Kozu, Toshiaki↗

How typical is Halley's Comet?

Comet Halley spacecraft encounters and observations in 1985 to 1986 are compared to all c omets, both long and short-period. Halley's orbit is quite unusual for a short-period (SP) comet, characterized by a very small perihelion distance and a retrograde inclination. The comet is much brighter than most SP comets, and is even relatively bright for a long-period comet. Although Halley's orbit crosses the orbits of seven of the nine planets, it can currently make close approaches to only Venus, Earth, and Mars, planets likely too small to have played a major role in capturing Halley to a short-period orbit. This, and other evidence, suggests that Halley has been in its current orbit for many returns. A variety of dynamical paths for evolving Halley to its present orbit from either the inner or outer Oort clouds are possible, and thus only probabilistic arguments can be made as to the comet's past physical and dynamical history.

Weissman, Paul R.↗

Spiral Orbit Tribometry I: Description of the Tribometer

A new rolling contact tribometer based on a planar thrust bearing geometry is described. The bearing 'races' are flat plates that drive a ball into a near-circular, spiral path. The spiraling ball is returned to its initial radius each revolution around the race by a 'guide plate' backed by a force transducer. The motions of the ball are analyzed and the force exerted by the ball on the guide plate is related to the friction coefficient of the system. The experimental characteristics of the system are presented and the system is shown to exhibit the behavior expected for a tribometer.

Pepper, Stephen V.↗

Pupil Alignment Considerations for Large, Deployable Space Telescopes

For many optical systems the properties and alignment of the internal apertures and pupils are not critical or controlled with high precision during optical system design, fabrication or assembly. In wide angle imaging systems, for instance, the entrance pupil position and orientation is typically unconstrained and varies over the system s field of view in order to optimize image quality. Aperture tolerances usually do not receive the same amount of scrutiny as optical surface aberrations or throughput characteristics because performance degradation is typically graceful with misalignment, generally only causing a slight reduction in system sensitivity due to vignetting. But for a large deployable space-based observatory like the James Webb Space Telescope (JWST), we have found that pupil alignment is a key parameter. For in addition to vignetting, JWST pupil errors cause uncertainty in the wavefront sensing process that is used to construct the observatory on-orbit. Furthermore they also open stray light paths that degrade the science return from some of the telescope s instrument channels. In response to these consequences, we have developed several pupil measurement techniques for the cryogenic vacuum test where JWST science instrument pupil alignment is verified. These approaches use pupil alignment references within the JWST science instruments; pupil imaging lenses in three science instrument channels; and unique pupil characterization features in the optical test equipment. This will allow us to verify and crosscheck the lateral pupil alignment of the JWST science instruments to approximately 1-2% of their pupil diameters.

Bos, Brent J.↗

A Modular Atmospheric Propagation Program (MAPP)

A computer model of the atmosphere has been developed that will solve a wide variety of lidar and atmospheric propagation problems. The lidar system calculations involve the prediction of path loss and lidar signal return for a variety of atmospheric conditions and lidar system configurations. The program contains a very large data base of absorption and attenuation coefficients for all of the naturally occurring gases and several gaseous pollutants such as S02, N02, NO, N20, 03, HCL, etc. The spectral range of this data base extends from the ultra-violet (1200 angstroms) through the infra-red. Several aerosol models are included in the program to account for the effects of this important scattering mechanism.

Wright, M. L.↗