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51 records · Page 3

A Self-Stabilizing Hybrid Fault-Tolerant Synchronization Protocol

This paper presents a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. The strategy consists of two parts: first, converting Byzantine faults into symmetric faults, and second, using a proven symmetric-fault tolerant algorithm to solve the general case of the problem. A protocol (algorithm) is also present that tolerates symmetric faults, provided that there are more good nodes than faulty ones. The solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. The solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. A mechanical verification of a proposed protocol is also present. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period.

Malekpour, Mahyar R.

Euler study on porous transonic airfoils with a view toward multipoint design

Euler solutions for steady transonic flow (Free-stream Mach 0.63-0.8, alpha = 0-2 deg) over NACA 0012 and supercritical airfoils with solid as well as porous surfaces suggest porosity as a means to realize multipoint design for transonic airfoils. The porous surfaces extend over at least 90 percent of the chord. The porosity distribution is described by a modified sine wave with several amplitudes. Either connected or separated cavities are assumed to lie underneath the upper and lower surfaces. Applied to an NACA 0012 airfoil, porosity generally increases lift, in some instances by up to 65 percent. Porous NACA 0012 airfoils in supercritical flow yield reductions of an order of magnitude in wave drag at constant lift, compared to their solid counterpart. Making the surface of a supercritical airfoil permeable also leads to sizeable reductions in wave drag at constant lift for overspeed conditions. The discussion of the computed results addresses issues such as grid sensitivity and checks for systematic errors.

Hartwich, Peter M.

Estimating Soil Moisture from Satellite Microwave Observations

Cooperative research in microwave remote sensing between the Hydrological Sciences Branch of the NASA Goddard Space Flight Center and the Earth Sciences Faculty of the Vrije Universiteit Amsterdam began with the Botswana Water and Energy Balance Experiment and has continued through a series of highly successful International Research Programs. The collaboration between these two research institutions has resulted in significant scientific achievements, most notably in the area of satellite-based microwave remote sensing of soil moisture. The Botswana Program was the first joint research initiative between these two institutions, and provided a unique data base which included historical data sets of Scanning Multifrequency Microwave Radiometer (SN4NM) data, climate information, and extensive soil moisture measurements over several large experimental sites in southeast Botswana. These data were the basis for the development of new approaches in physically-based inverse modelling of soil moisture from satellite microwave observations. Among the results from this study were quantitative estimates of vegetation transmission properties at microwave frequencies. A single polarization modelling approach which used horizontally polarized microwave observations combined with monthly composites of Normalized Difference Vegetation Index was developed, and yielded good results. After more precise field experimentation with a ground-based radiometer system, a dual-polarization approach was subsequently developed. This new approach realized significant improvements in soil moisture estimation by satellite. Results from the Botswana study were subsequently applied to a desertification monitoring study for the country of Spain within the framework of the European Community science research programs EFEDA and RESMEDES. A dual frequency approach with only microwave data was used for this application. The Microwave Polarization Difference Index (MPDI) was calculated from 37 GHz data and used to derive the one-way canopy transmissivity. Using a simple radiative transfer model, this information was combined with horizontally polarized 6.6 GHz SMMR observations to derive a 9-year time series of soil moisture for all of Spain at a one quarter degree spatial scale. Both day and night SMMR observations were used independently, in order to check the consistency of the results. A first order Fourier Transform was performed on the mean monthly soil moisture values to identify major characteristics of time series such as trend, amplitude, and phase shift.

Owe, M.

Saving Space and Time: The Tractor That Einstein Built

In 1984, NASA initiated the Gravity Probe B (GP-B) program to test two unverified predictions of Albert Einstein s theory of general relativity, hypotheses about the ways space, time, light, and gravity relate to each other. To test these predictions, the Space Agency and researchers at Stanford University developed an experiment that would check, with extreme precision, tiny changes in the spin direction of four gyroscopes contained in an Earth satellite orbiting at a 400-mile altitude directly over the Earth s poles. When the program first began, the researchers assessed using Global Positioning System (GPS) technology to control the attitude of the GP-B spacecraft accurately. At that time, the best GPS receivers could only provide accuracy to nearly 1 meter, but the GP-B spacecraft required a system 100 times more accurate. To address this concern, researchers at Stanford designed high-performance, attitude-determining hardware that used GPS signals, perfecting a high-precision form of GPS called Carrier-Phase Differential GPS that could provide continuous real-time position, velocity, time, and attitude sensor information for all axes of a vehicle. The researchers came to the realization that controlling the GP-B spacecraft with this new system was essentially no different than controlling an airplane. Their thinking took a new direction: If this technology proved successful, the airlines and the Federal Aviation Administration (FAA) were ready commercial markets. They set out to test the new technology, the "Integrity Beacon Landing System," using it to automatically land a commercial Boeing 737 over 100 times successfully through Real-Time Kinematic (RTK) GPS technology. The thinking of the researchers shifted again, from automatically landing aircraft, to automating precision farming and construction equipment.

Source record

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power 'leakage'. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of 568 +/- 10 days and a l/f(exp 3) power-law noise component in pulse phase with a noise strength S(sub infinity)=(1.24 +/- 0.067) x 10(exp 16) cycles(exp 2)/sec(exp 2) over the analysis frequency range f=0.003- 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either l/f(sub 4) power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 +/- 2.4) x 10(exp -16) solar mass and a companion mass, M(sub c) is greater than or equal to 3.2 solar mass assuming a Crab pulsar mass of 1.4 solar mass.

Scott, D. M.

Space Shuttle Dynamic Integrated Tests - Concept and results for STS-1

It is pointed out that ground tests, which involve end-to-end checks of various subsystems often by stimulating an input device and examining the resultant effect, do not exercise dynamically all subsystem interactions encountered during a real flight. The development and implementation of the Dynamic Integrated Test (DIT) for the Space Transportation System, patterned on the ASIST (Avionics System Integration Self Test) concept, are examined. It is noted that the complete hardware-software data paths which are utilized in flight simply do not exist until the vehicle is assembled. The integrated test is considered necessary in order to verify the integrity of these paths, that is, to establish that proper connections have been made, that correct polarity is maintained, and that no unexpected interference is generated. As a result of four tests carried out on the Space Transportation System, hardware and software problems, both on-board the vehicle and within the launch support complex, were identified and resolved. Significant return was also realized in the training of the launch and flight crews.

Brody, S.

Formal verification of algorithms for critical systems

We describe our experience with formal, machine-checked verification of algorithms for critical applications, concentrating on a Byzantine fault-tolerant algorithm for synchronizing the clocks in the replicated computers of a digital flight control system. First, we explain the problems encountered in unsynchronized systems and the necessity, and criticality, of fault-tolerant synchronization. We give an overview of one such algorithm, and of the arguments for its correctness. Next, we describe a verification of the algorithm that we performed using our EHDM system for formal specification and verification. We indicate the errors we found in the published analysis of the algorithm, and other benefits that we derived from the verification. Based on our experience, we derive some key requirements for a formal specification and verification system adequate to the task of verifying algorithms of the type considered. Finally, we summarize our conclusions regarding the benefits of formal verification in this domain, and the capabilities required of verification systems in order to realize those benefits.

Rushby, John M.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Buttrill, Carey S.

What would it take to manufacture perovskite solar cells in space?

Imagine, astronauts land on the moon. They verify their arrival with mission control, and perform system checks and validations. After the dust settles, they open the airlock of the landing vehicle and venture outside. A side hatch opens, and a flexible substrate slowly unfurls on a boom. A series of printer heads raster, hovering over the substrate and sequentially vapor-depositing the constituent layers of a perovskite solar module (Figure 1). In time, a 1-megawatt array has been manufactured on the moon and can now be connected to supply power to the Artemis Base Camp. This ambitious vision could someday become a reality. On August 29, 2021, a SpaceX Falcon 9 rocket launched a commercial resupply payload from Kennedy Space Center en route to the International Space Station (ISS). On board were perovskite solar cells that will fly for 6 months outside the ISS in low earth orbit (LEO) on the 15th Materials International Space Station Experiment (MISSE-15). This will be the first long duration flight of perovskite solar cell devices in LEO and a major step toward realizing the in-space operation and, potentially, manufacture of perovskite solar cells.

Lyndsey McMillon-Brown

Sensitivity of the Tropical Atmosphere Energy Balance to ENSO-Related SST Changes: How Well Can We Quantify Hydrologic and Radiative Responses?

The continuing debate over feedback mechanisms governing tropical sea surface temperatures (SSTs) and tropical climate in general has highlighted the diversity of potential checks and balances within the climate system. Competing feedbacks due to changes in surface evaporation, water vapor, and cloud long- and shortwave radiative properties each may serve critical roles in stabilizing or destabilizing the climate system. It is also intriguing that even those climate variations having origins internal to the climate system-- changes in ocean heat transport for example, apparently require complementary equilibrating effects by changes in atmospheric energy fluxes. Perhaps the best observational evidence of this is the relatively invariant nature of tropically averaged net radiation exiting the top-of-atmosphere (TOA) as measured by broadband satellite sensors over the past two decades. Thus, analyzing how these feedback mechanisms are operating within the context of current interannual variability may offer considerable insight for anticipating future climate change. In this paper we focus on how fresh water and radiative fluxes over the tropical oceans change during ENSO warm and cold events and how these changes affect the tropical energy balance. At present, ENSO remains the most prominent known mode of natural variability at interannual time scales. Although great advances have been made in understanding this phenomenon and realizing prediction skill over the past decade, our ability to document the coupled water and energy changes observationally and to represent them in climate models seems far from settled (Soden, 2000 J Climate). Our analysis makes use a number of data bases, principally those derived from space-based measurements, to explore systematic changes in rainfall, evaporation, and surface and top-of-atmosphere (TOA) radiative fluxes, A reexamination of the Langley 8-Year Surface Radiation Budget data set reveals errors in the surface longwave emission due to use of biased SSTs. Subsequent correction allows subsequent use of this data set along with ERBE TOA fluxes to infer net atmospheric radiative beating. Further analysis of recent rainfall algorithms provides new estimates for precipitation variability in line with interannual evaporation changes inferred from the da Silva, Young, Levitus COADS analysis. The overall results from our analysis suggest an increase (decrease) of the hydrologic cycle during ENSO warm (cold) events at the rate of about 5 Wm-2 per K of SST change. This rate is slightly less than that which would be expected for constant relative humidity over the tropical oceans. Corresponding radiative fluxes seem systematically smaller resulting in a enhanced (suppressed) export of energy from the tropical ocean regions during warm (cold) SST events. Discussion of likely errors due to sampling and measurement strategies are discussed along with their impacts on our conclusions.

Robertson, Franklin R.

Miniature Sapphire Acoustic Resonator - MSAR

A room temperature sapphire acoustics resonator incorporated into an oscillator represents a possible opportunity to improve on quartz ultrastable oscillator (USO) performance, which has been a staple for NASA missions since the inception of spaceflight. Where quartz technology is very mature and shows a performance improvement of perhaps 1 dB/decade, these sapphire acoustic resonators when integrated with matured quartz electronics could achieve a frequency stability improvement of 10 dB or more. As quartz oscillators are an essential element of nearly all types of frequency standards and reference systems, the success of MSAR would advance the development of frequency standards and systems for both groundbased and flight-based projects. Current quartz oscillator technology is limited by quartz mechanical Q. With a possible improvement of more than x 10 Q with sapphire acoustic modes, the stability limit of current quartz oscillators may be improved tenfold, to 10(exp -14) at 1 second. The electromagnetic modes of sapphire that were previously developed at JPL require cryogenic temperatures to achieve the high Q levels needed to achieve this stability level. However sapphire fs acoustic modes, which have not been used before in a high-stability oscillator, indicate the required Q values (as high as Q = 10(exp 8)) may be achieved at room temperature in the kHz range. Even though sapphire is not piezoelectric, such a high Q should allow electrostatic excitation of the acoustic modes with a combination of DC and AC voltages across a small sapphire disk (approximately equal to l mm thick). The first evaluations under this task will test predictions of an estimated input impedance of 10 kilohms at Q = 10(exp 8), and explore the Q values that can be realized in a smaller resonator, which has not been previously tested for acoustic modes. This initial Q measurement and excitation demonstration can be viewed similar to a transducer converting electrical energy to mechanical energy and back. Such an electrostatic tweeter type excitation of a mechanical resonator will be tested at 5 MHz. Finite element calculation will be applied to resonator design for the desired resonator frequency and optimum configuration. The experiment consists of the sapphire resonator sandwiched between parallel electrodes. A DC+AC voltage can be applied to generate a force to act on a sapphire resonator. With the frequency of the AC voltage tuned to the sapphire resonator frequency, a resonant condition occurs and the sapphire Q can be measured with a high-frequency impedance analyzer. To achieve high Q values, many experimental factors such as vacuum seal, gas damping effects, charge buildup on the sapphire surface, heat dissipation, sapphire anchoring, and the sapphire mounting configuration will need attention. The effects of these parameters will be calculated and folded into the resonator design. It is envisioned that the initial test configuration would allow for movable electrodes to check gap spacing dependency and verify the input impedance prediction. Quartz oscillators are key components in nearly all ground- and space-based communication, tracking, and radio science applications. They play a key role as local oscillators for atomic frequency standards and serve as flywheel oscillators or to improve phase noise in high performance frequency and timing distribution systems. With ultra-stable performance from one to three seconds, an Earth-orbit or moon-based MSAR can enhance available performance options for spacecraft due to elimination of atmospheric path degradation.

Wang, Rabi T.

Diagnostic Techniques Used to Study Chemical-Vapor-Deposited Diamond Films

The advantages and utility of chemical-vapor-deposited (CVD) diamond as an industrial ceramic can only be realized if the price and quality are right. Until recently, this technology was of interest only to the academic and basic research community. However, interest has grown because of advances made by leading CVD diamond suppliers: 1) Reduction of the cost of CVD polycrystalline diamond deposition below $5/carat ($8/sq cm); 2) Installation of production capacity; 3) Epitaxial growth of CVD single-crystal diamond. Thus, CVD diamond applications and business are an industrial reality. At present, CVD diamond is produced in the form of coatings or wafers. CVD diamond film technology offers a broader technological potential than do natural and high-pressure synthetic diamonds because size, geometry, and eventually cost will not be as limiting. Now that they are cost effective, diamond coatings - with their extreme properties - can be used in a variety of applications. Diamond coatings can improve many of the surface properties of engineering substrate materials, including erosion, corrosion, and wear resistance. Examples of actual and potential applications, from microelectromechanical systems to the wear parts of diamond coatings and related superhard coatings are described. For example, diamond coatings can be used as a chemical and mechanical barrier for the space shuttles check valves, particularly on the guide pins and seat assemblies.

Miyoshi, Kazuhisa

Human Stability While Exercising on a VIS Device in Zero Gravity

BACKGROUND: A Vibration Isolation and Stabilization (VIS) system is being designed for use with the European Enhanced Exploration Exercise Device (E4D) [1]. The exercise bar is attached to cables that extend and retract through openings in the E4D platform, which the subject stands on while exercising. Since the E4D is mounted on a moving VIS device, the whole system moves under the subject’s feet. While tension in the cables does help stabilize a crew member in 0g by bracing him or her against the moving platform, flexible cables do not offer full support against falling. This raises the question of whether various exercises that are successfully performed in 1g on a stationary device can be performed without losing balance in 0g on a moving device. Quantifying stability conditions and establishing stability requirements for exercise countermeasure systems is a long-standing challenge and this work helped to inform this specific need for integrated E4D/VIS flight project development. METHODS AND RESULTS: A simplified stability analysis can be attempted based on platform accelerations generated by the VIS device simulation. In this type of analysis, the subject is conceived as standing on the platform in 0g while being held down to it by the tension in the cables. If the sideways acceleration of the platform is such that the cables cannot generate a sufficient moment relative to, e.g., the heels or the toes of the subject to overcome the tipping moment from the inertial forces on the accelerated subject’s body, the subject becomes unstable. This approach, which we refer to as the ‘static’ approximation, indicated failure of all the exercises that were considered in the comprehensive VIS analysis of the E4D. It was realized, however, that platform accelerations are not externally imposed but are themselves induced by the motion of the subject’s body during exercise, and a model calculation confirmed that this drastically altered the tipping moment on the subject, with the potential to even switch the direction in which the body would tip over. This made it imperative to consider in a coupled manner both the motion of the exercising subject’s body and the induced VIS platform motion while considering stability. The coupled dynamics requirement was met by the VIS simulation incorporating time-dependent human mass properties atop the platform and driven by the inertial forces from the prescribed subject motion relative to the platform based on motion-capture recorded human trajectories in 1g on a stationary E4D [2]. To analyze simulation results, a stability criterion was also needed. We do not know how to account for the human ‘control system’ that would take visual and vestibular cues as inputs as the platform moves in 0g. We thus chose to follow an approach we had previously used to analyze the dynamic feasibility of performing a task in lunar gravity along the human body trajectory recorded in 1g [3]. In this approach, one analyzes the center of pressure (COP) between the shoes and the ground (or platform) and checks if the COP remains within the convex hull of the footprints on the ground (or platform), commonly referred to as base of support (BOS). Since pressure is vertical and, in the absence of foot restraints, positive, the COP going outside the BOS indicates that the trajectory recorded in 1g is not dynamically feasible in microgravity and/or on the moving platform of the device. The outcome of the COP-based analysis was that some of the key exercises, especially the deadlift and the back squat exercises, were found to be dynamically feasible for at least some number of the exercise cycles, this number increasing with the cable tension. While this type of stability analysis does not account for the likely alteration of the exercise trajectory from its 1g form in space, it does show that there exist at least some realistic trajectories that pass the dynamic feasibility criterion. This adds confidence that, with further adjustment by the subject of the exercise form in 0g on a moving device, a number of exercises can be performed without losing balance.

D Frenkel

NASA's Deep Space Network (DSN) Lunar Exploration Upgrades (DLEU)

In the near future, the National Aeronautics and Space Administration (NASA) will return to the moon beginning the next era of human exploration. NASA’s Space Communications and Navigation (SCaN) program will play a vital role in establishing communications and navigation support to realize the ambitious goals of the Artemis program. SCaN’s overall lunar communications support plan will be covered in a separate 2023 SpaceOps paper: “NASA’s Communications and Navigation Architecture Plans to Support the Return to the Moon and a Sustainable Lunar Presence”. The plan as it currently stands, includes a three-fold approach of lunar relay services, a dedicated set of new ground stations and support through the Deep Space Network (DSN). This paper will have a more granular focus on the DSN and NASA’s plans to upgrade and expand the network to be better suited for human spaceflight on and around the lunar surface. NASA’s Deep Space Network (DSN) will be a critical communications component for the upcoming lunar activities. There will be multiple spacecraft, using different bands, and some of those spacecraft will be transmitting and receiving using multiple bands, requiring DSN support of S-band (2 GHz), X-band (7 GHz up, 8 GHz down), and K-band (22.5 GHz up, 26 GHz down). Since there may be more than one spacecraft in the beamwidth of the DSN antennas, the DSN support will require an extension of the DSN’s capability to support multiple spacecraft using one antenna, expanding it to provide two simultaneous uplinks in the different bands at each antenna. Achieving this requires using new techniques for manufacturing the frequency selective surfaces, called dichroics, which steer the different frequency beams from and to the appropriate transmitting and receiving equipment, along with the addition of a new K-band uplink system. Additionally, due to the relative closeness of the moon from Earth (as opposed to the planetary missions the DSN supports daily), significantly higher data rates on both uplink and downlink are required, specifically up to 20 Mbps on the uplink and 150 Mbps on the downlink, both using Low Density Parity Check (LDPC) error correcting codes. And, again due to the relative closeness of the moon, there is a need for low latency data delivery of the high rate downlink telemetry which requires a change in the current DSN paradigm of delivering higher rate data with higher latency.

deep space network

NASA’s Deep Space Network (DSN) Lunar Exploration Upgrades (DLEU)

In the near future, the National Aeronautics and Space Administration (NASA) will returnhumansto the moon beginning the next era of human exploration. NASA’s Space Communications and Navigation (SCaN) program will play a vital role in establishing communications and navigation support to realize the ambitious goals of the Artemis program. SCaN’s overall lunar communications support plan will be covered in a separate 2023 SpaceOps paper: “NASA’s Communications and Navigation Architecture Plans to Support the Return to the Moon and a Sustainable Lunar Presence.” The four-point plan,as it currently stands, includes lunar relay services, a dedicated set of new ground stations, international partner contributions,and supportthrough the Deep Space Network (DSN)and associated upgrades. This paper will have a more granular focus on the DSN and NASA’s plans to upgrade and expand the network to be better suited for human spaceflight on and around the lunar surface. NASA’s Deep Space Network (DSN) will be a critical communications component for the upcoming lunar activities. There will be multiple spacecraft, using different bands, and some of those spacecraft will be transmitting and receiving using multiple bands, requiring DSN support of S-band (2 GHz), X-band (7 GHz up, 8 GHz down), and K-band (22.5 GHz up, 26 GHz down). Since there may be more than one spacecraft in the beamwidth of the DSN antennas, the DSN support will require an extension of the DSN’s capability to support multiple spacecraft using one antenna, expanding it to provide two simultaneous uplinks in the different bands at each antenna. Achieving this requires using new techniques for manufacturing the frequency selective surfaces, called dichroics, which steer the different frequency beams from and to the appropriate transmitting and receiving equipment, along with the addition of a new K-band uplink system. Additionally, due to the relative closeness of the moon from Earth (as opposed to the planetary missionsthe DSN supports daily), significantly higher data rates on both uplink and downlinkare requiredare possible and desirable by the lunar missions, specifically up to 20 Mbps on the uplink and 150 Mbps on the downlink, both using Low Density Parity Check (LDPC) error correcting codes. And, again due to the relative closeness of the moon, there is a need for low latency data delivery of the high rate downlink telemetry which requires a change in the current DSN paradigm of delivering higher rate data with higher latency.

Moon