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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Observation of Gravitational Waves from Two Neutron Star-Black Hole Coalescences

We report the observation of gravitational waves from two compact binary coalescences in LIGO's and Virgo's third observing run with properties consistent with neutron star-black hole (NSBH) binaries. The two events are named GW200105_162426 and GW200115_042309, abbreviated as GW200105 and GW200115; the first was observed by LIGO Livingston and Virgo, and the second by all three LIGO-Virgo detectors. The source of GW200105 has component masses 8.9(exp +1.2/-1.5) M⨀ and 1.9(exp +0.3/-0.2) M⨀, whereas the source of GW200115 has component masses 5.7(exp +1.8/-2.1) M⨀ and 1.5(exp +0.7/-0.3) M⨀ (all measurements quoted at the 90% credible level). The probability that the secondary's mass is below the maximal mass of a neutron star is 89%-96% and 87%-98%, respectively, for GW200105 and GW200115, with the ranges arising from different astrophysical assumptions. The source luminosity distances are 280(exp +110/-110) Mpc and 300(+150/-100) Mpc, respectively. The magnitude of the primary spin of GW200105 is less than 0.23 at the 90% credible level, and its orientation is unconstrained. For GW200115, the primary spin has a negative spin projection onto the orbital angular momentum at 88% probability. We are unable to constrain the spin or tidal deformation of the secondary component for either event. We infer an NSBH merger rate density of 45(exp +75/-33) Gpc(exp -3) yr(exp -1) when assuming that GW200105 and GW200115 are representative of the NSBH population, or 130(+112/-69) Gpc(exp -3) yr(exp -1) under the assumption of a broader distribution of component masses.

R Abbott↗
NASA NTRS1989

Doppler measurements of an interplanetary satellite with a VLBI antenna

In preparation for the Ulysses Gravitational Wave Experiment a Doppler detector has been constructed for the Bologna VLBI antenna and tested in a differential mode with the spacecraft Voyager 2 at 25 AU. In this mode the signal was sent from the Deep Space Network station in Canberra and received at Madrid and Bologna. The correlation between the received signals allows a discrimination between local and common noise sources. The successful test was performed in August, 1988 showed that special communication procedure will have to be implemented to allow a smooth and reliable operation during the real experiment.

Gomoretto, G.↗
NASA NTRS2019

Multi-messenger Astrophysics with Pulsar Timing Arrays: Astro2020 Science White Paper

Pulsar timing arrays (PTAs) are on the verge of detecting low-frequency gravitational waves (GWs)from supermassive black hole binaries (SMBHBs). With continued observations of a large sampleof millisecond pulsars, PTAs will reach this major milestone within the next decade. Already,SMBHB candidates are being identied by electromagnetic surveys in ever-increasing numbers;upcoming surveys will enhance our ability to detect and verify candidates, and will be instrumentalin identifying the host galaxies of GW sources. Multi-messenger (GW and electromagnetic) obser-vations of SMBHBs will revolutionize our understanding of the co-evolution of SMBHs with theirhost galaxies, the dynamical interactions between binaries and their galactic environments, and thefundamental physics of accretion. Multi-messenger observations can also make SMBHBs `standardsirens' for cosmological distance measurements out to z ~ 0.5 LIGO has already ushered in break-through insights in our knowledge of black holes. The multi-messenger detection of SMBHBs withPTAs will be a breakthrough in the years 2020-2030 and beyond, and prepare us for LISA to helpcomplete our views of black hole demographics and evolution at higher redshifts.

Kelley, L. Z.↗
NASA NTRS1997

The Evolving Universe: Structure and Evolution of the Universe Roadmap 2000-2020

The Roadmap for the Structure and Evolution of the Universe (SEU) theme embraces three fundamental, scientific quests: (1) To explain structure in the Universe and forecast our cosmic destiny. (2) To explore the cycles of matter and energy in the evolving Universe. (3) To examine the ultimate limits of gravity and energy in the Universe. These quests are developed into six, focused research campaigns addressing the objectives of one or more quests: Identify dark matter and learn how it shapes galaxies and systems of galaxies; Find out where and when the chemical elements were made; Understand the cycles in which matter, energy, and magnetic field are exchanged between stars and the gas between stars; Discover how gas flows in disks and how cosmic jets are formed; Identify the sources of gamma-ray bursts and high-energy cosmic rays; and Measure how strong gravity operates near black holes and how it affects the early Universe. These campaigns lead to a portfolio of future major missions of strong scientific and popular appeal, strongly endorsed by the scientific community and which has undergone significant initial study. Some of these missions are in a state of readiness that makes ideal candidates for the present Office of Space Science Strategic Plan; others may well feature in the next Strategic Plan. Each provides a golden scientific opportunity to advance our understanding of the Universe. Our highest priority science objectives are addressed by five Observatory Class Missions, unranked by science, but in approximate order of readiness: A high-energy gamma-ray facility that will observe relativistic jets and study the sources of cosmic gamma ray bursts; An ultra-sensitive X-ray telescope, optimized for spectroscopy, to examine the hot gas linked with clusters of galaxies, the disks around black holes, and supernova explosions; A large, radio telescope in deep space to map central regions of distant quasars and perform astrometric investigations; An orbiting gravitational coalescing, massive black holes and test how gravity waves distort spacetime; A pair of Earth-orbiting, optical telescopes that will detect flashes of light produced when ultra high-energy cosmic rays impact the upper atmosphere so as to determine their arrival directions and energies. A new program for supporting pertinent international collaboration is strongly endorsed and maintaining a strong Explorer program is important. The flexibility to exploit exceptional opportunities, such as attaching payloads to space station, should also be acquired. A strong technology development program must be initiated now to enable this mission set.

Source record↗
NASA NTRS2008

LISA Pathfinder

USA Pathfinder is a space mission dedicated to demonstrating technology for the Laser Interferometer Space Antenna (LISA). LISA is a joint ESA/NASA mission to detect low-frequency gravitational waves on the 0.0001 to 0.1 Hz frequency band. LISA is expected to observe 100's of merging massive black hole binaries out z-15, tens of thousands of close compact binary systems in the Milky Way, merging intermediate-mass black hole binaries, tens of stellar-mass black holes falling into supermassive black holes in galactic centers, and possibly other exotic sources. Several critical LISA technologies have not been demonstrated at the requisite level of performance. In spaceflight, and some fight hardware cannot be tested in a 1-g environment. Hence, the LISA Pathfinder mission is being implemented to demonstrate these critical LISA technologies in a relevant flight environment. LISA Pathfinder mimics one arm of the LISA constellation by shrinking the 5-million-kilometer armlength down to a few tens of centimeters. The experimental concept is to measure the relative separation between two test masses nominally following their own geodesics, and thereby determine the relative residual acceleration between them near 1 mHz, about a decade above the lowest frequency required by LISA. To implement such a concept, disturbances on the test masses must be kept very small by many design features, but chiefly by "drag-free" flight. A drag-free spacecraft follows a free-falling test mass which it encloses, but has no mechanical connection to. The spacecraft senses it's orientation and separation with respect to the proof mass, and its propulsion system is commanded to keep the spacecraft centered about the test mass. Thus, the spacecraft shields the test mass from most external influences, and minimizes the effect of force gradients arising from the spacecraft, and acting on the test mass. LISA Pathfinder will compare the geodesic of one test mass against that of the other. Only a metrology system based on interferometry can achieve the displacement sensitivity. Interferometers monitor the separation of both test masses with a sensitivity comparable to that required by LISA, and using the same technologies. LISA Pathfinder is scheduled to be launched in the first half of 1020 to a Lissajous orbit around the first Sun-Earth Lagrange point, L1. In addition to a complete European technology package (the LISA Technology Package, or LTP), LISA Pathfinder will also carry thrusters and software, known as ST-7, a part of NASA's New Millennium Program.

Stebbins, Robin↗
NASA NTRS2022

Space Communications Responsive to Events Across Missions (SCREAM): An Investigation of Network Solutions for Transient Science Space Systems

Space Communications Responsive to Events Across Missions (SCREAM): An Investigation of Network Solutions for Transient Science Space Systems The National Academies have prioritized the pursuit of new scientific discoveries using diverse and temporally coordinated measurements from multiple ground and space-based observatories. Networked communications can enable such measurements by connecting individual observatories and allowing them to operate as a cohesive and purposefully designed system. Timely data flows across terrestrial and space communications networks are required to observe transient scientific events and processes. Currently, communications to space-based observatories experience large latencies due to manual service reservation and scheduling procedures, intermittent signal coverage, and network capacity constraints. If space communications network latencies could be reduced, new discoveries about dynamic scientific processes could be realized. However, science mission and network planners lack a systematic framework for defining, quantifying and evaluating timely space data flow implementation options for transient scientific observation scenarios involving multiple ground and space-based observatories. This dissertation presents a model-based systems engineering approach to investigate and develop network solutions to meet the needs of transient science space systems. First, a systematic investigation of the current transient science operations of the National Aeronautics and Space Administration’s (NASA) Tracking and Data Relay Satellite (TDRS) space data network and the Neil Gehrels Swift Observatory resulted in a formal architectural model for transient science space systems. Two methods individual missions may use to achieve timely network services were defined, quantitatively modeled, and experimentally compared. Next, the architectural model was extended to describe two alternative ways to achieve timely and autonomous space data flows to multiple space-based observatories within the context of a purposefully designed transient science observation scenario. A quantitative multipoint space data flow modeling method based in queueing theory was defined. General system suitability metrics for timeliness, throughput, and capacity were specified to support the evaluation of alternative network data flow implementations. A hypothetical design study was performed to demonstrate the multipoint data flow modeling method and to evaluate alternative data flow implementations using TDRS. The merits of a proposed future TDRS broadcast service to implement multipoint data flows were quantified and compared to expected outcomes using the as-built TDRS network. Then, the architectural model was extended to incorporate commercial network service providers. Quantitative models for Globalstar and Iridium short messaging data services were developed based on publicly available sources. Financial cost was added to the set of system suitability metrics. The hypothetical design study was extended to compare the relative suitability of the as-built TDRS network with the commercial Globalstar and Iridium networks. Finally, results from this research are being applied by NASA missions and network planners. In 2020, Swift implemented the first automated command pipeline, increasing its expected gravitational wave follow-up detection rate by greater than 400%. Current NASA technology initiatives informed by this research will enable future space-based observatories to become interoperable sensing devices connected by a diverse ecosystem of network service providers.

Christopher J. Roberts↗
NASA NTRS2012

Discovery of the Millisecond Pulsar PSR J2043+1711 in a Fermi Source with the Nancay Radio Telescope

We report the discovery of the millisecond pulsar PSR J2043+1711 in a search of a Fermi Large Area Telescope (LAT) source with no known associations, with the Nancay Radio Telescope. The new pulsar, confirmed with the Green Bank Telescope, has a spin period of 2.38 ms, is relatively nearby (d approx. < 2 kpc) and is in a 1.48-d orbit around a low-mass companion, probably an He-type white dwarf. Using an ephemeris based on Arecibo, Nancay and Westerbork timing measurements, pulsed gamma-ray emission was detected in the data recorded by the Fermi LAT. The gamma-ray light curve and spectral properties are typical of other gamma-ray millisecond pulsars seen with Fermi. X-ray observations of the pulsar with Suzaku and the Swift X-ray Telescope yielded no detection. At 1.4 GHz, we observe strong flux density variations because of interstellar diffractive scintillation; however, a sharp peak can be observed at this frequency during bright scintillation states. At 327 MHz, the pulsar is detected with a much higher signal-to-noise ratio and its flux density is far more steady. However, at that frequency the Arecibo instrumentation cannot yet fully resolve the pulse profile. Despite that, our pulse time-of-arrival measurements have a post-fit residual rms of 2 micro s. This and the expected stability of this system have made PSR J2043+1711 one of the first new Fermi-selected millisecond pulsars to be added to pulsar gravitational wave timing arrays. It has also allowed a significant measurement of relativistic delays in the times of arrival of the pulses due to the curvature of space-time near the companion, but not yet with enough precision to derive useful masses for the pulsar and the companion. Nevertheless, a mass for the pulsar between 1.7 and 2.0 solar Mass can be derived if a standard millisecond pulsar formation model is assumed. In this paper, we also present a comprehensive summary of pulsar searches in Fermi LAT sources with the Nancay Radio Telescope to date.

general aEuro" pulsars↗
NASA NTRS1981

Relativistic astrophysics - The view from Texas in Baltimore /Review/

Recent observational and theoretical work presented at the Tenth Texas Symposium on Relativistic Astrophysics held in Baltimore, Maryland from December 15-19, 1980, is outlined. Areas covered include the theoretical foundations of relativistic astrophysics in general relativity, quantum gravitational theory and the association of grand unification with astronomical and cosmological issues, the cosmic microwave, X-ray, gamma-ray, UV, cosmic ray and gravitational wave backgrounds, the current expansion rate and average mass-energy density of the universe, and mechanisms of galaxy formation. Also discussed are the characteristics of active galaxies and clusters emitting in the gamma-ray and X-ray regions, and compact objects formed from supernova explosions, including pulsars, X-ray-emitting neutron stars, Sco X-1 and SS 433, gamma-ray sources, and X-ray and gamma-ray bursters.

Trimble, V. L.↗
NASA NTRS2016

Swift follow-up of gravitational wave triggers: results from the first aLIGO run and optimization for the future

During its first observing run, in late 2015, the advanced Laser Interferometer Gravitational-wave Observatory facility announced three gravitational wave (GW) triggers to electromagnetic follow-up partners. Two of these have since been confirmed as being of astrophysical origin: both are binary black hole mergers at ∼500 Mpc; the other trigger was later found not to be astrophysical. In this paper, we report on the Swift follow-up observations of the second and third triggers, including details of 21 X-ray sources detected; none of which can be associated with the GW event. We also consider the challenges that the next GW observing run will bring as the sensitivity and hence typical distance of GW events will increase. We discuss how to effectively use galaxy catalogues to prioritize areas for follow-up, especially in the presence of distance estimates from the GW data. We also consider two galaxy catalogues and suggest that the high completeness at larger distances of the 2MASS Photometric Redshift catalogue makes it very well suited to optimize Swift follow-up observations.

P. A. Evans↗
NASA NTRS1996

Reducing On-Board Computer Propagation Errors Due to Omitted Geopotential Terms by Judicious Selection of Uploaded State Vector

Several future, and some current missions, use an on-board computer (OBC) force model that is very limited. The OBC geopotential force model typically includes only the J(2), J(3), J(4), C(2,2) and S(2,2) terms to model non-spherical Earth gravitational effects. The Tropical Rainfall Measuring Mission (TRMM), Wide-field Infrared Explorer (WIRE), Transition Region and Coronal Explorer (TRACE), Submillimeter Wave Astronomy Satellite (SWAS), and X-ray Timing Explorer (XTE) all plan to use this geopotential force model on-board. The Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) is already flying this geopotential force model. Past analysis has shown that one of the leading sources of error in the OBC propagated ephemeris is the omission of the higher order geopotential terms. However, these same analyses have shown a wide range of accuracies for the OBC ephemerides. Analysis was performed using EUVE state vectors that showed the EUVE four day OBC propagated ephemerides varied in accuracy from 200 m. to 45 km. depending on the initial vector used to start the propagation. The vectors used in the study were from a single EUVE orbit at one minute intervals in the ephemeris. Since each vector propagated practically the same path as the others, the differences seen had to be due to differences in the inital state vector only. An algorithm was developed that will optimize the epoch of the uploaded state vector. Proper selection can reduce the previous errors of anywhere from 200 m. to 45 km. to generally less than one km. over four days of propagation. This would enable flight projects to minimize state vector uploads to the spacecraft. Additionally, this method is superior to other methods in that no additional orbit estimates need be done. The definitive ephemeris generated on the ground can be used as long as the proper epoch is chosen. This algorithm can be easily coded in software that would pick the epoch within a specified time range that would minimize the OBC propagation error. This techniques should greatly improve the accuracy of the OBC propagation on-board future spacecraft such as TRMM, WIRE, SWAS, and XTE without increasing complexity in the ground processing.

Greatorex, Scott↗
NASA NTRS2000

Calibrating Atmospheric Delay for the Cassini Gravitational Wave Experiment

The Cassini spacecraft together with one of the stations of the Deep Space Network (DSN) have been instrumented to carry out extremely precise Doppler tracking that will be used to search for the direct evidence of Gravitational radiation passing through our solar system. The two-way communications link between the ground antenna and the spacecraft constitute an "antenna" for gravitational waves that would perturb the phase of the RF signal in the link. The experiments will be carried out during the long cruise phase of the spacecraft on its journey to Saturn and will be sensitive to gravitational wave perturbations larger than the noise level fluctuations of 3 x 10(exp -15) as measured in the Allan Standard Deviation domain. The use of simultaneous, coherent X- and Ka-Band up and down signals will reduce the errors associated with charged particle fluctuations in the interplanetary medium and Earth's ionosphere to a negligible level. The primary fluctuations in the phase of the signals both to and from the spacecraft are expected to be caused by fluctuations in water vapor in the Earth's atmosphere We have designed and are testing a new atmospheric calibration system (with duplicate components) to sense line-of-sight water vapor and its physical temperature with a goal of calibrating 95% or more of tropospheric path delay fluctuations during the Cassini Gravitational Wave Experiment (GWE). The critical component of the calibration system consists of a newly designed water vapor radiometer having a I degree sensing beamwidth and 0.01 K brightness temperature stability over hour time scales. Auxiliary instrumentation includes a microwave temperature profiler to retrieve the vertical distribution of the vapor physical temperature, and surface meteorology. A detailed error budget has been developed to account for all of the possible sources of error during calibration of the GWE and will be discussed. Two identical calibration systems have been constructed in order to provide capability as well as backup during the actual GWE experiment. We will report on side-by-side testing of the vapor and temperature sensing components of this calibrations system as well as a comparison with a short baseline radio interferometric measurement at our Goldstone complex.

Resch, G. M.↗
NASA NTRS2014

Free-Flight Experiments in LISA Pathfinder

The LISA Pathfinder mission will demonstrate the technology of drag-free test masses for use as inertial references in future space-based gravitational wave detectors. To accomplish this, the Pathfinder spacecraft will perform drag-free flight about a test mass while measuring the acceleration of this primary test mass relative to a second reference test mass. Because the reference test mass is contained within the same spacecraft, it is necessary to apply forces on it to maintain its position and attitude relative to the spacecraft. These forces are a potential source of acceleration noise in the LISA Pathfinder system that are not present in the full LISA configuration. While LISA Pathfinder has been designed to meet it's primary mission requirements in the presence of this noise, recent estimates suggest that the on-orbit performance may be limited by this 'suspension noise'. The drift-mode or free-flight experiments provide an opportunity to mitigate this noise source and further characterize the underlying disturbances that are of interest to the designers of LISA-like instruments. This article provides a high-level overview of these experiments and the methods under development to analyze the resulting data.

The technique of drag-free↗
NASA NTRS2010

A LISA Interferometry Primer

A key challenge for all gravitational wave detectors in the detection of changes in the fractional difference between pairs of test masses with sufficient precision to measure astrophysical strains with amplitudes on the order of approx.10(exp -21). ln the case of the five million km arms of LISA, this equates to distance measurements on the ten picometer level. LISA interferometry utilizes a decentralized topology, in which each of the sciencecraft houses its own light sources, detectors, and electronics. The measurements made at each of the sciencecraft are then telemetered to ground and combined to extract the strain experienced by the constellation as a whole. I will present an overview of LISA interferometry and highlight some of the key components and technologies that make it possible.

Thorpe, James Ira↗
NASA NTRS2008

Dynamic Stability and Gravitational Balancing of Multiple Extended Bodies

Feasibility of a non-invasive compensation scheme was analyzed for precise positioning of a massive extended body in free fall using gravitational forces influenced by surrounding source masses in close proximity. The N-body problem of classical mechanics is a paradigm used to gain insight into the physics of the equivalent N-body problem subject to control forces. The analysis addressed how a number of control masses move around the proof mass so that the proof mass position can be accurately and remotely compensated when exogenous disturbances are acting on it, while its sensitivity to gravitational waves remains unaffected. Past methods to correct the dynamics of the proof mass have considered active electrostatic or capacitive methods, but the possibility of stray capacitances on the surfaces of the proof mass have prompted the investigation of other alternatives, such as the method presented in this paper. While more rigorous analyses of the problem should be carried out, the data show that, by means of a combined feedback and feed-forward control approach, the control masses succeeded in driving the proof mass along the specified trajectory, which implies that the proof mass can, in principle, be balanced via gravitational forces only while external perturbations are acting on it. This concept involves the dynamic stability of a group of massive objects interacting gravitationally under active control, and can apply to drag-free control of spacecraft during missions, to successor gravitational wave space borne sensors, or to any application requiring flying objects to be precisely controlled in position and attitude relative to another body via gravitational interactions only.

Quadrelli, Marco↗
NASA NTRS2011

Time Domain Simulations of Arm Locking in LISA

Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA). a gravitational-wave observatory sensitive' in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking including the expected limiting noise sources (shot noise, clock noise. spacecraft jitter noise. and residual laser frequency noise). The effect of imperfect a priori knowledge of the LISA heterodyne frequencies and associated "pulling" of an arm locked laser is included. We find that our implementation meets requirements both on the noise and dynamic range of the laser frequency.

Thorpe, J. I.↗
NASA NTRS2003

Possible Class of Nearby Gamma-Ray Burst/Gravitational Wave Sources

A possible subclass of gamma-ray bursts - those with few, wide pulses, spectral lags of order one to several seconds, and soft spectra - has been identified. Their Log[N]-Log[Fp] distribution approximates a -3/2 power-law, suggesting homogeneity and relatively nearby sources. These mostly dim bursts account for approximately 50% of the BATSE sample of long bursts near that instrument s trigger threshold, suggesting that this subluminous class constitutes a more common variety than the more familiar burst sources which lie at truly cosmological distances. Theoretical scenarios predicted such a class, motivated by their exemplar GRB 980425 (SN 1998bw) lying at a distance of approximately 38 Mpc. The observations are explained by invoking off-axis viewing of the GRB jet and/or bulk Lorentz factors of order a few. Long-lag bursts show a tendency to concentrate near the Supergalactic Plane with a quadrupole moment of -0.10 plus or minus 0.04, similar to that for SNe type Ib/c within the same volume. The rate of the observed subluminous bursts is of order 1/4 that of SNe Ib/c. Evidence for a sequential relationship between SNe Ib/c and GRBs is critiqued for two cases, as simultaneity of the SN and GRB events may be important for detection of the expected gravitational wave signal; at most, SN to GRB delays appear to be a few days. SN asymmetries and ultrarelativistic GRB jets suggest the possibility of rapid rotation in the pre-collapse objects, a primary condition required for highly nonaxisymmetric SN collapse to produce strong gravitational waves.

Norris, Jay P.↗
NASA NTRS2010

Merging Black Holes

Black-hole mergers take place in regions of very strong and dynamical gravitational fields, and are among the strongest sources of gravitational radiation. Probing these mergers requires solving the full set of Einstein's equations of general relativity numerically. For more than 40 years, progress towards this goal has been very slow, as numerical relativists encountered a host of difficult problems. Recently, several breakthroughs have led to dramatic progress, enabling stable and accurate calculations of black-hole mergers. This article presents an overview of this field, including impacts on astrophysics and applications in gravitational wave data analysis.

Centrella, Joan↗
NASA NTRS2002

Media Calibration in the Deep Space Network: A Status Report

A new media calibration system (MCS) has been implemented at the Goldstone complex of the DSN (Deep Space Network). It is intended to calibrate the delay of radio signals imposed by the neutral atmosphere. The system provides periodic measurements of both the static dry and fluctuating wet components of this delay. In particular, the system will calibrate the fluctuations in line of sight path delay due to atmospheric water vapor that we believe will dominate the error budget for several radio science and radio astronomy experiments. We have compared two of these media calibration systems with a connected element interferometer on a 21 km baseline. In this report we describe a total of 30 observations in which a radio source was tracked for an hour or more and the delay residuals then calibrated using the MCS. The accuracy of the comparison appears to be limited by systematic errors in the interferometer, which are under investigation. However, our results do indicate that the MCS can meet or exceed the two-way Allan standard deviation specification of 1.5 x 10( exp -15) on time scales of 2,000 - 10,000 sec, as required by the Cassini GWE (Gravitational Wave Experiment) for two way Doppler tracking.

Naudet, Charles J.↗