Doppler Tracking Analysis
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doppler doppler radar signal processing gravity gr↗
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Digital Receiver Phase Meter
The software of a commercially available digital radio receiver has been modified to make the receiver function as a two-channel low-noise phase meter. This phase meter is a prototype in the continuing development of a phase meter for a system in which radiofrequency (RF) signals in the two channels would be outputs of a spaceborne heterodyne laser interferometer for detecting gravitational waves. The frequencies of the signals could include a common Doppler-shift component of as much as 15 MHz. The phase meter is required to measure the relative phases of the signals in the two channels at a sampling rate of 10 Hz at a root power spectral density <5 microcycle/(Hz)1/2 and to be capable of determining the power spectral density of the phase difference over the frequency range from 1 mHz to 1 Hz. Such a phase meter could also be used on Earth to perform similar measurements in laser metrology of moving bodies. To illustrate part of the principle of operation of the phase meter, the figure includes a simplified block diagram of a basic singlechannel digital receiver. The input RF signal is first fed to the input terminal of an analog-to-digital converter (ADC). To prevent aliasing errors in the ADC, the sampling rate must be at least twice the input signal frequency. The sampling rate of the ADC is governed by a sampling clock, which also drives a digital local oscillator (DLO), which is a direct digital frequency synthesizer. The DLO produces samples of sine and cosine signals at a programmed tuning frequency. The sine and cosine samples are mixed with (that is, multiplied by) the samples from the ADC, then low-pass filtered to obtain in-phase (I) and quadrature (Q) signal components. A digital signal processor (DSP) computes the ratio between the Q and I components, computes the phase of the RF signal (relative to that of the DLO signal) as the arctangent of this ratio, and then averages successive such phase values over a time interval specified by the user.
Marcin, Martin↗
Simulation of Laser Cooling and Trapping in Engineering Applications
An advanced computer code is undergoing development for numerically simulating laser cooling and trapping of large numbers of atoms. The code is expected to be useful in practical engineering applications and to contribute to understanding of the roles that light, atomic collisions, background pressure, and numbers of particles play in experiments using laser-cooled and -trapped atoms. The code is based on semiclassical theories of the forces exerted on atoms by magnetic and optical fields. Whereas computer codes developed previously for the same purpose account for only a few physical mechanisms, this code incorporates many more physical mechanisms (including atomic collisions, sub-Doppler cooling mechanisms, Stark and Zeeman energy shifts, gravitation, and evanescent-wave phenomena) that affect laser-matter interactions and the cooling of atoms to submillikelvin temperatures. Moreover, whereas the prior codes can simulate the interactions of at most a few atoms with a resonant light field, the number of atoms that can be included in a simulation by the present code is limited only by computer memory. Hence, the present code represents more nearly completely the complex physics involved when using laser-cooled and -trapped atoms in engineering applications. Another advantage that the code incorporates is the possibility to analyze the interaction between cold atoms of different atomic number. Some properties that cold atoms of different atomic species have, like cross sections and the particular excited states they can occupy when interacting with each other and light fields, play important roles not yet completely understood in the new experiments that are under way in laboratories worldwide to form ultracold molecules. Other research efforts use cold atoms as holders of quantum information, and more recent developments in cavity quantum electrodynamics also use ultracold atoms to explore and expand new information-technology ideas. These experiments give a hint on the wide range of applications and technology developments that can be tackled using cold atoms and light fields. From more precise atomic clocks and gravity sensors to the development of quantum computers, there will be a need to completely understand the whole ensemble of physical mechanisms that play a role in the development of such technologies. The code also permits the study of the dynamic and steady-state operations of technologies that use cold atoms. The physical characteristics of lasers and fields can be time-controlled to give a realistic simulation of the processes involved such that the design process can determine the best control features to use. It is expected that with the features incorporated into the code it will become a tool for the useful application of ultracold atoms in engineering applications. Currently, the software is being used for the analysis and understanding of simple experiments using cold atoms, and for the design of a modular compact source of cold atoms to be used in future research and development projects. The results so far indicate that the code is a useful design instrument that shows good agreement with experimental measurements (see figure), and a Windows-based user-friendly interface is also under development.
Ramirez-Serrano, Jaime↗
Upper limits on the isotropic gravitational radiation background from pulsar timing analysis
A pulsar and the earth may be thought of as end masses of a free-mass gravitational wave antenna in which the relative motion of the masses is monitored by observing the Doppler shift of the pulse arrival times. Using timing residuals from PSR 1133 + 16, 1237 + 25, 1604-00, and 2045-16, an upper limit to the spectrum of the isotropic gravitational radiation background has been derived in the frequency band 4 x 10 to the -9th to 10 to the -7th Hz. This limit is found to be S(E) = 10 to the 21st f-cubed ergs/cu cm Hz, where S(E) is the energy density spectrum and f is the frequency in Hz. This would limit the energy density at frequencies below 10 to the -8th Hz to be 0.00014 times the critical density.
Hellings, R. W.↗
On the detection of a stochastic background of gravitational radiation by the Doppler tracking of spacecraft
Consideration is given to the possibility of detection of an isotropic background gravitational radiation of a stochastic nature by the method of Doppler tracking of spacecraft. Attention is given in the geometrical optics limit, to the general formula for the frequency shift of an electromagnetic signal in the gravitational radiation field, and it is shown to be gauge independent. The propagation of a free electromagnetic wave in a gravitational radiation field is examined with the conclusion that no resonance phenomena can be expected. Finally, the 'Doppler noise' due to a stochastic background is evaluated, and it is shown to depend on the total energy density of the background and a parameter that is a characteristic of the radiation spectrum and the detection system used.
Mashhoon, B.↗
Interplanetary Scintillation
Interplanetary scintillation (IPS) has been used as a diagnostic of solar wind speed and interplanetary plasma turbulence, allowing inference of speed and electron density power spectrum close to the Sun and out of the ecliptic. In that context, IPS is 'signal' and provides scientifically interesting data. IPS is also of interest because amplitude and phase perturbations imposed on radio waves are 'noise' for telemetry and precision Doppler tracking of deep space probes and for some radio astronomical observations. This paper briefly reviews the connection between scattering observables and the electron density power spectrum. Interplanetary phase scintillation on time scales of 100 to 10 000 seconds is an important noise in mass determinations of small solar system bodies during space-probe fly-bys and in searches for low-frequency gravitational radiation.
waves deep space probes electron density power spe↗
Spacecraft Doppler Tracking as a Xylophone Detector
We discuss spacecraft Doppler tracking in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot and Levine, we derive a new method for removing from the combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. Our method provides also for reducing by several orders of magnitude, at selected Fourier components, the frequency fluctuations due to other noise sources, such as the clock on board the spacecraft or the antenna and buffeting of the probe by non-gravitational forces. In this respect spacecraft Doppler tracking can be regarded as a xylophone detector. Estimates of the sensitivities achievable by this xylophone are presented for two tests of Einstein's theory of relativity: searches for gravitational waves and measurements of the gravitational red shift. This experimental technique could be extended to other tests of the theory of relativity, and to radio science experiments that rely on high-precision Doppler measurements.
Tinto, Massimo↗
Gravitational waves and red shifts - A space experiment for testing relativistic gravity using multiple time-correlated radio signals
A two-step satellite mission for improving the accuracy of gravitational wave detection and for observing actual gravity waveforms is proposed. The spacecraft would carry both a highly stable hydrogen maser, which would control a transmitter sending signals to earth, and a Doppler transponder operating in the two-way mode. The use of simultaneous one- and two-way Doppler transmissions offers four time records of frequency pulsations, which can reveal gravitational radiation at 1-10 MHz with an amplitude accuracy of a factor of six. The first mission phase would consist of a Shuttle launch into a highly eccentric orbit to obtain measurements of the gravitational redshift using gravitational potentials of different earth regions to establish that gravity is describable by a metric theory. Then, after a boost into a heliocentric orbit at 6 AU, the earth-satellite system could detect gravitational waves in the solar system, as well as bursts emitted by the collisions of supermassive black holes.
Smarr, L. L.↗
The confrontation between general relativity and experiment
Experiments that test the foundations of gravitation theory in terms of the Einstein equivalence principle are discussed along with solar system tests of general relativity at the post-Newtonian level. These include classical (light-deflection, time delay and perihelion shift) tests as well as tests of the strong equivalence principle. The binary pulsar is discussed as an extra-solar-system gravitational testing ground, and attention is given to the multipolarity of the waves and the amount of radiation damping. The mass function, periastron shift, redshift-Doppler parameter and rate of change of the orbit period (Pb) of the binary pulsar are also considered, and it is suggested that the measurement of Pb represents the first observation of the effects of gravitational radiation.
Will, C. M.↗
Galileo Gravity Results and the Internal Structure of Io
Doppler data generated with the Galileo spacecraft's radio carrier wave were used to measure Io's external gravitational field. The resulting triaxial field is consistent with the assumption that Io is in tidal and rotational equilibrium. The inescapable conclusion is that it has a large metallic core. If the core is a eutectic mixture of iron and iron sulfide, it comprises 20.2 +/- 7.4 percent of the satellite's total mass with a radius that is about 52 percent of lo's mean radius of 1821.3 kilometers; if the core is pure iron, it comprises 10.5 +/- 3.7 percent of the total mass with a radius of about 36 percent of the mean radius.
Anderson J. D.↗
Response functions of free mass gravitational wave antennas
The work of Gursel, Linsay, Spero, Saulson, Whitcomb and Weiss (1984) on the response of a free-mass interferometric antenna is extended. Starting from first principles, the earlier work derived the response of a 2-arm gravitational wave antenna to plane polarized gravitational waves. Equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) are obtained by a simple differencing of the '3-pulse' Doppler response functions of two 1-arm antennas. A '4-pulse' response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions ('3n+1 pulse') for antennas having multiple passes or more arms.
Estabrook, F. B.↗
Gravity field and interior structure of Rhea
Doppler data generated with the Cassini spaceraft's radio carrier waves at X and Ka band can be used to determine the quadrupole moments of Rhea's gravitational field.
Cassini gravitational field Rhea gravity↗
Measuring Gravitation Using Polarization Spectroscopy
A proposed method of measuring gravitational acceleration would involve the application of polarization spectroscopy to an ultracold, vertically moving cloud of atoms (an atomic fountain). A related proposed method involving measurements of absorption of light pulses like those used in conventional atomic interferometry would yield an estimate of the number of atoms participating in the interferometric interaction. The basis of the first-mentioned proposed method is that the rotation of polarization of light is affected by the acceleration of atoms along the path of propagation of the light. The rotation of polarization is associated with a phase shift: When an atom moving in a laboratory reference interacts with an electromagnetic wave, the energy levels of the atom are Doppler-shifted, relative to where they would be if the atom were stationary. The Doppler shift gives rise to changes in the detuning of the light from the corresponding atomic transitions. This detuning, in turn, causes the electromagnetic wave to undergo a phase shift that can be measured by conventional means. One would infer the gravitational acceleration and/or the gradient of the gravitational acceleration from the phase measurements.
Matsko, Andrey↗
Europa's differentiated internal structure: inferences from two Galileo encounters
Doppler data generated with the Galileo spacecraft's radio carrier wave during two Europa encounters on 19 December 1996 (E4) and 20 February 1997 (E6) were used to measure Europa's external gravitational field. The measurements indicate that Europa has a predominantly water ice-liquid outer shell about 100 to 200 kilometers thick and a deep interior with a density in excess of about 4000 kilograms per cubic meter. The deep interior could be a mixture of metal and rock or it could consist of a metal core with a radius about 40 percent of Europa's radius surrounded by a rock mantle with a density of 3000 to 3500 kilograms per cubic meter. The metallic core is favored if Europa has a magnetic field.
Flight Experiment↗
Europa's Differentiated Internal Structure: Inferences from Two Galileo Encounters
Doppler data generated with the Galileo spacecraft's radio carrier wave during two Europa encounters on 19 December 1996 (E4) and 20 February 1997 (E6) were used to measure Euroapa's external gravitational field. The measurements indicate that Europa has a predominantly water ice-liquid outer shell about 100 to 200 klilometers thick and a deep interior with a density in excess of about 4000 kilograms per cubic meter.
Galileo↗
Simultaneous dual-frequency, round-trip calibration of Doppler data with application to radio science experiments
Simultaneous dual-frequency, round-trip calibration of Doppler data is discussed in light of unequal spacecraft turnaround ratios at S- and X-band. The impact of unequal turnaround ratios on calibration accuracies in the specific cases of the Gravitational Wave Detection Experiment and the Solar Gravitational Quadrupole Moment Experiment is considered.
Berman, A. L.↗
Atomic clocks for astrophysical measurements
It is noted that recently developed atomic hydrogen masers have achieved stability well into the 10 to the -16th domain for averaging time intervals beyond 1000 sec and that further improvements are in prospect. These devices are highly adaptable for space use in very high precision measurements of angle through Very Long Baseline Interferometry (VLBI) and of range and range-rate through Doppler techniques. Space missions that will use these clocks for measuring the sun's gravity field distribution and for testing gravitation and relativity (a project that will include a search for pulsed low-frequency gravitational waves) are discussed. Estimates are made of system performance capability, and the accuracy capability of relativistic measurements is evaluated in terms of the results from the 1976 NASA/SAO spaceborne clock test of the Einstein Equivalence Principle.
Vessot, R. F. C.↗
Navigation between the planets
Recent advances in spacecraft tracking, chronometry, ephemerides, and orbit and trajectory determinations are reviewed. Improvements in timekeeping are reviewed, as well as precision distance and range measurements; orbit determinations, trajectory-correction maneuvers, flight path optimization, and information provided by rotation of the tracking station with the earth's surface. Doppler and tropospheric wave propagation effects are dealt with. Nongravitational perturbations (solar radiation pressure, release of gases from the spacecraft, stochastic unmodeled accelerations and sequential estimation to cope with them), the effect of the target planet's gravitational field upon close approach, and navigation problems in the outer reaches of the solar system (TV data telemetered back for inertial navigation) are covered. By-products of the research include: refined data on the mass of planets, on planetary mass distributions, planet configurations, on physical properties of the atmospheres and ionospheres of planets, and opportunities for refined tests of gravitation and relativity theories and models.
Melbourne, W. G.↗