Theory of Spacecraft Doppler Tracking
We present a review of the spacecraft Doppler tracking technique used in broad band searches for gravitational waves in the millihertz frequency band.
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We present a review of the spacecraft Doppler tracking technique used in broad band searches for gravitational waves in the millihertz frequency band.
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.
This oral presentation discusses spacecraft Doppler tracking in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. Methods are proposed to remove or reduce frequency fluctuations from the data that are caused by multiple circumstances. The resultant data from these proposed methods may have applicability in testing relativity theory.
Spacecraft Doppler tracking is discussed for detecting gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. A new method is derived for removing from combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. The remaining non-zero gravitational wave signal could be used for detecting gravitational waves.
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The prospects of using spacecraft Doppler tracking, in NASA missions, for the detection of gravitational waves are examined. The sensitivity limits of such detection are characterized in terms of plasma scintillation, troposphere scintillation, receiver noise, MDA and ODA quantization error, and clock jitter. Current and possible future NASA missions that will involve gravitational wave experiments are briefly reviewed, including the Galileo, solar polar, Halley/Tempel-2, and solar probe missions.
We discuss spacecraft Doppler tracking for detecting gravitational waves 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.
A calculation is made of the effect of gravity waves on the observed Doppler shift of a sinusoidal electromagnetic signal transmitted to, and transponded from, a distant spacecraft. We find that the effect of plane gravity waves on such observations is not intuitively immediate and in fact can have surprisingly different spectral signatures for different spacecraft directions and distances. We suggest the possibility of detecting such plane waves by simultaneous coherent Doppler tracking of several spacecraft.
The signal-to-noise ratio received at Earth is typically larger than 10 dB-Hz for radio tracking of a spacecraft in deep space, allowing a phase-locked loop to execute reliable carrier tracking. Recently, missions have been proposed to utilize low-gain antennas for Doppler tracking where the signal-to-noise ratio may be at the single-digit (dB-Hz) level. In this work, we discuss spacecraft Doppler tracking at these low signal-to-noise ratios through an analysis of thermal noise on the radio link, results from ground testing with the Deep Space Network, and demonstrations with an active spacecraft. We show that by utilizing an open-loop receiver to capture the carrier signal and by applying post-processing techniques, radio data with the signal-to-noise ratio as low as 4 dB-Hz can be used to derive Doppler data with precision sufficient for tracking a spacecraft in deep space.
We discuss a filtering technique for reducing the frequency fluctuations due to the troposphere, ionosphere, and mechanical vibrations of the ground antenna in spacecraft Doppler tracking searches for gravitational radiation. This method takes advantage of the sinusoidal behavior of the transfer function to the Doppler observable of these noise sources, which displays sharp nulls at selected Fourier components.
We discuss a filtering technique for reducing the two-way Doppler frequency fluctuations of noise sources localized in space that affect the sensitivity of spacecraft Doppler tracking searches for gravitational radiation.
The sensitivity of NASA's Deep Space Network spacecraft tracking system to an isotropic cosmological background of gravitational radiation is analyzed. It is found that by using the autocovariance function of the Doppler record in the so-called 'three-way' tracking mode to dig into the noise it is possible to put significant limits on this background with current and future planned deep-space missions.
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The Deep Space Network generates accurate radio science data observables for investigators who use radio links between spacecraft and the Earth to examine small changes in the phase and/or amplitude of the signal to study a wide variety of structures and phenomena in space. Several such studies are directed at aspects of the theory of general relativity such as gravitational redshift and gravitational waves. A gravitational wave is a propagating, polarized gravitational field, a ripple in the curvature of space-time. In Einstein's theory of general relativity, the waves are propagating solutions of the Einstein field equations. Their amplitudes are dimensionless strain amplitudes that change the fractional difference in distance between test masses and the rates at which separated clocks keep time. Predicted by all relativistic theories of gravity, they are extremely weak (the ratio of gravitational forces to electrical forces is about 10(sup -40)) and are generated at detectable levels only by astrophysical sources - very massive sources under violent dynamical conditions. The waves have never been detected but searches in the low-frequency band using Doppler tracking of many spacecraft have been conducted and others are being planned. Upper limits have been placed on the gravitational wave strength with the best sensitivities to date are for periodic waves being 7 x 10(sup -15).
Preliminary results are reported from Doppler-shift measurements to the Voyager-2 spacecraft at a distance of 26 AU, obtained using the 32-m VLBI antenna at Medicina (Italy) during July and August 1988. The apparatus comprises the el-az antenna, an S-X-band receiver, a hydrogen maser to generate the reference signal, a Mark III VLBI terminal, and a digital tone extractor capable of isolating a tone of known frequency from a noisy signal and giving its phase and amplitude. A signal transmitted in S-band from the NASA Deep Space Network (DSN) station in Australia and retransmitted coherently in X-band by Voyager, was received 7 h 6 min later at Medicina and at the DSN station in Madrid. Sample data are presented graphically and shown to be of generally high quality; further in-depth analysis is under way.
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