Subnanoradian, Groundbased Tracking of Spaceborne Lasers

Over the next few decades groundbased tracking of lasers on planetary spacecraft will supplement or replace tracking of radio transponders. This paper describes research on two candidate technologies for groundbased, angular, laser tracking: the infrared interferometer and the optical filled-aperture telescope. The motivation for infrared and optical tracking will be followed by a description of the current (10-50 nanoradian) and future (subnanororadian) stellar tracking demonstrations with the University of California-Berkeley Infrared Spatial Interferometer (ISI) and the University of California-San Diego Optical Ronchi Telescope

Deep space tracking in local reference frames

A self-calibrating deep space tracking technique is described which can potentially produce two nanoradian angular spacecraft determinations. The technique uses very long base interferometric observations of a spacecraft and several radio sources. The currently employed single source technique is described as a parameter estimation procedure. Then, the number of parameters and observations leads to the proposed local reference frame technique. Station clock, Earth rotation, and tropospheric parameters are estimated along with spacecraft position from the multisource observation sequence. The contributions to spacecraft angular uncertainty from system noise, tropospheric fluctuations, and uncalibrated radio source structure are evaluated. Of these experimental errors, radio source structure dominates the determination of the spacecraft position in the radio reference frame. It is shown, however, that the sensitivity of relative spacecraft position accuracies to time-invariant radio source structure effects may be on the order of 2 nanoradians

A nanoradian differential VLBI tracking demonstration

The shift due to Jovian gravitational deflection in the apparent angular position of the radio source P 0201+113 was measured with very long baseline interferometry (VLBI) to demonstrate a differential angular tracking technique with nanoradian accuracy. The raypath of the radio source P 0201+113 passed within 1 mrad of Jupiter (approximately 10 Jovian radii) on 21 Mar. 1988. Its angular position was measured 10 times over 4 hours on that date, with a similar measurement set on 2 Apr. 1988, to track the differential angular gravitational deflection of the raypath. According to general relativity, the expected gravitational bend of the raypath averaged over the duration of the March experiment was approximately 1.45 nrad projected onto the two California-Australia baselines over which it was measured. Measurement accuracies on the order of 0.78 nrad were obtained for each of the ten differential measurements. The chi(exp 2) per degree of freedom of the data for the hypothesis of general relativity was 0.6, which suggests that the modeled dominant errors due to system noise and tropospheric fluctuations fully accounted for the scatter in the measured angular deflections. The chi(exp 2) per degree of freedom for the hypothesis of no gravitational deflection by Jupiter was 4.1, which rejects the no-deflection hypothesis with greater than 99.999 percent confidence. The system noise contributed about 0.34 nrad per combined-baseline differential measurement and tropospheric fluctuations contributed about 0.70 nrad. Unmodeled errors were assessed, which could potentially increase the 0.78 nrad error by about 8 percent. The above chi(exp 2) values, which result from the full accounting of errors, suggest that the nanoradian gravitational deflection signature was successfully tracked

Tropospheric monitoring technology for gravity wave experiments

Tropospheric refractivity fluctuations are an important error source for gravity wave detection by Doppler tracking in that they alter the phase and phase rate of electromagnetic signals. Estimates are presented of the effect of tropospheric fluctuations on the Doppler signal and some examples are suggested of methods which minimize the effect. A model of the fluctuations is utilized to achieve those goals. Four possible methods for reducing the fluctuation effect are suggested: (1) observation and analysis strategies, which separate the atmospheric and gravity wave signatures; (2) water vapor radiometry for the wet component; (3) calibration using Global Positioning System (GPS) satellites; and (4) Doppler observations from multiple antennas to average fluctuation effects. The last two techniques could be used to calibrate both wet and dry fluctuations, or could be used in conjunction with water vapor radiometry to calibrate only the dry component

The effect of the dynamic wet troposphere on VLBI measurements

Calculations using a statistical model of water vapor fluctuations yield the effect of the dynamic wet troposphere on Very Long Baseline Interferometry (VLBI) measurements. The statistical model arises from two primary assumptions: (1) the spatial structure of refractivity fluctuations can be closely approximated by elementary (Kolmogorov) turbulence theory, and (2) temporal fluctuations are caused by spatial patterns which are moved over a site by the wind. The consequences of these assumptions are outlined for the VLBI delay and delay rate observables. For example, wet troposphere induced rms delays for Deep Space Network (DSN) VLBI at 20-deg elevation are about 3 cm of delay per observation, which is smaller, on the average, than other known error sources in the current DSN VLBI data set. At 20-deg elevation for 200-s time intervals, water vapor induces approximately 1.5 x 10 to the minus 13th power s/s in the Allan standard deviation of interferometric delay, which is a measure of the delay rate observable error. In contrast to the delay error, the delay rate measurement error is dominated by water vapor fluctuations. Water vapor induced VLBI parameter errors and correlations are calculated. For the DSN, baseline length parameter errors due to water vapor fluctuations are in the range of 3 to 5 cm. The above physical assumptions also lead to a method for including the water vapor fluctuations in the parameter estimation procedure, which is used to extract baseline and source information from the VLBI observables

The Proper Motion of SgrA*: I. First VLBA Results

We observed Sgr A* and two extragalactic radio sources nearby in angle with the VLBA over a period of two years and measured relative positions with an accuracy approaching 0.1 mas. The apparent proper motion of Sgr A* relative to J1745-283 is 5.90 +/- 0.4 mas/yr, almost entirely in the plane of the Galaxy. The effects of the orbit of the Sun around the Galactic Center can account for this motion, and any residual proper motion of Sgr A*, with respect to extragalactic sources, is less than about 20 km/s. Assuming that Sgr A* is at rest at the center of the Galaxy, we estimate that the circular rotation speed in the Galaxy at the position of the Sun is 219 +/- 20 km/s, scaled by Ro/8.0 kpc. Current observations are consistent with Sgr A* containing all of the nearly 2.6 x 10^6 solar masses, deduced from stellar proper motions, in the form of a massive black hole. While the low luminosity of Sgr A*, for example, might possibly have come from a contact binary containing of order 10 solar masses, the lack of substantial motion rules out a "stellar" origin for Sgr A*. The very slow speed of Sgr A* yields a lower limit to the mass of Sgr A* of about 1,000 solar masses. Even for this mass, Sgr A* appears to be radiating at less than 0.1 percent of its Eddington limit

Toward astrometric tracking with the infrared spatial interferometer

Infrared interferometric demonstrations with the University of California, Berkeley's infrared spatial interferometer (ISI) on Mt. Wilson explore the potential of infrared and optical astrometry for deep space tracking, reference frame development, and DSN science. Astrometric data taken and analyzed over the last five years from the ISI have shown that instrumental and atmospheric effects limit current demonstrations. The benefits of sensitivity upgrades, which were performed in 1991 and 1992, have been demonstrated by comparing point-to-point phase fluctuations for the fall 1989 and fall 1992 observing epochs. This comparison showed that point-to-point phase fluctuations due to tropospheric and quantum noise, for optimal integration times of 0.2 sec, are approaching the 0.1-cycle level needed to reliably connect the interferometric phase. The increase in sensitivity, coupled with that arising from very recent hardware upgrades, will greatly enhance phase-connection capabilities necessary for astrometry in the presence of atmospheric refractivity fluctuations. The current data set suggests that atmospheric fluctuations on Mt. Wilson during the best seeing are dominated by a low-lying component, approximately 25 m high, which may be minimized with in situ calibration in the future. During poor seeing conditions that currently prohibit the interferometric phase connection necessary for astrometry, fluctuations seem to be generated by atmospheric inhomogeneities at much higher altitudes above Mt. Wilson. Data taken over the last year suggest that the ISI will soon be able to achieve 50- to 100-nrad astrometry in a single observing session, employing current ground-based laser distance interferometer calibrations to minimize atmospheric effects

The Impact of Atmospheric Fluctuations on Degree-scale Imaging of the Cosmic Microwave Background

Fluctuations in the brightness of the Earth's atmosphere originating from water vapor are an important source of noise for ground-based instruments attempting to measure anisotropy in the Cosmic Microwave Background. This paper presents a model for the atmospheric fluctuations and derives simple expressions to predict the contribution of the atmosphere to experimental measurements. Data from the South Pole and from the Atacama Desert in Chile, two of the driest places on Earth, are used to assess the level of fluctuations at each site.Comment: 29 pages, 7 figures, 1 table, appears in The Astrophysical Journa

A test of water vapor radiometer-based troposphere calibration using VLBI observations on a 21-kilometer baseline

Simultaneous very long baseline interferometry (VLBI) and water vapor radiometer (WVR) measurements on a 21 km baseline showed that calibration by WVRs removed a significant fraction of the effect of tropospheric delay fluctuations for these experiments. From comparison of the residual delay variations within scans and between scans, the total tropospheric contribution t the delay residuals for each of the three 5 to 20 hour sessions was estimated as 1, 17, and 10%, with the first value being uncertain. The observed improvement in rms residual delay from WVR calibration during these three sessions was 4, 16, and 2%, respectively. The improvement is consistent with the estimated 2 to 3 mm path delay precision of current WVRs. The VLBI measurements, of natural radio sources, were conducted in April and May 1993 at Goldstone, California. Dual-frequency (2.3 and 8.4 GHz) observations were employed to remove the effects of charged particles from the data. Measurements with co-pointed WVRs, located within 50 m of the axis of each antenna, were performed to test the ability of the WVRs to calibrate line-of-sight path delays. Factors that made WVR performance assessment difficult included (1) the fact that the level of tropospheric fluctuations was smaller than is typical for Goldstone during these experiments and (2) VLBI delay variations on longer time scales (i.e., over multiple scans) contained uncalibrated instrumental effects (probably a result of slow temperature variations in the VLBI hardware) that were larger than the tropospheric effects