The accuracy of Earth-based radio astronomy is limited in a fundamental way by the variable delay of the troposphere and by the centimeter-scale motions of a dynamic Earth. Going to Earth orbit solves the variable delay problems, but problems with evolution of the baseline vector remain. The Moon can provide a stable platform where the potential accuracy of radio astromony is one or two orders of magnitude better than from the Earth

Linfield, Roger

English

NASA Technical Reports Server

LUNAR RADIO ASTROMETRY 
Roger Linfield 
NASA Je t  Propulsion Laboratory 
Pasadena, California 91109 
Abstract 
The accuracy of Earth-based radio astrometry is limited in a fundamental way by the variable 
delay of the troposphere and by the centimeter-scale motions of a dynamic Earth. Going to Earth 
orbit solves the variable-delay problems, but problems with evolution of the baseline vector remain. 
The Moon can provide a stable platform where the potential accuracy of radio astrometry is one to two 
orders of magnitude better than from the Earth. 
Background 
Radio astrometry can be broadly separated into two types. 
1. Connected-element interferometry - With this type of radio astrometry, the local oscillator 
(LO) signal is distributed and the relative phase at the two ends of a baseline is measured. The 
angular measurement precision is 
A 
A0 -  
D S N R  
where A is the wavelength of observation, D is the baseline, and S N R  is the signal-to-noise ratio; 
SNR 0: (BWtot)0.5, where BWtot is the total correlated bandwidth. 
2. VLBI - In this type of radio astrometry, independent LO’S are used and the relative arrival 
time at the two ends of a baseline is measured by bandwidth synthesis (BWS). The angular 
measurement precision is 
C 
A 0  - 
D B W  S N R  
span 
where c is the speed of light and BW,,,,, is the spanned bandwidth, which is generally larger than 
B Wtot. As in the other case, SNR a ( B  Wt,,)05. 
Current Accuracy and Limitations 
Currently, on Earth, very-long-baseline interferometry (VLBI) yields higher accuracy 
astrometry than does connected-element interferometry. The accuracy, a s  determined by comparing 
independent VLBI catalogs, is approximately 3 marcsec and is limited primarily by two effects. The 
first is the delay introduced by the troposphere: typically 7 nsec and highly variable. Much of this 
variation is due to water vapor and is difficult to calibrate. Water vapor radiometers enable an  
estimate of the delay by measurement of the brightness temperature of atmospheric water vapor 
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emission a t  22 GHz. The accuracy of this method is limited by uncertainty in the (variable) vertical 
distribution of water vapor in the troposphere; this effect may fundamentally limit the accuracy of 
Earth-based astrometry at about the l-marcsec level. 
The second major error source involves the evolution of the baseline vector between the two 
telescopes. This evolution is  primarily the result of the (nearly) constant rotation of the Earth, but 
numerous secondary effects (e.g., polar motion, short-term variations in rotation rate, solid Earth 
tides, variable atmospheric and ocean loading on the continents) are  important for accuracies below 
about 50 marcsec. Because of the active dynamics of the Earth, it is difficult to calibrate these effects 
to high precision. Their short time scales ( < 1 day) and stochastic nature may also introduce a n  
ultimate limitation of - 1 marcsec to Earth-based astrometric accuracy. I 
Lunar Radio Astrometrv 
Use of the Moon as a platform for astrometry offers a chance to completely escape the effects of 
the troposphere and to greatly reduce the effects of baseline evolution. Consider a n  instrument of 
three identical antennas on the Moon arranged in a n  equilateral triangle. Antenna separations 
(baselines) would lie somewhere in the 100- to 2000-km range. The lunar environment would allow 
use of very lightweight (possibly remotely deployed) antennas with diameters of 10 to 15 m. Whether 
the instrument would give higher accuracy in  a connected-element (distributed LO) mode or VLBI 
(separate LO’S) mode is not certain. Over short distances, the LO signal could probably be distributed 
very accurately by cable or microwave link between relay towers; over longer distances, it might have 
to travel by satellite, and the path length uncertainty would be a problem. Both operating modes will 
be considered. For either mode, the received data would be amplified, mixed to a lower frequency, and 
transmitted to a single site (probably at a human colony) for real-time correlation of -500-MHz 
Earth for analysis. Either a low-bandwidth link or the regular delivery of data on tape would suffice. 
Power for the antennas could be supplied by solar cells with storage batteries for the lunar night; by 
this means, the instrument could operate continuously. 
~ 
, bandwidth. Correlated data plus calibration and bookkeeping information could be transmitted to 
Error Analysis of Proposed Instrument 
Propagation effects are  a major error source on Earth. The Moon has no troposphere, but there 
will be some delay introduced by charged particles in the lunar ionosphere, in the solar wind, and 
(occasionally) in the Earth’s magnetotail. This effect, already small, can probably be reduced to 
insignificance by observing a t  high frequencies (20 to 30 GHz), since the delay varies as the square of 
the observing wavelength. If necessary, the effect of charged particles can be completely removed 
with dual-frequency observations, a s  is often done on Earth with simultaneous 2 2-GHz and 8.4-GHz 
measurements. I 
Baseline knowledge is the other limiting error source on Earth. As revealed by lunar laser 
ranging, the situation on the Moon is quite different. The nonlinear terms in the lunar rotation rate 
are  as large as for the Earth, but they are much more predictable. The Moon has no fluid sheath 
around it and is much quieter dynamically than is the Earth. At the level of 0.1 marcsec, there are  
about 30 constant terms in the lunar potential and elasticity (e.g., Love numbers for solid-body tides) 
which would need to be measured to adequately describe the baseline evolution. These quantities 
would be solved for a s  part of a global fit to the delay or phase measurements made with the 
interferometer. The stochastic component of the Moon’s motion is about 100 times smaller than that 
of the Earth,  and it varies much more slowly (time scales of 1 month and longer). Therefore, it can 
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94 
easily be solved for from the data. Lunar motions should have no effect on accuracy a t  the 0.1- 
marcsec level if appropriate care is taken. 
Source structure will cause systematic errors in astrometric measurements. This effect is most 
serious for bandwidth-synthesis measurements of a source which is significantly resolved, and can be 
many milliarcseconds in size. The baselines of the proposed lunar interferometer are sufficiently 
short that  there will be many nearly unresolved sources (especially a t  20 to 30 GHz); the 
interferometer could concentrate exclusively on such objects. In that case, the measured astrometric 
position will be the emission centroid a t  that  frequency. 
High observing frequencies (20 GHz or higher) are  thus desirable, a s  source sizes shrink with 
increasing frequency for most sources, and the centroid should be closer to the massive “central 
engine” powering the source than at lower frequencies. At 30 GHz, many sources will be 0.1 to 
1.0 marcsec in extent. Time variation of the emission centroid is of concern, particularly for super- 
luminal sources of moderate size such a s  3C 345 and 3C 273. The VLBI maps made on Earth will be of 
help in this instance and should be useful in calibrating this time variation to 0.1 marcsec or better. 
Many sources will have structure much less variable than that of 3C 345, and this calibration will not 
be necessary. 
Signal to noise will be more of a limitation than for Earth-based astrometry. When compared 
to antennas and receivers used on Earth,  the lunar antennas will be smaller, and, because of the 
expense of refrigeration, the receivers may be of lesser quality. Furthermore, the baselines are  
shorter, and the required accuracy is higher. A l-year observing program on 500 sources will allow 
100 10-minute scans per source. The sensitivity limitations on angular accuracy are  as follows. 
1. For BWS (VLBI), 
0.06 marcsec T - -  su 
AQ = 
0.5 2 
loo0 ’0.2 (B  500) 15 span 
2. For radiofrequency (RF) phase measurement (connected-element interferometry), 
0.006 marcsec T,, 
Here, T50 is the system temperature in units of 50 K ,  D is the antenna separation (in units of 1000 km 
for VLBI, 100 km for connected-element interferometry), 5’0.2 is the correlated flux in units of 0.2 Jy,  
B W 5 0 0  is the correlated bandwidth in units of 500 MHz, d15 is the antenna diameter in units of 15 m, 
B Wspan is the spanned bandwidth in units of 1 GHz, and ~ 3 0  is the observing frequency in units of 
30 GHz. 
Instrumental effects will be a major problem. For VLBI observations, the quality of the local 
oscillators will probably be the critical issue. Hydrogen masers have errors of -40 psec in 104 sec, but 
0.1 marcsec corresponds to a delay precision of 1.5 psec over a 1000-km baseline. A new generation of 
frequency standards would be required. 
For connected-element observations, the clock quality is not critical. However, a s  0.1 marcsec 
corresponds to a delay of only 0.15 psec (0.05 mm light travel time) over a 100-km baseline, extreme 
care would be needed in the distribution of the local oscillator signal and in the calibration of any 
instrumental phase and delay effects. This constraint would probably pose the greatest technical 
95 
difficulty to performance of astrometry with a n  accuracy of 0.1 marcsec or better. Three possible ways 
to improve the accuracy are 
1. Increase baseline length to decrease the sensitivity to the effect. 
2. Use round-trip transmission to cancel out length variations in the LO signal transmission 
path. 
3. Distribute the LO signal from a satellite in Earth geosynchronous orbit. Any errors in 
knowledge of the satellite orbit would be reduced by the ratio of baseline length to Earth-Moon 
separation. 
Applications of Sub-0. l-Milliarcsecond Astrometry 
An improvement in astrometric accuracy by more than an  order of magnitude would have 
significant astronomical implications. A search for quasar proper motions would be of interest. The 
absolute motions of components in superluminal sources could be measured. On a galactic scale, it  
would be possible to measure the Sun’s motion about the galactic center (5 marcsecfyr, allowing a 2% 
measurement in just 1 year). By observing a number of water masers (not possible with BWS) and 
radio stars, definitive studies of galactic dynamics become possible. 
Spacecraft navigation would be helped by such high-precision astrometry. Missions to the 
outer solar system and beyond would benefit especially. An error of 0.1 marcsec corresponds to 2 km 
a t  Neptune’s orbit and 15 000 km (0.0001 AU) a t  1 pc. 
96 


Lunar radio astrometry

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