An array of three radio telescopes on the Moon, separated by 100-1000 km, could measure the positions of compact radio sources 50-100 times more accurately than can be done on Earth. These measurements would form an all-sky reference frame of extreme precision (5-10 micro-arcsec) and stability, with applications to the dynamics of the solar system, our galaxy, and nearby galaxies

Linfield, R. P.

English

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321
RADIO ASTROMETRY
R. P. Linfield
jet Propulsion Laboratory
4800 0ak Grove D_e
Pasadena CA 91109
 93-17452
An array of three ra_'o telescopes on the Moon, separated by 100-1000 km, could measure the positions
of compact radio sources 50-100 times more accurately than can be done on Earth. These
mea_rements would form an all-sky reference frame of extrenw lZnA'Lclon (5-I0 var_ec) and stabiliO,,
with applications to the dynamics of the solar system, our galaxy, and nearby galaxies.
RADIO ASTROMETRY:
EARTH-BASED LIMITATIONS
The angular resolution, 0, of a telescope of diameter d receiving
electromagnetic radiation at a wavelength h is limited by
diffraction to 0 _h/d. At optical wavelengths, the diffraction limit
is <1" for telescopes larger than about lOcm. At radio wave-
lengths of l-6cm, where telescopes of diameter 50-100m op-
erate, the diffraction limit is 20"-10". This would seem to favor
optical wavelengths for high angular resolution. However, the use
of superheterodyne detectors at radio wavelengths allows data
from widely separated telescopes to be coherently combined, thus
synthesizing very large apertures. The angular resolution of this
technique, radio interferometry, is limited only by the physical
separation of the antennas.
The precision of radio astrometry, the measurement of angular
positions on the sky, can be superior to the angular resolution.
However, a number of systematic error sources limit the accuracy.
The two most serious such error sources for Earth-based
measurements arise from the troposphere and from deformations
and irregular rotation of the Earth.
The troposphere introduces a delay of about 7 nsec to incoming
wavefronts. The component of this delay due to water vapor is
difficult to calibrate precisely because the distribution of water
vapor is very inhomogenous, both spatially and temporally. Water
vapor radiometers measure the integrated fine-of-sight emi._sion
from the 22-GHz water line, an imperfect measurement of the
column density of water vapor along that line of sight. Even with
parameter estimation from the astrometric measurements, this
limits the accuracy of the measurements. Future water vapor
radiometers will improve the acctwacy by an unknown amount.
Based on current experience, tropospheric water vapor may well
limit the accuracy of radio astrometry to 300-500 parcsec.
The rotation of the Earth is uniform to first order, both in rate
and in the direction of the rotation axis. However, there are
second-order perturbations in both quantities due to a variety of
effects with large stochastic (i.e., unpredictable) components.
These stochastic terms arise from the evolving fluid sheath of the
Earth, as well as the large fluid core. At the submiUiarcsecond
level of accuracy, the rotation phase will need to be measured
several times per day, or perhaps even much more often,
precluding the possibility of estimating it from astrometric
measurements. The largest variation in the shape of the Earth is
due to lunar tides, and can be modeled. However, more minor
deformations due to the variable distribution of the atmosphere
and of liquid and solid water greatly complicate the time variation
of the vector between the two radio telescopes (the b,'tseline
vector). One or several of these rotational and tidal effects may
impose a fundamemal limit of 300-500 #arcsec on the accuracy
of grotmd-based radio astrometry.
Differential Earth.based observations can determine small
angular separations (i.e., between two closely spaced radio
sources) to an accuracy of better than 500 parcsec. However, the
accuracy of an all-sky astrometric catalog is limited by the effects
discussed above.
ADVANTAGES OF THE MOON
The Moon allows an opportunity to escape from the two largest
error sources of Earth-based radio astrometry. The Moon has a
negligible neutral-gas atmosphere, and because it has no fluid
sheath or sizable liquid core, its rotation and deformations can
be modeled to very high accuracy. This latter facet gives it a large
advantage over Earth orbit as a site for high-precision astrometry.
PROPOSED LUNAR
ASTROMETRIC INSTRUMENT
I propose an array of three radio telescopes on the Moon. They
would be arranged very roughly in an equilateral triangle located
near the lunar equator (thus allowing most of the sky to be
accessible). The distance between telescopes would be in the
100-1000 km range (it is not dear what separation will give the
best accuracy). IJghtweight antennas of about 15-m diameter with
surface tolerance in the range 0.2-0.5 mm would be used.
Microwave finks or coaxial cables would connect the three
antennas to a control center (this could be located near one of
the antennas). Local oscillator phase would be distributed to the
antennas, with intermediate frequency (IF) data transmitted back
for correlation. The correlation process would reduce the data
volume to a few kilobytes per hour, which would be sent to Earth
for subsequent analysis.
SOURCES OF
ERROR AND ESTIMATED ACCURACY
This instrument would concentrate on several hundred
compact radio sources, distributed more or less uniformly over
the sky. It would observe the entire .set of sources 3-20 times
during a month (only half of them are visible at any one time).
https://ntrs.nasa.gov/search.jsp?R=19930008263 2020-03-17T09:05:52+00:00Z
322 2nd Conference on Lunar Bases and Space Activities
This observing strategy reveals .systematic effects in the data much
better than king integrations on individual sources. A one-year
observing program on 500 sources would give a total integration
time of about 15 hours per source. This yields a precision from
S/N limitations of
8_arcsec Ts0
AO = D S :D_v: _os._2
100" I00 K °wG|Iz I _ I _/2._
Ts0 is the _.'stem temperature in units of 50 K, DIt_) is the antenna
separation in units of 100 kin, S100 is the source correlated flux
in units of 100 mJy, BWGttz is the IF bandwidth in GHz, dts is
the antenna diameter in units of 15 m, and v_0 is the sky frequency
in units of 30 GHz.
The absence of a neutral-gas atmosphere eliminates one large
error source. The delay introduced by charged particles in the
solar wind and the Earth's magnetosphere can be measured and
removed by dual frequency observations (e.g., 40GHz and
2 GHz). The bandwidth at the lower frequency can be much
smaller than at the higher frequency.
The rotation of the Moon must be either modeled or
determined s_ia parameter estimation. Because the Moon is
geologically quiet, with no atmosphere or oceans, its motions are
very deterministic. Libration (nonlinear rotation) terms due to
gravitational harmonics up to degree and order 4 ( 18 terms), with
perhaps a few fifth degree terms, will be important for accuracies
in the microarcsecond regime. In addition, Love numbers through
degree 3 or 4 ( 12-18 parameters) will be required to model tidal
deformations.
The proposed astrometric instrument will therefore be required
to solve for 30-40 time-invariant lunar motion parameters. These
parameters are ofgreat interest in their own right, :is they pro_Sde
information on the physical properties of the lunar interior. In
addition, there may be a small stochastic component to lunar
rotation. It is at least 100 times smaller than its terrestrial
equivalent, and varies on much longer timescales, allowing it to
be easily determined from the data. The fundamental limitation
on astrometric accuracy from lunar motions appears to be below
10 _arcsec.
Source structure effects may cause the largest errors. Compact
extragalactic radio .sources have nonzero sizes and time-variable
structure. The relatively short baselines (<1000km) of the
proposed instrument will result in many sources being only
slightly resolved. The measured positions for them .sources will
be that of the emission cemroid. In general, the smallest apparent
position shifts will _x:cur for the most compact sources. There
are many moderately weak (100mJy) sources with estimated
sizes under 50_aresec at observing frequencies of 30-50 GHz. The
_ariation in emi_ion centroid will generally be <20 _arcsec.
Measurements of many sources will determine a global frame to
an accuracy at least a factor of 2 better, or <10 _arcsec. The desire
to minimize source structure effects on the data forces the sky
frequency to be at least 30GHz, with 40-50GHz desirable. Yet
larger frequencies are disadvantageous due to higher system
temperatures and degraded antenna performance.
The control of instrumental errors will be a major problem at
this level. Thermal and gravitational dcflcctions in the antennas
will have to be known to better than 0.1 mm. Systematic
instrumental phase errors must be smaller than 0.5 ° for
10 garcsec accuracy at 40-GHz sky frequency on a 200-kin
baseline. Very careful design and construction will be required,
but this should not be the limiting source of error.
CONCLUSIONS AND APPLICATIONS
The overall limiting astrometric accuracy of this instrument is
estimated at 5-10 #arcsec, a factor of 50-100 improvement over
Earth-based capability. A global reference flame with this accuracy
would yield significant .scientific results. The dynamics of our own
galaxy could be determined to high accuracy through the study
of the proper motions and parallaxes of compact galactic radio
sources. The galactic rotation curve and deviations from rotational
motion would be revealed in detail. Proper motions of nearby
(diStance less than 5 Mpc) galaxies would be me_le.
_is reference frame would have other appi_cations. The
positions of planets could be determined in the frame through
VLBI observations of spacecraft in orbit about those planets. This
would allow very precise studies of solar system dynamics.
Acknowledgments. i thank ILTrcuhaft and J. Williams for helpful
diK'ugsiorLs.


Radio astrometry from the Moon

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