Viking radio data analysis and synthesis was used for the following: (1) Solar System Model and Data Set; (2) Rotation of Mars; and (3) Solar System Constants and Tests of Relativity

Shapiro, I. I.

English

The rotational motion of Mars and its geophysical ramifications were investigated. Solar system dynamics and the laws of gravitation were also studied. The planetary ephemeris program, which was the central element in data analysis for this project, is described in brief. Viking Lander data were used in the investigation

NASA Technical Reports Server

VIKING RADIO SCIENCE DATA ANALYSIS AND SYNTHESIS
Grant NAGW-411
Semiannual Status Report No. 3
For the period 30 December 1983 through 30 June 1984
Principal Investigator
Irwin I. Shapiro
September 1984
Prepared for
National Aeronautics and Space Administration
Washington, DC 20546
Smithsonian Institution
Astrophysical Observatory
Cambridge, Massachusetts 02138
The Smithsonian Astrophysical Observatory
is a member of the
Harvard-Smithsonian Center for Astrophysics
The NASA Technical Officer for this grant is Mr. Henry C. Brinton. Code EL-4,
Solar System Exploration Division, NASA Headquarters, Washington, D. C. 20546.
https://ntrs.nasa.gov/search.jsp?R=19840026314 2020-03-20T21:36:36+00:00Z
VIKING RADIO SCIENCE DATA ANALYSIS AND SYNTHESIS
Grant NAGW-411
Semiannual Status Report No. 3
For the period 30 December 1983 through 30 June 1984
Principal Investigator
Itwin I. Shapiro
September 1984
Prepared for
National Aeronautics and Space Administration
Washington, DC 20546
Smithsonian Institution
Astrophysical Observatory
Cambridge, Massachusetts 02138
The Smithsonian Astrophysical Observatory
is a member of the
Harvard-Smithsonian Center for Astrophysics
The NASA Technical Officer for this grant is Mr. Henry C. Brinton, Code EL-4,
Solar System Exploration Division, NASA Headquarters, Washington, D. C. 20546.
Page 2
During the reporting period, we made progress toward our primary
objectives: (a) an investigation of the rotational motion of Mars and its
geophysical ramifications, and (b) the study of solar-system dynamics and
the laws of gravitation. We obtained a new bound on the rate of change of
the constant of gravity G measured in atomic units
|G/G| < 2xlO~n per year
and our studies continue to show that we can expect to reduce the
uncertainty to 10 per year or less. This and other new results were
presented at the May 1984 meeting of the AAS, Division of Dynamical
Astronomy (DDA).
In the remainder of this report, we consider the recent technical
progress which made possible our new results and which will be the basis of
additional scientific results in the near future. This discussion is
divided into three parts: A. Solar System Model and Data Set; B. Rotation
of Mars; and C. Solar System Constants and Tests of Relativity. The last
part includes the planetary masses and relativity results that were
presented at the DDA Meeting.
A. Solar System Model and Data Set
The central element in our data analysis is the Planetary Ephemeris
Program (PEP) which embodies our mathematical models of the solar system
and observables. It functions as a weighted-least-squares fitting (and
Kalman filtering) facility for observations related to the positions,
velocities, rotations, etc. of solar-system bodies, natural and manmade.
PEP contains approximately 10 lines of code, which is written mostly in
Fortran with a small part in assembly language. It was originally
Page 3
developed at the BUT Lincoln Laboratory where it is still in nse. Over
most of the past 17 years, the principal center of development has been the
MIT Dept. of Earth and Planetary Sciences; at the beginning of CY1983, that
center shifted to the Harvard-Smithsonian Center for Astrophysics. During
the past few years, PEP has been systematically upgraded to take advantage
of changes in computing and software-development techniques.
During CT83, the asteroid model in PEP was changed. We had been able
to estimate the mass of a fictitious uniform ring and the masses of eight
separate asteroids. (In an earlier modification, the latter had been
increased from four.) During the reporting period, the model was enhanced
so that it is now also possible to estimate the densities of asteroids in
up to five classes. This new model serves to include, at least
approximately, the effects of up to 200 asteroids which are too small to
consider individually but which may be important collectively. For each,
the mass is the product of the density estimated for its class and an
externally provided volume. Although this model has serious shortcomings,
the dearth of applicable auxiliary data makes it a reasonable compromise.
In our recent numerical experiments with the data, we have made nse of the
ability to estimate the larger number of individual asteroid masses and
densities for the different asteroid classes.
Shortly before the start of the reporting period, we iterated the
estimator a total of four times to obtain a stable, converged solution.
During the first iteration, we added some new terms associated with the
orientation of the planetary orbits. At the last iteration, we
reintegrated all of the variational equations and included all of the new
"cross partial" terms. At this time, we also increased the number of
outer-planet orbital elements that could be estimated by including the
Page 4
required additional variational equations. Finally, we recalculated the
entire sensitivity matrix and recomputed the prefit residuals.
To investigate the results of the iterations, we performed a series of
numerical experiments during the reporting period; we found our solutions
to show more stability and the postfit residuals to show less systematic
signature than before. Before the iteration, we had been unsuccessful in
including in our solutions the Viking Lander delay data taken after
5 August 1980: When included, these data showed, and.caused the other
Lander delay data to show, a large systematic signature; their prefit
residuals had a systematic signature with about a 5 us peak. (The same
problem was encountered at JPL.) After the iteration, the postfit
systematic signature was found to be reduced by roughly one-third. By
increasing the number of estimated asteroid masses, we were able to remove
about half of the remaining systematic signature. Finally, we included the
outer-planet NPs (Earth-planet time-delay pseudo-data derived from the
Doppler and ranging observations of spacecraft at encounter with the
planet) and optical observations which permitted us to estimate an enlarged
set of outer-planet orbital elements; the systematic signature became lost
in the noise.
Our present, recently enlarged working set of data is listed in
Table 1. For discussion, we divide the Viking Lander delay data into two
groups: those taken through S August 1980, when the last dual-band
calibration data were received from the Orbiter; and those taken between
6 August 1980 and November 1982, when the last Viking failed. Although the
latter set lacks corrections for the effects of the solar plasma, the data
that we use from this set are restricted to those taken at a time when the
Sun-Earth-Mars angle was large and thus the plasma-induced errors in the
Page 5
measurement of the vacuum delay can be corrected approximately in the mean
I
by use of a simple model. Thus, we have discarded the data taken near the
time of the Mars superior conjunction of 2 April 1981; they require large
plasma corrections that cannot be made usefully with a model. The errors
assigned to the remaining data range from 2.5 to 5 times those that are
*
assigned to data for which there are plasma density estimates from the
Orbiter dual-band tracking.
A comparison of Table 1 with Table 2 of Reasenberg [1983], which is
reproduced in the Appendix, shows four recently enlarged sets of data. The
extra plasma-corrected Lander delays are the result of the "discovery" in
November 1983 of 150 lost data, an improved plasma correction method, and a
re-evaluation of previously discarded data made fruitful in part by the
improved solar-system model. The increased number of Lunar Laser NPs were
obtained from our HIT colleagues (R. W. King, private communication). The
two sets of radar data show a dramatic increase in the number of
observations. This is the result of an implementation at Arecibo of a
technique (Shapiro et al.. 1972) by which simultaneous observations are
made of a contiguous series of small regions along the planet's Doppler
equator.
i
B. Rotation of Mars
In addition to precession and nutation [Reasenberg and King, 1979],
our model of the rotation of Mars includes a secular rate of change of the
period and both annual and semiannual variations in the phase of rotation
[Williams, 1977, private communication; Philip, 1979; Reasenberg and King,
1979]. Our preliminary investigation with a 400-day set of Lander delay
data provided a marginal detection of the semiannual terms [Reasenberg et
Page 6
al.. 1979] and showed that these could not be clearly distinguished from
the annual terns with such a small span of data. A better result was
provided by our initial study with an 800-day data set to which we applied
the improved plasma estimates and data weights: The annual terms are found
to be small and only moderately correlated in the estimator with the
semiannual terms. The semiannual terms have an amplitude (expressed as an
equatorial surface displacement) and a phase (11.5 +5 m, -2° +25°)
consistent with the model of Davies et al. [1977] (10.5 m, -36°), but not
so consistent with the model of Philip [1979] (9.6 m, -58°). The published
measurements of atmospheric pressure [Hess et al.. 1979] cover a time span
insufficient for a meaningful comparison. The results of an analysis of a
much longer span of Lander pressure measurements have been supplied to us
by James Tillman who is preparing this material for publication [private
communication, 1983, 1984] and distributed through the NSSDC. These data
show that the general features of the annual and semiannual pressure
fluctuations at the Landers repeat from year to year. The use of the
Viking data to determine the amplitude and phase of the annual and
semiannual terms in the rotation of Mars will provide one of the few
independent constraints on global models of the circulation and
condensation of the atmosphere of Mars. (See, for example, Shimazaki and
Shimizn [1979] and references therein.)
During the reporting period, we modified our model of the rotation of
Mars. In the old model, the seasonal irregularities were added to a spin
rate that was constant in ephemeris time. In the new model, that spin rate
-9is constant in Mars proper time, and therefore varies by about +10 in
ephemeris time. The associated rotational phase shift is of the same order
and phase as the predicted annual effect of the atmospheric condensation at
Page 7
the poles. The new relativistic correction is thus critical for the
accurate determination of the amplitudes and phases of the proposed
meteorological effects.
C. Solar System Constants and Tests of Relativity
At the June 1984 meeting of the AAS, Division of Dynamical Astronomy,
Babcock [1984] and Chandler [1984] presented some of our recent results.
Table 2 contains the values of planetary masses from Babcock's
presentation. In general, our results agree well with the latest values
published in the Astronomical Almanac. Other results that they presented
were improved estimates of the relativistic parameters; these are listed in
Table 3.
Page 8
REFERENCES
Babcock, R. W., J. F. Chandler, R. D. Reasenberg, and I. I. Shapiro,
"Limits on Metric Parameters 0 and y, BAAS, in press, 1984.
Chandler, J. P., R. W. Babcock, R. D. Reasenberg, and I. I. Shapiro, "New
Limit on G." BAAS, in press, 1984.
Davies, D. W., C. B. Farmer, and D. D. LaPorte, "Behavior of Volatiles in
Mars' Polar Areas: A Model Incorporating New Experimental Data," J.
Geophvs. Res.. 82, 3815-3822, 1977.
Hess, S. L., R. M. Henry, and J. E. Tillman, "The Seasonal Variation of
Atmospheric Pressure on Mars as Affected by the South Polar Cap," J.
Geophvs. Res.. 84, 2923-2927, 1979.
Philip, J. R., "Angular Momentum of Seasonally Condensing Atmosphere, with
Special Reference to Mars," Geophys. Res. Letters. 6, 727-730, 1979.
Reasenberg, R. D. and R. V. King, "The Rotation of Mars," J. Geophys. Res..
84. 6231-6240, 1979.
Reasenberg, R. D., R. B. Goldstein, P. E. MacNeil, and I. I. Shapiro, "Mars
Rotation: Bound on Seasonal Variation," Bull. Am. Astron. Soc.. 11.
571, 1979.
Reasenberg, R. D., "The Constancy of G and Other Gravitational
Experiments," Philo. Trans. R. Soc. Ser A (Proceedings of the
Discussion Meeting on the Constants of Physics, The Royal Society,
25-26 May 1983), A310, 227-238, 1983.
Shapiro, I. I., S. H. Zisk, A. E. E. Rogers, M. A. Slade, and T. W.
Thompson, "Lunar Topography: Global Determination by Radar," Science.
178. 939-948, 1972.
Shimazaki, T. and M. Shimizn, "The Seasonal Variation of Ozone Density in
the Martian Atmosphere," J. Geophys. Res.. 84, 1269-1276, 1979.
Prepared 19 September 1984 by R. D. Reasenberg, Room B-217, FTS 830-7108.
Page 9
Table 1. Combined Sets of Data
Approximate Time Span
of Observations
Number of Data Prom To
VIKING
Lander delay
(plasma corrected) 1041
Lander delay
(not plasma corrected) 239
Orbiter NP> 4060
Lander Doppler 1075
LLR
Observing session NP3 3074
MARINER 9
Orbiter NP* 185
RADAR
Mercury 4339
Venus 5464
MERIDIAN CIRCLE4
Sun 1023
Moon 212
Inner planets (M.V.M) 1518
Outer planets (J.S.U.N) 1643
OUTER PLANET NP> 6
July 1976
Aug. 1980
June 1976
Sept.1979
Aug. 1980
Nov. 1982
Aug. 1977
Aug. 1980
Nov. 1971
1969
1970
Oct. 1972
1982
1978
see note 5
1
 All observables are time delays except for the Viking Lander Doppler
and for the meridian circle data.
* The spacecraft Normal Point (NP) is a compressed datum: the equivalent
Earth-planet time delay that would have been measured between the centers
of mass of the planets. All spacecraft NPs were obtained from the Jet
Propulsion Lab where they were derived from the tracking data.
1
 The Lunar Laser Ranging (LLR) Normal Point (NP) is a single estimate of
the round trip propagation time between a tracking station and a single
lunar retroreflector. The estimate is an average based on all photons
received during an observing sequence. Under good conditions, there are
as many as three sequences per day.
4
 The data are a mixture of right ascension and declination measurements.
5
 The epochs of the four Jupiter data are 12/4/73, 12/3/74.
3/5/79. and 7/10/79; those of Saturn are 11/13/80 and 8/26/81.
Page 10
Table 2. Planet Mass Estimates1
Planet1
Mercury
Venus
Earth + Moon
Mars*
Jupiter
Saturn
Uranus
Neptune
Earth/ Moon
Mass Estimates Differences Standard
Analysis Astron. Between Deviation
at CfA Almanac (1984) Estimates (CfA)
6,023,700 6,023,600
408,523.1 408,523.5
328,900.554 328,900.550
3,098,750 3,098,710
1,047.3482 1,047.350
3,497.90 3,498
22,830 22,960
19,480 19.314
81.300565 81.300588
100 1000
0.4 1
0.004 0.003
40 60
0.0018 0.002
0.10 0.3
130 300
166 500
2.3zlO~5 1.5xlO~5
1
 All planet masses in inverse solar mass units.
2
 The data are not sensitive to the mass of Pluto.
3
 The CfA estimates of the mass of Mars does not use the spacecraft
encounter data which dominate the estimate given in the Astronomical
Almanac (1984, DS Government Printing Office).
Page 11
Table 3. Relativity Results Presented at the DDA Meeting, May 1984
J2
P-1
Y-l
G/G
N/A -3+3
0 -0.025+0.05
0 0. +0.002
N/A»
Estimates1
#2
-0.01+0.02
0. +0.0015
#3
-610 *
0+2 10~ per year
1
 Each column represents a summary of results from a large number of
solutions of the least-squares normal equations. The errors shown are
realistic estimates of the standard deviation.
2
 Although general relativity does not address the possible time
dependence of the^relation between atomic and gravitational times, one
normally assumes G/G = 0 in classical physics.
Phil. Tram. R. Soc. Land. A 310, 227-238 (1983)
Printed in Great Britain
APPENDIX
Page 12
The constancy of G and other gravitational experiments
BY R. D. R E A S E N B E R G
Radio and Geoastronomy Division, Smithsonian Astrophysical Observatory, Harvard-Smithsonian
Center for Astrophysics, Cambridge, Massachusetts 02138, U.S.A.
Traditionally, theories of gravitation have received their most demanding tests in the
solar-system laboratory. Today, electronic observing technology makes possible solar-
system tests of substantially increased accuracy. We consider how these technologies
are being used to study gravitation with an emphasis on two questions:
(i) Dirac and others have investigated theories in which the constant of gravitation,
G, appears to change with time. Recent analyses using the Viking data yield \G/G\
< 3 x 10~u per year. With further analysis, the currently available ensemble of data
should permit an estimate oFG/G with an uncertainty of 10~u per year. At this level it
will become possible to distinguish among competitive theories.
(ii) Shapiro's time-delay effect has provided the most stringent solar-system test of
general relativity. The effect has been measured to be consistent with the predictions of
general relativity with a fractional uncertainty of 0.1%. An improved analysis of an
enhanced data set should soon permit an even more stringent test.
Technology now permits new kinds of tests to be performed. Among these are some
that measure relativistic effects due to the square of the (solar) potential and others
that detect the Earth's 'gravitomagnetic' field (the Lense-Thirring effect). These
experiments, and the use of astrophysical systems are among the experimental challenges
for the coming decades.
TABLE 2. COMBINED SETS OF DATA
approximate range of
error assumed in estimator
sourcej no. of data • min max unit
Viking
Lander delay
(plasma corrected) 798 20 60 ns
Lander delay
(not plasma corrected) 263 50 300 ns
Orbiter n.p.J 4060 100 900 ns
, Lander Doppler 1075 20 40 mHz
l.l.r.
Observing session n.p.§ 2613 6 14 ns
Mariner 9
Orbiter n.p. + 185 0.1 10 us
radar
Mercury 642 1 15 ps
Venus 784 1 15 MS
meridian circle||
Sun 1023 « 2
Moon 212 K 0.5
inner planets (M, V, M) 1518 «1
outer planets (J, S, U, N) 1643 «1
outer planet n.p. 6 25 500 us
| All observables are time delays except for the Viking Lander Doppler and meridian circle data.
J The orbiter normal point (n.p.) is a compressed datum: the equivalent Earth-Mars time delay measured
between the centres of mass of the planets.
§ The lunar laser ranging (l.l.r.) normal point (n.p.) is a single estimate of the round trip propagation time
between a tracking station and a single lunar retroreflector. The estimate is an average based on all photons
received during an observing sequence.
|| The data are a mixture of right ascension and declination measurements.
^J The outer planet normal point (n.p.) is a compressed datum from a spacecraft encounter with either Jupiter
or Saturn. The n.p. is the equivalent Earth-planet time delay measured between the centres of mass of the planets.


Viking radio science data analysis and synthesis

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server

NASA Technical Reports Server