Radio science experiments: The Viking Mars orbiter and Lander

IcArus 16, 57-73 (1972)

Radio Science Experiments: The Viking Mars Orbiter and Lander W. H. MICHAEL, J R . NASA--Langley Research Center, Hampton, Virginia 23365

D. L. CAIN, G. F J E L D B O , AND G. S. L E V Y Jet Propulsion Laboratory, California Institute of Technology Pasadena, California 91103

J. G. DAVIES University of Manchester, Nu~eld Radio Astronomy Laboratories Mavzlesfield, Cheshire, England SK11 9 D L

M. D. GROSSI Raytheon Company, Sudbury, Massachusetts 01776

I. I. S H A P I R O Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 AND

G. L. T Y L E R Stanford University, Stanford, California 94305 Received May 5, 1971 The objective of the radio science investigations is to extract the m a x i m u m scientific information from the data provided by the radio and radar systems on the Viking Orbiters and Landers. Unique features of the Viking missions include tracking of the landcrs on the surface of Mars, dual-frequency S- and Xband tracking data from tho orbiters, lander-to-orbiter communications system data, and lander rddar data, all of which provide sources of information for a number of scientific investigations. Post-flight analyses will provide both new and improved scientific information on physical and surface properties of Mars, on atmospheric and ionospheric properties of Mars, and on solar system properties.

I. INTRODUCTION For the Viking 1975 Mars missions, the celestial mechanics, radio occultation, and a number of other investigations are combined in the activities of the Radio Science Team. The objective of the radio science investigations is to extract the maximum scientific information from the data provided b y the radio and radar systems on the Viking Orbiters and Landers. Analyses of these data should provide information on physical and surface properties of Mars, on atmospheric and ionospheric properties of Mars, and on solar system properties. The Viking radio science investigations will, in some aspects, extend the scientific ~) 19"/2by AcademicPress, Inc.

results provided b y previous Mariner flyby missions and the Mariner Mars 1971 orbiter missions (Lorell, Anderson, and Shapiro, 1970; Kliore et al., 1970). For a number of investigations, analyses of the combined Viking and previous mission data will provide increased accuracy and will allow additional parameters to be included in the solutions. Unique features of the Viking missions include the tracking data from the landers on the surface of Mars, the dual-frequency S- and X-band data from the orbiters, lander-to-orbiter communications system data, and lander radar data, all of which provide sources of information for additional scientific investigations. 57

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RADIO SCIENCE EXPERIMENTS

The presently defined Viking radio science objectives, categorized b y properties investigated and b y the types of measurements involved, are discussed in the following sections.

II. R F SrSTE~S USED FOR RADIO SCIENCE The radio and radar systems normally used for mission functions are to be used for radio science investigations. The overall communications systems are illustrated in Fig. 1. The Viking Lander communication system has a uhf transmitter that is used to relay data to the orbiter. It also has a two-way S-band link which is capable of direct communications with the Earth. The S-band transponder can be used for coherent Doppler and turn-around ranging. In addition to the communication radio system, the lander also has a radar altimeter and a terminal descent landing radar. The characteristics of these radars are presented in Table I and discussed more fully in Section III, 2. The orbiter has uhfreccption capabilities and an S-band transponder system. The planetary-type S-band transponder has been modified so that it also transmits a coherent X-band signal on the downlink. The S- and X-band portion of the orbiter radio system is illustrated in Fig. 2. The uplink signal at 2116MHz will come through the low-gain antenna and diplexer to the transponder receiver. The voltage-

59

controlled oscillator (VC0) of the receiver is phase locked with the uplink carrier. In the standard S-band transponder, the VCO, which is at a frequency of approximately 19MHz, is multiplied b y 120 to produce an S-band downlink frequency of 2298 MHz. This S-band signal is modulated with the turn-around ranging code and/or the communication telemetry. I f the receiver is not in lock, a transfer command switches the auxiliary oscillator (Aux Osc) into the circuit in place of the VCO (in this case there will not be any ranging). The transmitter is modified so that the 19MHz exciter chain (from either the VCO or Aux Osc) goes through an isolation amplifier to an isolator switch and then to a multiplier chain which multiplies the 19MHz b y a factor of 440. The ranging code from the receiver comes via an isolation amplifier to a final X5 multiplier stage where it is phase modulated onto the X-band carrier. The output of both transmitters goes to the high-gain antenna. The 64-m (210ft) antenna ground stations will be equipped with feed systems that divide the frequencies into two separate channels. Liquid helium-cooled, traveling-wave masers will amplify the signals at both frequencies to assure best signal-to-noise ratio performance. A new ground station receiver system will separately phase lock and track both frequencies. The new receiver system has been designed for maximum stability for both phase and modulation delay. The phase delay will be compared b y use of two high-resolution Doppler extractors. The

TABLE I VIKING RADAR CHARACTERISTICS Parameter

Terminal descent landing radar

Radar altimeter

Altitude range Velocity range Accuracy

1.5 m - 5 k m 0.3-210 m / s e c 1.5 % or 0.3 m / s e e

30m to 45km

RF power Frequency

80mW/beam 13.1-13.4 G H z

Other

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61

RADIO SCIENCE EXPERIMENTS

range modulations will be analyzed b y using a two-channel modification of the sequential coding technique (Martin, 1969). The stability of the entire system for the duration of an 8-hr pass is the important design criterion in measuring rate of change of electron content. The ground equipment can be calibrated before and after each pass but the differential modulation delay through the spacecraft cannot. The design of the spacecraft system must provide high group-delay stability, and it must also allow group-delay changes caused b y variations in voltage and temperature to be calibrated out. The rf system provided on the Viking spacecraft will be utilized for a variety of measurements, including dispersive measurements, very-long-baseline interferometry (VLBI) measurements, and simultaneous spacecraft observations, all of which contribute to the scientific objectives and also provide corrections to the tracking data. Dispersive measurements will be made of the difference in propagation velocity of the S- and X-band signals due to the medium. These phase-advance, groupretardation effects can be used to determine the columnar electron concentration and its rate of change. The range and range-rate tracking data are inherently contaminated b y these effects. Thus, the dual S/X-band system will make it possible to simultaneously collect range, range-rate, and dispersive data, permitting correction for the interplanetary medium and the Earth's ionosphere. Quite promising are the gains in tracking accuracy that can be obtained b y the direct differencing of the counted Doppler, or received phase, from two or more spacecraft at one site, the so-called dualor multispacecraft observable. Except for the Martian troposphere and ionosphere, all sources of error from the propagation medium virtually disappear for this observable. To make full use of it the tracking system must be carefully designed. With the advanced systems expected to be used for the Viking missions, this and the other techniques mentioned should

provide a new level of tracking data accuracy for planetary missions. B y observing two or more of the spacecraft simultaneously at two or more ground sites, extraordinary accuracy can be obtained in the estimation of the relative directions of the various spacecraft. Almost all sources of error cancel in the differential fringe phases, since the signals from each spacecraft pass through nearly the same interplanetary paths and virtually identical paths through the Earth's atmosphere and ionosphere. I I I . PHYSICAL AND SURFACE PROPERTIES

OF MARS 1. Celestial Mechanics Measurements Post-flight analyses using the Viking spacecraft tracking data should provide improved determinations of physical properties of Mars, including its mass and gravitational field characteristics, its figure, the orientation and motion of its spin axis, and its internal properties. The measurements consist primarily of rangerate and range measurements between Earth tracking stations and the two Viking Landers and Orbiters, and make use of the continually increasing accuracy and sophistication provided by the NASA Deep-Space Network. Two features of the Viking tracking systems, the S-band tracking data from the spacecraft landed on the surface of Mars and the simultaneous S- and X-band tracking data from the orbiters, provide new measurements and data calibration sources as compared with previous NASA Mars missions. These data enhance determinations of physical properties of Mars and contribute to a number of other radio science objectives. Analysis techniques using combined or simultaneous orbiter and lander tracking information, or using the simultaneous tracking information from both landers or both orbiters, provide means for better elimination of data and model biases and for improvements in physical properties determinations. Determinations from Orbiter Tracking Data. Tracking data from the two Viking Orbiters will be used for determinations

62

w.H.

MICHAEL~ J R . E T A L.

of the mass and gravitational field pro- which a given set of gravitational coperties of Mars and of the planetary radii efficients may be estimated using a at locations at which the tracking signals typical Viking spacecraft orbit which is are occulted by the surface of Mars. I t synchronous with the rotational period of may be possible to define local mass Mars (Compton and Daniels, 1971). A anomalies, but such results will require a priori statistics were assumed for the considerably lower periapsis altitude than solution vector, which included gravitapresently planned in order to produce tional coefficients through fourth degree orbital perturbations which could be and order. Both range and range-rate detected. The main orbiter objectives tracking data were used in the analysis. related to physical properties, therefore, From this analysis it was apparent that will be the determinations of the radii significant improvement over the a priori at various occultation locations and of the values could only be obtained for the lower degree and order coefficients in the second-degree harmonic coefficients. Furspherical harmonic expansion of the Mars ther, it was noted that the mass is so gravitational potential function. coupled with other parameters that its Present knowledge of the gravitational estimation from the orbiter data may field of Mars, in addition to fairly precise require special techniques to improve the estimates of its mass, consists of deter- current knowledge. Improvements in the gravitational field minations of its second-degree zonal harmonic. Determination of all the second- determination statistics were noted in a degree harmonic coefficients will be of preliminary analysis which used nonparticular interest. These coefficients will synchronous-type orbits (1 hr difference be utilized to estimate the moments of in the period from the synchronous inertia of Mars and the orientation of its period). Similar improvements can be principal axes, to improve the knowledge anticipated with orbits with periapsis of the dynamical flattening of Mars, and to altitudes considerably lower than nominal derive internal density distribution models Viking orbits (approximately 1500km periapsis altitude). These considerations for further analysis. The primary data analysis technique for would allow the orbiter to sample the orbit determination and gravitational field gravitational field of Mars over a much analyses will be that of iterated differential wider range of longitudes and also to corrections of solution parameters using increase the gravitational perturbations numerical integration procedures for the on the orbiter at periapsis and hence equations of motion and variational equa- increase the information content in the tions, and using weighted least-squares tracking data. The lower periapsis altitudes procedures to fit the range-rate and range may allow a detection of local mass data. An alternate approach, to be con- anomalies such as those disclosed in the ducted in parallel, is that of analysis of the tracking data taken from the Lunar long-period and secular variations in the Orbiter spacecraft. A combination of the tracking data or orbital elements ; this procedure has advantages for recovering certain gravitational information obtained from the Mariner coefficients. Direct analysis of the Doppler 1971 missions with the Viking tracking residuals for determining local accelera- data should improve the determination of tions will also be employed if the procedure gravitational coefficients because of the is advantageous. All of these techniques increased number of observations and the have been utilized extensively in the different orbital geometries. Determinations from Lander Tracking analysis of the Lunar Orbiter data for the determination of the physical properties Data. Objectives of analyses of tracking of the Moon (Muller and Sjogren, 1968; data from the Viking Landers are deterMichael, Blackshear, and Gapcynski, 1969). minations of the orientation and motion Preliminary analyses have been per- of the spin axis of Mars and of the locations formed to determine the accuracy with of the landers on the surface of Mars.

RADIO SCIENCE EXPERIMENTS

T h e s e d a t a will also c o n t r i b u t e signific a n t l y in i m p r o v i n g t h e e p h e m e r i d e s of Mars a n d t h e E a r t h . K n o w l e d g e of t h e l a n d e r locations, p a r t i c u l a r l y t h e radius of t h e lander f r o m t h e center of m a s s of Mars, is i m p o r t a n t for i n t e r p r e t a t i o n of l a n d e r d a t a f r o m o t h e r Viking experim e n t s a n d for p r o v i d i n g reference points for M a r t i a n t o p o g r a p h y m e a s u r e m e n t s from Earth-based radar data. P r e l i m i n a r y analyses h a v e b e e n cond u c t e d to e s t i m a t e t h e accuracies of t h e spin axis o r i e n t a t i o n a n d lander location p a r a m e t e r s ( B l a c k s h e a r a n d Williams, 1971) using a w e i g h t e d least-squares technique similar to t h a t to be u s e d for t h e o r b i t e r analyses. These results include consideration of t h e effects of c u r r e n t u n certainties in D S N s t a t i o n locations, Mars ephemeris, a n d t h e r o t a t i o n a l r a t e of Mars. T h e results indicate t h a t t h e spin axis o r i e n t a t i o n a n d t w o c o m p o n e n t s of

63

t h e l a n d e r l o c a t i o n - - l o n g i t u d e a n d distance f r o m t h e spin a x i s - - c a n be d e t e r m i n e d r a t h e r a c c u r a t e l y w i t h one to t w o w e e k s o f t r a c k i n g d a t a , as i l l u s t r a t e d in T a b l e I I . T h e e s t i m a t e of t h e r e m a i n i n g lander location p a r a m e t e r - - t h e d i s t a n c e of t h e lander f r o m t h e Mars e q u a t o r i a l plane, Z - - c a n be seen to d e p e n d s t r o n g l y on t h e m a g n i t u d e of t h e Mars e p h e m e r i s errors. (The increase in t h e s t a n d a r d deviations of s o m e of t h e p a r a m e t e r s a f t e r analysis of 15 d a y s of d a t a , as c o m p a r e d to t h e s t a n d a r d d e v i a t i o n s for 5 d a y s of d a t a , is due to t h e increased effect of e p h e m e r i s errors o v e r this longer t i m e span. This increased s e n s i t i v i t y to e p h e m e r i s errors could h a v e b e e n a n a l y z e d to a c h i e v e e p h e m e r i s i m p r o v e m e n t ; h o w e v e r , such analysis is being c o n d u c t e d only for m u c h longer d a t a s p a n s in order to achieve b e t t e r s e p a r a t i o n of e p h e m e r i s p a r a m e t e r s . ) W i t h t h e e s t i m a t e of 1 3 k m for t h e s t a n d a r d

TABLE I I LANDER LOCATIONAND MAXS SPIN AXIS ORIENTATIONACCURACYESTIMATES Standard deviations, km 5-day tracking data coverage a

Parameter Longitude Distance off spin axis Z distance along spin axis Spin axis orientation

0kin Ephemeris error A priori Range-rate Range

5kin Ephemeris error b Range -rate Range

200km Ephemeris error ~ Range -rate Range

70km

0.15

0.69

0.17

5.1

0.17

14.

40kin

0.08

0.18

0.11

5.2

0.13

17.

100km 70kin

40. 0.38

0.40 1.5

64. 0.48

15. 14.

99. 0.48

98. 48.

15-Day tracking data coverage a Longitude Distance off spin axis Z distance along spin axis Spin axis orientation

70kin

0.03

0.10

0.04

40km

0.03

0.03

0.07

100km 70kin

30. 0.09

0.10 0.23

66. 0.20

14.

0.04

24.

0.10

5.

13.

99.

98.

31.

0.26

51.

2.7

a Six hours of continuous tracking per day; assumed accuracies are 1 mm/sec for range-rate and 15m for range. b Ephemeris velocity error of 5 × 10-Tkm/sec assumed. Ephemeris errors not solved for.

64

w . H . MICHAEL~ JR. E T A L .

deviation in Z, as given in the lower portion of Table I I for range data corresponding to 5km ephemeris error, and with the accurate values of the other lander components from range-rate data, the standard deviation of the lander radius to the center of mass would be approximately 13km times the sine of the lander latitude. The lander location radius is thus not well determined over short tracking intervals, except for landings at the equator. One possibility for improving the Zcomponent determination is an application of long baseline interferometric techniques in which the lander range data are received simultaneously at E a r t h tracking stations with a long north-south separation. For anticipated accuracies obtainable with such techniques, the error in Z could be reduced by about one order of magnitude. Such techniques could also contribute to the spin axis orientation determinations. Another possibility is t h a t of using both range-rate and range data from the landers over an extended lifetime of about four months to effectively eliminate the ephemeris errors, which could possibly reduce the standard deviation in Z by one, or perhaps two, orders of magnitude. There is a possibility t h a t changes in the orientation of the Mars spin axis may be measurable. In t h a t event, subsequent analysis should yield improved estimates of moment of inertia ratios and, hence, a better determination of the polar moment of inertia of Mars. Improved values of moments of inertia and of dynamical and geometric flattening will have an impact upon theories of the internal composition of Mars.

2. Surface Reflectivity Measurements Radar Measurements. The Viking landing radars can be used to obtain centimeter to meter wavelength data which characterize the surface electromagnetic properties and the surface relief in the vicinity of the landing site on Mars. Two properties of particular importance are the bulk density of the near-surface material and the surface rms slopes. Since the scattering depends on surface structure which is roughly wavelength size or larger, the

resolution which will be obtained will be less than t h a t obtained optically from orbit and better than t h a t which may be inferred from photometric studies. In addition, a comparison of the radar data taken along the entry ground track and orbital photography may be useful in determining the precise location of the landing site on Mars. The Viking lander will carry two radars of different type. The Terminal Descent and Landing Radar (TDLR) is a fourbeam instrument for the determination of the horizontal and vertical components of the vehicle velocity with respect to the local terrain underneath the vehicle. This radar operates on several frequencies near 13GHz using continuous wave transmissions. The four antenna beams are about 3 ° wide and are arranged symmetrically about the descent axis. For this radar, the scattering regions on Mars will be sharply limited by the width of the antenna beams. Oblique incidence echoes will be obtained from four separate regions--the intersections of the four antenna beams with the Martian surface--which will converge at the landing site. Radiated and received power in each of the four beams will be measured and telemetered to Earth. This experiment is similar to those which have been carried out on the Surveyors (Muhleman et al., 1968). A second, independent radar system will be used to provide altimetry. This radar is not as yet fully specified. However, some of its general characteristics are known. The operating wavelength is likely to be in the range 0.1 to 1 m; the antenna beamwidth will be very broad to insure operation over a wide range of vehicle attitudes; and the transmission will carry some sort of broadbeam modulation, such as a short pulse or linear frequency chirp from which range information may be extracted. This radar will be instrumented to measure the ratio of transmitted to received power. Means to indicate pulse dispersion will be provided. The Viking radar altimeter will obtain surface-limited echoes very similar to those observed in Earth-based radar experiments, albeit at much higher surface

RADIO SCIENCE EXPERIMENTS

resolutions. The total received power is proportional to the surface reflectivity of the planet and is only weakly dependent on the surface slope distributions. But the time dispersion of the echo is nearly independent of the reflectivity and depends directly on the slopes, providing t h a t sufficiently high time-resolution waveforms are used. Thus, on the assumption t h a t the scattering is highly quasi-specular, independent measurements of the received echo power and time dispersion will provide weakly coupled measurements of the surface reflectivity and slope distributions. In the case of commonly occurring dry terrestrial materials, surface reflectivity may be interpreted directly in terms of the density of the surface material. I t seems plausible t h a t a similar interpretation may also be possible on Mars. These inferences will be corrupted by the presence of the diffuse component to a degree t h a t will depend on the choice of landing site and entry ground track, but the error from this source is not expected to be large. The Viking Lander will not be instrumented to measure the diffuse component directly. Beam-limited data will be obtained from the TDLR. In the case of this instrument, it will not be possible to separate the effects of surface material from those of roughness. A received power measurement on each beam will correspond to a measurement of the incremental radar cross section in the area where each beam intersects the surface. An increase in the observed echo power may be due to either an increase in surface reflectivity and/or surface roughness, or even to large-scale surface tilts (Thompson et al., 1970). Since the T D L R wavelength is much shorter than t h a t of the radar altimeter, the T D L R should be highly sensitive to the components of the surface t h a t are responsible for the diffuse scattering at the longer wavelength. Thus, the T D L R should provide a valuable indication of the importance and variability of the diffuse component in the radar altimeter data. Such data may also be useful as an indicator of the variability of surface structure on a wavelengthrelated scale ; or, if suitable photography is

65

available, in interpretation of observed features. At least two other radar experiments potentially able to provide surface data may be possible at Mars. Bistatic-radar measurements of Martian terrain characteristics are within the capability of the orbiter-Earth links. There is also some possibility t h a t an electromagnetic sensor will be employed to determine the altitude at which the braking rockets will be shut down. This sensor is potentially useful for the measurement of the electromagnetic impedance of the surface at the landing site. Finally, the lander-to-orbiter link provides another opportunity for surface measurements. Measurements with the Lander-to-Orbiter U H F Link. Because of the low directivity of the 400MHz antenna on the lander, reception on the orbiter of lander signals will take place via a direct and a surfacereflected path. The two paths give rise in reception to situations of constructive and destructive interference, while the orbiter moves above the lander. Absolute signal intensity, the ratio between signal maxima and minima, and their angular spacing, contain information (the system's parameters and the link geometry being known) on the reflectivity of the surface in the vicinity of the lander. By using TV observations of the surroundings of the lander in conjunction with the radio and radar data to gather information on the surface roughness and slope distribution, it is possible to infer the value of the dielectric constant of the surface material, and from this its density. IV. ATMOSPHERIC AND IONOSPHERIC :PROPERTIES OF MARS

1. Occultation Measurements of the Atmospheric and Ionospheric Profiles The orbiter-to-Earth links will be utilized to conduct dual-frequency radio occultation measurements at Mars. Correlation of these new measurements with results of other scientific experiments and with the S-band radio data obtained during the Mariner series of missions (Cain et al.,

66

w . H . MICHAEL~ JR. ]"-T A L .

1965; Kliore et al., 1965; Levy et al., 1967; Fjeldbo and Eshleman, 1968; Harrington et al., 1968; Eshleman, 1970; and Kliore et al., 1970) is expected to increase our knowledge about the temporal and spatial variations in the Martian atmosphere and ionosphere, and about the physical figure of the planet. The first planetary dual-frequency occultation measurements were conducted with the Mariner V spacecraft as it flew by Venus in 1967 (Mariner Stanford Group, 1967). The Viking mission offers the first opportunity to apply this technique on Mars. Basically, the measurements will consist of digital samples (taken at a rate of 1 to 10 per second) of the amplitude and frequency of the S- and X-band signals to be received from the orbiters during immersions and emersions. These data will be utilized to calculate vertical refractivity profiles for both the neutral gas and the free electrons above the occultation points. The principal source of noise in the dispersive measurement of the electron density distribution in the Martian ionosphere is phase scintillations imposed on the occulting radio link by plasma irregularities in the interplanetary medium and the terrestrial ionosphere. I t should be possible to calibrate out most of this noise, however, by simultaneously monitoring the dispersive phase changes on the radio link from the nonocculted orbiter. This calibration technique yields the highest accuracy when both orbiters are tracked from the same station. I t is therefore desirable to implement at least one DSN station with four receiver channels so t h a t dual-spacecrai~ tracking becomes possible at both S- and X-band. In the absence of such calibration data, the scintillation noise would be expected to prevent the detection of any dayside ionization above approximately 200kin altitude 1 (including the plasmapause, i.e., the boundary between the Martian ionosphere and the interplanetary medium) and a]~o to mask the effects of possibly the eJitire nightside ionosphere. 1 This v a l u e applies to c o n d i t i o n s o f m i n i m u m solar a c t i v i t y .

Below 50 km altitude, the radio measurements will be utilized to calculate vertical refractivity profiles of the neutral gas, and surface radii at the occultation points. From these refractivity data and the composition measurements to be made with the Viking Landers, profiles in height of molecular number density, pressure, and temperature will be derived. The main sources of noise in the measurements of the neutral gas density distribution are frequency instabilities in the radio system, errors in modeling the forces acting on the orbiters, and phase scintillations in the terrestrial troposphere. Earlier experiments show t h a t the first error source predominates during one-way tracking. (Due to difficulties in acquiring two-way tracking instantly upon exit from occultation, past successful emersion measurements have all been conducted in the one-way mode.) The precision is then limited by frequency instabilities in the onboard crystal oscillator. 2 It is hoped that the planned improvements in the oscillator design will reduce this noise. As for the dispersive measurements, the scintillation noise can be reduced by monitoring both spacecraft simultaneously. In addition to the refractivitv measurements discussed above, the dual-frequency radio occultation experiment can also be used to search for possible dispersive microwave loss (either absorption or scattering) in the neutral Martian atmosphere. Since the refractive defocusing will be the same at both wavelengths, one can simply take changes in the difference between the two signal levels as indicative of dispersive loss. Such differential amplitude measurements would essentially yield the X-band loss since previous experiments showed no detectable loss at the lower frequency. Carbon dioxide, which is known to be the principal constituent in the Martian atmosphere, will not produce significant absorption. Thus, should microwave loss be detected, it would have to be caused by one or more minor constituents. Dispersive amplitude measurements of the 2 P r e v i o u s oscillator designs h a v e p r o v i d e d a s t a b i l i t y o f a few p a r t s in 10 l° (after linear d r i f t was r e m o v e d ) .

R A D I O SCIE]ffCE E X P E R I M E N T S

type described here require dual-spacecraft tracking so that path loss changes originating in the terrestrial troposphere m a y be calibrated out. Phase and amplitude data of the orbiterto-Earth links will be specifically searched for evidence of dust clouds in the Martian atmosphere (Gifford, 1963 and 1964; Gierasch and Goody, 1968). These clouds m a y appear as "scintillating" refractivity perturbations. Clouds of particulate matter, with a certain dielectric constant for the grains, have an index of refraction that can be evaluated after Van de Hulst (1957) ; they should also be characterized b y detectable amplitude scintillation effects. The refractivity distribution of the atmosphere can be studied b y inverting the Doppler data with a digital computer (Fjeldbo and Eshleman, 1968; Fjeldbo, Kliore, and Eshleman, 1971). In the case of a single occultation, one must specify the horizontal changes before the vertical profile can be calculated (or vice versa). With multiple occultations, one can study both spatial and temporal changes in the atmosphere (including horizontal gradients). The inherent accuracy of the computer software far exceeds the anticipated precision of the measurements. The accuracy of the atmospheric profiles will, therefore, be limited b y the data noise sources described above. For discussions of other inversion methods, the reader is referred to Jones, Fischbach, and Peterson (1962) and to Phinney and Anderson (1968). The last paper describes an inversion technique commonly used in seismology and which was developed b y Herglotz (1907) and Wiechert and Geiger (1910). In the course of the Radio Science Team activity, the applicability to Viking of these additional methods of inversion will be investigated. 2. Lander-to-Orbiter Link Measurements Atmospheric Turbulence. The 400MHz lander-to-orbiter link is characterized b y an overall gain stability better than 0.3 db. Amplitude changes larger than this value and beyond the statistical fluctuations of the noise would constitute valuable scientific information.

67

For radio paths far from the lander zenith, signal fading will originate mostly from multipath due to surface reflections. For the directions near the zenith, presence of amplitude scintillation would be indicative of turbulence along the radio path, and the characteristics of the fading could be related to the statistical spatial characteristics of the index of refraction. Ionospheric Gradients. The Viking lander-to-orbiter link offers the possibility of performing measurements of the variations in columnar refractivity along the lander-to-orbiter radio path of the type traditionally done on Earth with satelliteto-ground links. Horizontal gradients become detectable from the slope of the curve of the columnar refractivity versus zenith angle. Figure 3 depicts three different models of day-tonight gradients, characterized respectively b y a width a of 2 °, 4 °, and 7.5 °. The columnar refractivity curves of the figure have been computed b y assuming that the lander is located on the terminator and that the propagation path is contained in a plane perpendicular to it. The actual configuration of the link will be somewhat different, according to present Viking mission plans, but the example of Fig. 3 still provides a typical answer. Around the zenith, the three rates of change of columnar refractivity at 400MHz are 0.173, 0.0267, and 0.0167cycle/deg, respectively, for ~ = 2°, 4 °, and 7.5 °. A typical rate of change of the lander-to-orbiter link angular direction is 0.2°/sec. The corresponding gradient-induced Dopplers are, therefore, approximately 34.60, 5.35, and 3.34mHz. Therefore, a Doppler noise in the lander-to-orbiter link in the order of a few millihertz would allow the detection of gradient widths narrower than 7.5 ° . The presently contemplated Doppler noise of 40mHz (after thermal drift correction, and within a 1-minute time interval) would allow the detection of gradients characterized b y widths smaller than 2 ° . 3. Orbital Drag Measurements Measurement of the acceleration of the mean anomaly of each orbiter will provide

68

W . H . MICHAEL, J R . E T ,4L. IO I

I

ZENITH

REFRACTIVE PHASEPATHo/(~-~)ds

IONOSPHERE+ ATMOSPHERE I00

4 0 0 MHz

~

z

:

.~?

DAY.

/\

-

toNIGHT

I(~;

I 90

80

70

60

50

40

30

20

I0

0

-I0

I -20

I

I

I

-30 -40 -50

I -60

I

I

-70 -80-90

ZENITH AN GI.E ~),"

FIG. 3. Lander-to-orbiter celumnar path length as a function of the zenith angle. information on the atmosphere density in the periapse region and its possible time variations. The spatial and temporal resolutions achievable will depend primarily on the periapse altitude and on the eccentricity of the orbit. For periapse altitudes of about 1000 to 1200km, one or two weeks of tracking data may be sufficient to obtain the sensitivity required to determine air density values. The spatial resolution of such measurements will depend on eccentricity ; the higher the eccentricity the sharper will be the localization of the region contributing appreciably to the drag effect. I f the two orbiters can be tracked simultaneously, the differ-

ence observable will be freed from the corrupting effects of the Earth's atmosphere and will allow a far more precise --perhaps more than one order of magnitude more precise--determination of the spacecrafts' orbital positions, thus improving the accuracy and temporal resolution of the air density values. The interpretation may be hindered, however, by uncertainties in the contributions of gas leakage and thruster imbalances insofar as they add (or subtract) orbital energy and hence mask atmospheric drag effects. The level of such contributions can probably be estimated fairly well from comparison with the corresponding nongravitational

RADIO SCIENCE EXPERIMENTS

"noise" introduced into the other orbital parameters. For times when the spacecraft passes through Mars' shadow, sunlightpressure perturbations will also change the orbital energy. These contributions, however, can be calculated accurately. The instantaneous spacecraft acceleration due to air drag can be expressed as

aD-

CDA

2 ^

~ ~pv v

where CD is the drag coefficient; A is the spacecraft area as projected normal to the spacecraft velocity v = v V ; M is the spacecraft mass; and p the atmospheric density. The value of A will change during an orbit due to the asymmetry of the spacecraft and the changing orientation of the spacecraft with respect to ~, but it can easily be calculated. More uncertain is the proper value to use for CD. At all contemplated orbital altitudes, the free molecular flow regime is appropriate, but nonetheless, the uncertainty in CD will probably be about 10% and will be reflected directly in an air density uncertainty. Measured variations in air density will still retain their relative accuracy, as long as the orientation of the spacecraft with respect to V remains nearly constant at periapse. Air density determinations will also be made from the Mariner 1971 tracking data. Comparisons with Viking results, to be obtained five years later, should give valuable insights into the solar cycle variations in exospheric densities. Coupled with the information from lower atmospheric observations, a comprehensive model of the Martian atmosphere will be developed. V . SOLAR

SYSTEM

PROPERTIES

1. Celestial Mechanics Measurements Ephemerides of Mars and Earth. Interest in studying the ephemerides of the Earth and Mars stems primarily from the opportunity it affords to compare the observations with theories being developed. A second source of interest comes from the needs of interplanetary navigation.

69

At present, the ephemerides of the planets are constructed from a combination of optical, radar-bounce, and flyby spacecraft tracking data. The radar data is the stronger in determining the geocentric orbit of Mars, especially the inplane parameters of Mars with respect to Earth (i.e., the difference of perihelions, semimajor axis, and eccentricity of both, and difference of longitudes at epoch). The limitation at present in the accuracy of these determinations is partly due to errors in identifying the first arrival echo and partly due to problems of modeling the topography of Mars. The Mariner Mars 1971 orbiters will allow determinations of those orbital characteristics independent of topography, hopefully reducing the errors in the determinations b y about one order of magnitude. Although independent of topographic effects, the Mariner orbit estimates will be degraded by the addition of uncertainties in the gravity field. The net effect of the Mariner Mars 1971 90 days of tracking will be more accurate geocentric range data. Somewhat the same situation obtains for the Viking landers, but here the equivalent range data should be better because of the more accurate knowledge of Mars rotational motion as compared to that of the motion of satellites in the gravity field. The combination of all data at this point will be far stronger than without the spacecraft data because of the time of separation between Mariner and Viking ; this "spread-out" geometry will allow improvement in all of the orbital elements of the Earth and Mars. Even though the out-of-plane errors will be greater than the in-plane errors (due to Mars and Earth being nearly coplanar), this fact should not be viewed as too serious a fault, because the in-plane motion is the most sensitive to differences between various theories of motion. Relativistic Effects. [1] Deflection and Echo Time Delay Experiments. The classical "bending of light" experiment can be performed as Mars passes through superior conjunction (Shapiro, 1967). The characteristics of (1) simultaneous observations at two frequencies, (2) high signal-to-noise

70

w.H.

MICI~AEL~ J R . E T A L .

ratio, (3) near occultation of the spacecraft by the Sun, and (4) the point-source nature of the spacecraft signal, all combine to make this experiment one of potentially very high accuracy. The orbit of the spacecraft will be known with respect to the E a r t h with errors under 1 km. Hence, the a priori direction from the Earth to the spacecraft near superior conjunction will be known with errors of only about 2.5 × 10-grad (~0'.'0005). The maximum predicted relativistic effect (for Sun-grazing signals) is 1':75 with this value falling off inversely with the distance of closest approach of the ray path to the Sun's center. The interpretation of the S- and X-band observations, made simultaneously at two sites to obtain the angle of arrival information, will then be limited mainly by uncertainties in variations of the electrical pathlength of the Earth's atmosphere. These uncertainties can be greatly reduced, for example, by simultaneous radiometric observations of the atmosphere along the same line-of-sight at two frequencies near the 23GHz water vapor spectral line. One may anticipate an overall uncertainty of perhaps 0.1% of the predicted effect. Such accuracy would, of course, be of tremendous importance as a test of the basic interaction between electromagnetic radiation and gravitational fields. Viking may represent the first opport u n i t y to perform a really precise test of the effects of gravitation on the speed (as opposed to the direction) of propagation of electromagnetic signals in the presence of strong gravitational fields (Shapiro, 1964 ; Shapiro et al., 1968). The main impediments to an accurate experiment are the solar corona and the nongravitational forces acting on the spacecraft. The solar corona effects will be substantially reduced by the dual frequency downlink ranging capability of the orbiters. The effect of nongravitational forces (and, in addition, the unmodeled part of Mars' gravitational field) will probably represent the accuracy limit for the orbiter measurements. If, however, the geometry were favorable and the lander S-band ranging signals passed through the same part of the corona as

one of the spacecraft signals during their periods of mutual visibility, then the lander, which is essentially free from unmodeled gravitational and nongravitational effects, would be used to determine the geometry and the spacecraft to determine the coronal effects. Left uncertain would be the (small) Martian atmospheric and ionospheric effects. Still, if the geometry is properly arranged, the errors should be reducible to 0.1%. The overall effect, which is a maximum of 200/xsec for grazing rays and falls logarithmically with increasing ray path distance from the Sun's center, should be measurable with an error of no more than 0.1/~sec. [2] Perihelion Precession. The Viking spacecraft tracking data serve to determine the orbits of Earth and Mars. When combined with the results from Mariner 1971 and radar observations, they will provide important information on the perihelion advance of Mars and a consequent useful test of the non-Newtonian contribution to the advance which is predicted to be about 0'.'01 per year. The accuracy in such a determination, of course, increases with the total span in time of the observations. I f long gaps (say, many years) occur in the data, it is very useful to have a fixed external reference frame to which to relate the perihelion positions determined on the different sides of the gap. VLBI observations of spacecraft and quasars can be used for this purpose. Using such techniques, it may be possible to relate Mars' and Earth's orbits to the quasar frame with uncertainties as small as 0"001. I t should be emphasized t h a t Earthbased VLBI observations of quasars cannot, by themselves, be used to relate even the Earth's orbit to an inertial frame. Spacecraft orbiters or landers observed along with quasars in the VLBI mode offer the only possibility to accomplish this feat and thereby enable an accurate "tie" to be made between perihelion position determinations made at widely separated epochs. Thus, a determination of the perihelion positions from Viking and the Mariner 1971 mission could be combined with ones made decades hence to

RADIO SCIENCE EXPERIMENTS

check accurately on the advance with respect to the quasar frame. [3] Principles of Equivalence. The fundamental question as to whether gravitational binding energy centributes equally to both gravitational and inertial mass cannot possibly be answered with laboratory experiments because the gravitational binding energy represents far too small a fraction of the total mass. For planets the contributions are also small, only about 10-s even for Jupiter. Although the corresponding number for the Sun is 10-5 , it is not operationally detectable; only in three- or four-body problems is there any possibility of testing this aspect of the principle of equivalence which predicts that all binding energies will contribute equally to gravitational and inertial mass. Preliminary analysis indicates that a useful test cannot be made from the Viking determinations of the differential perturbations of Jupiter on the orbits of Mars and the Earth. But, in combination with the Mariner 1971 data, a significant test might be obtainable. The detection of the effect requires data over a large fraction of Jupiter's orbit. Even then the "noise" introduced b y the asteroid belt might prevent a useful deduction from being made about the principle of equivalence. [4] Variations in Gravitational Constant. It is doubtful that the Viking radiotracking data will, b y themselves, allow any improvement to be placed on the bounds on possible time and spatial variations of the gravitational constant, G. In conjunction with the Mariner 1971 data and, perhaps more important, with the radar observations of Mercury and Venus, a more stringent test of the possible time variation of G may be possible. A quantitative statement must await the results of detailed covariance analyses.

2. Dispersive Measurements The Viking coherent S/X-band system will be used for a dual-frequency determination of the integrated electron content along spacecraft-to-ground station ray path, according to the method first described b y Eshleman, Gallagher, and

71

Barthle (1960). Data collection will be incorporated in the operations of the Deep Space Network's 210-ft dish antenna sites. These measurements will be similar to those carried out previously with the Pioneers and Mariner V, using dualfrequency transmissions from the ground. The dispersive measurements are based on the difference in propagation velocity of the S- and X-band signals in the interplanetary medium. The propagation-delay time due to plasma effects is inversely proportional to the square of the microwave frequency. B y using the coherently derived S- and X-band telemetry carriers from the Viking Orbiter and coherently superheterodyning them to a common intermediate frequency, the phase relationship of the two received signals can be observed. This phase information will permit the determination of the change in electron content. However, it cannot give an absolute value of the total content. By measuring the differential group delay, one can determine the absolute electron content as well. Measurement of phase shift of the carrier gives very high resolution as long as the system stays in lock. Group delay has poorer resolution and is subject to errors introduced b y the spacecraft transponder aging. Numerically, the plasma-induced increment in group and phase delay have the same value b u t opposite signs. The S/X-band frequencies will suffer a onecycle differential delay (13cm change in apparent path length at S-band relative to X-band) for a change in the electron content of 1.76 × 101%lectrons/m 2. The goals of the Viking dispersive experiment design are for a resolution of 1015 electrons/ m 2 from phase-path data and about 101~ electrons/m 2 from group-path data. Interplanetary Medium. Near the Earth's orbit, the interplanetary medium is a tenuous plasma of average density near 7 electrons/cm a. The fluctuations in this value are large, with the variance on the order of the mean. These fluctuations arise from two major sources, long-lived corotating plasma streams from active regions and sector structure, and burst, or rather discrete local inhomogeneities, including

72

w.H. MICHAEL~JR. ET AL.

shock fronts, in the solar wind which propagate outward from the Sun. Through the use of dispersive data taken over diverse ray paths, from the Earth to several spacecraft, it has been possible to separate large-scale time and spatial variations in the interplanetary medium from one another (Croft, 1971). Interplanetary dispersive data have been collected over about one-half of the solar cycle (since 1965). Sufficient trends in the observations to permit an empirical definition of the solar wind activity over the cycle are now beginning to emerge. Viking will contribute significantly to solar wind investigations b y providing an additional ray path along the Earth-Mars line, and b y extending the time period of the solar wind observations into the latter part of the decade. Solar Corona. As Viking approaches solar conjunction, the radio propagation path will pass through successively lower layers of the solar corona. Variations in large-scale structures of the corona will be easily detected through total electron content measurements. Propagation paths successively closer to the Sun will become increasingly more time variable and more random. Eventually, communications with the spacecraft will be lost. With the S/X-band system it should be possible to track the spacecraft to within several degrees of the Sun-Earth line. In this region, the dispersive effects of the plasma are extreme. At S-band, the variations in average phase advance or group retardation are on the order of 10km. Prior to the loss of communication, the ray paths should pass sufficiently close to the Sun to permit the association of particular events with the solar features on the photosphere. Dispersive scintillation measurements on Viking can also be used to study the small-scale (Fresnel zone size) granularities in the coronal structure. The dependence of the plasma refractive index on frequency results in a varying sensitivity of the S- and X-band wavelengths to these inhomogeneities. Through the use of autocorrelation and cross-correlation techniques, applied to phase and amplitude perturbations observed on S- and X-band

frequencies, it will be possible to determine the location of inhomogeneous regions along the propagation path. It may also be possible to use these techniques to obtain a direct measure of the radial streaming velocity in the corona. Simultaneous observations from two or more Earth-based sites would also yield data on plasma streaming velocities.

~EFERENCES BLACKSI-IEAR, W. T., AND WILLIAMS, J. R. (1971). Accuracy of estimating the location of a landed spacecraft on Mars from range and range-rate data. N A S A Tech. Note, T N D.6109. CAIN, D. L., ESHLEMAN, V. 1=~., FJELDBO, G., KLIORE, A., AND LEVY, G. S. (1965). A summary of preliminary results of the Mariner IV radio occultation experiment. Proc. lonos. Res. Com. Avionics Panel, A G A R D , N A T O , Rome, ltaly. A G A R D P A P E R CP-3. COMPTON, H. n . , AND DANIELS, E. F. (1971). Error analysis of estimating the Max's gravitational field using range and range-rate from a Viking type orbiter. N A S A Tech. Note, T N D-6219. CROFT, T. A. (1971). Corotating regions in the solar wind, evident in number density measured by a radio-propagation technique. Radio Sci. 6, 55. ESHLEMAN, V. R. (1970). Atmospheres of Mars and Venus : A review of Mariner IV and V and Venera IV experiments. Radio Sci. 5, 325332. ESHLEMAN, Y. R., GALLAGHER, :P. B., AND BARTHLE, R. C. (1960). Rad ar methods of measuring the cislunar electron density. J . Geophys. Rcs. 65, 3079. FJELDBO, G., AND ESHLEMAN, V. R. (1968). The atmosphere of Mars analyzed by integral inversion of the Mariner IV occultation data Planet. Space Sci. 16, 1035. FJELDBO, G., KLIORE, A., AND ESHLEMAN, V. R. (1971). The neutral atmosphere of Venus as studied with the Mariner V radio occultation experiments. Astron. J. 76, 123. GIERASCH, P. J., AND GOODY, l~. (1968). A study of the thermal and dynamical structure of the Martian lower atmosphere. Planet. Space Sci. 16, 615. GIFFORD, F. A. (1963). The problem of the Martian yellow clouds. Monthly Weather Rev. 91, 610.

RADIO SCIENCE EXPERIMENTS GIFFORD, F. A. (1964). A study of Martian yellow clouds that display movement. Monthly Weather Rev. 92,435. ~'IARRINGTON, J. W., GROSSI, M. D., AND LANOWORTHY, B. M. (1968). Mars Mariner IV radio occultation experiment: Comments on the uniqueness of the results. J. Geophys. Res. 73, 3039. HERGLOTZ, G. (1907). ~ b e r das Benndorfsche Problem der Fortpflazungsgeschwindigkeit der Erdbebenstrahlen, Physik. Z. 8, 145. JONES, L. M., FISCHBACH,F. F., AND PETERSON, J. W. (1962). Satellite measurements of atmospheric structures by refraction. Planet. Space Sci. 9, 351. KLIORE, A., CAIN, D. L., LEVY, G. S., ESHLEMAN, V. R., FJELDBO, G., AND DRAKE, F. D. (1965). Occultation experiment : Results of the first direct measurement of Mars' atmosphere and ionosphere. Science 149, 1243. KLIORE, A., CAIN, D. L., SEIDEL, B. L., AND FJELDBO, G. (1970). S-band occultation experiment for Mariner Mars 1971. Icarus 12, 82. LEVY, G. S., OTOSHI, T. Y., AND SEIDEL, B. L. (1967). Ground instrumentation for Mariner IV occultation experiment. I E E E Trans. Instr. and Meas. 6, 110. LORELL, J., ANDERSON, J. D., AND SHAPIRO, I. I. (1970). Celestial mechanics experiment for Mariner Mars 1971. Icarus 12, 78. MARINER STANFORD GROUP (1967). Venus: Ionosphere and atmosphere as measured by dual-frequency radio occultation of Mariner V. Science 158, 1678. MARTIN, W. (1969). A binary coded sequential acquisition ranging system S P S 37-57, I I Jet Propulsion Lab., Calif. Inst. Technol., Pasadena, Calif. MICHAEL, W. H. JR., BLACKSHEAR, W. T., AND

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GAPCYNSHI, J. P. (1969). Results on the mass and gravitational field of the Moon as determined from dynamics of lunar satellites. I n "Dynamics of Satellites" (B. Morando, Ed.), Springer-Verlag, Berlin. MUHLEMAN, D. O., BROWN, W. E. JR., DAVIDS, L., AND PEAKE, W. H. (1968). L u n a r surface electromagnetic properties. "Surveyor Project Final Report, Part 11, Science Results." Jet Propulsion Lab. Tech. Rept. 32-1265, 245. MULLER, P. M., AND SJOGREN, W. L. (1968). Mascons: Lunar mass concentrations. Science 161, 680. PHINNEY, R. A., AND ANDERSON, D. L. (1968). On the radio occultation method for studying planetary atmospheres. J. Geophys. Res. 73, 1819. SHAPIRO, I. I., (1964). Fourth test of general relativity. Phys. Rev. Lett. 13,789. SHAPIRO, I. I. (1967). New method for the detection of light deflection by solar gravity. Science 157, 806. SHAPIRO, I. I., PETTENGILL, G. H., ASH, M. E., STONE, M. L., SMITH, W. B., INGALLS, R. P., AND BROCKELMAN, R. A. (1968). F o u r t h test of general relativity: Preliminary results. Phys. Rev. Lett. 29, 1265. THOMPSON,r . W., MASURSKY,H. M., SHORTHILL, R. W., ZISK, S. H., AND TYLER, G. L. (1970). A comparison of infrared, radar, and geological mapping of lunar craters. Proc. Syrup. Geophys. Interpretation of the Moon. Lunar Science Institute, Contribution No. 16, Clear Lake, Texas. VAN DE HULST, H. C. (1957). "Light Scattering by Small Particles." Wiley, New York, N.Y. WIECHERT, E., AND GEIGER, L. (1910). Bestimmung des Weges der Erdbebenwellen im Erdinnern. Physik. Z. 11, 294.