Doppler Tracking Data Research Articles

Probing the interior structure of Mercury from an orbiter plus single lander

The possibility of measuring the inclination of Mercury's spin axis and the amplitude of its 88‐day forced libration in longitude by a lander‐orbiter measurement system is investigated. The experiment would involve ranging to a small lander placed at a high latitude on Mercury from a satellite in a near‐circular polar orbit, which is accurately tracked from the Earth. These measurements can be used to determine the polar moment of inertia of the anticipated fluid outer core plus solid inner core, and thus to obtain information on the outer radius of the fluid core. Covariance analyses are carried out to assess the performance of a simulated data set consisting of 40 separate arcs with orbiter to lander ranging of about 1‐m accuracy and high‐accuracy Earth to orbiter ranging and Doppler tracking data. The effects of the uncertainties in a number of unestimated parameters are also considered. The force model includes the gravity field up to degree and order 14, solar tidal distortion of Mercury, and a fairly complex formulation for solar and Mercury radiation pressure on the spacecraft body and on the antenna. The total uncertainties for the estimated libration amplitude and the spin axis inclination are shown to be 0.26 and 0.03 arc seconds, respectively, for the model employed. The resulting uncertainty for the fractional moment of inertia of the core is 0.0045. Moreover, the Love number k2 can be determined with an accuracy of 0.01. Thus information on the elastic properties of Mercury's mantle also can be obtained.

The Isostatic State of Mead Crater

We have analyzed high-resolution Magellan Doppler tracking data over Mead crater, using both line-of-sight and spherical harmonic methods, and have found a negative gravity anomaly of about 4-5 mgal (at spacecraft altitude, 182 km). This is consistent with no isostatic compensation of the present topography; the uncertainty in the analysis allows perhaps as much as 30% compensation at shallow depths (∼25 km). This is similar to observations of large craters on Earth, which are not generally compensated, but contrasts with at least some lunar basins which are inferred to have large Moho uplifts and corresponding positive Bouguer anomalies. An uncompensated load of this size requires a lithosphere with an effective elastic lithosphere thickness greater than 30 km. In order for the crust-mantle boundary not to have participated in the deformation associated with the collapse of the transient cavity during the creation of the crater, the yield strength near the top of the mantle must have been significantly higher on Earth and Venus than on the Moon at the time of basin formation. This might be due to increased strength against frictional sliding at the higher confining pressures within the larger planets. Alternatively, the thinner crusts of Earth and Venus compared to that of the Moon may result in higher creep strength of the upper mantle at shallower depths.

An improved gravity model for Mars: Goddard Mars model 1

Doppler tracking data of three orbiting spacecraft have been reanalyzed to develop a new gravitational field model for the planet Mars, Goddard Mars Model 1 (GMM‐1). This model employs nearly all available data, consisting of approximately 1100 days of S band tracking data collected by NASA's Deep Space Network from the Mariner 9 and Viking 1 and Viking 2 spacecraft, in seven different orbits, between 1971 and 1979. GMM‐1 is complete to spherical harmonic degree and order 50, which corresponds to a half‐wavelength spatial resolution of 200–300 km where the data permit. GMM‐1 represents satellite orbits with considerably better accuracy than previous Mars gravity models and shows greater resolution of identifiable geological structures. The notable improvement in GMM‐1 over previous models is a consequence of several factors: improved computational capabilities, the use of optimum weighting and least squares collocation solution techniques which stabilized the behavior of the solution at high degree and order, and the use of longer satellite arcs than employed in previous solutions that were made possible by improved force and measurement models. The inclusion of X band tracking data from the 379‐km altitude, near‐polar orbiting Mars Observer spacecraft should provide a significant improvement over GMM‐1, particularly at high latitudes where current data poorly resolve the gravitational signature of the planet.

A high resolution gravity model for Venus: GVM‐1

A spherical harmonic model of the gravitational field of Venus complete to degree and order 50 has been developed using the S‐band Doppler tracking data of the Pioneer Venus Orbiter (PVO) collected between 1979 and 1982. The short wavelengths of this model could only be resolved near the PVO periapse location (∼14°N latitude), therefore a priori constraints were applied to the model to bias poorly observed coefficients towards zero. The resulting model has a half‐wavelength resolution of 400 km near the PVO periapse location, but the resolution degrades to greater than 1000 km near the poles. This gravity model correlates well with a degree 50 spherical harmonic expansion of the Venus topography derived from a combination of Magellan and PVO data. New tracking data from Magellan's gravity mission should provide some improvement to this model, although a complete model of the Venusian gravity field will depend on tracking of Magellan after the circularization of it's orbit using aerobraking.

New error calibration tests for gravity models using subset solutions and independent data: Applied to GEM‐T3

Orbit error projections based on the error covariance estimates of Goddard Earth Model (GEM)‐T3 have been shown to be reliable through their projection on observation residuals within independent data sets. Special geopotential solutions were developed based upon the same data set and weighting used in the GEM‐T3 gravity model, but with a significant satellite data set eliminated from the solution. These subset gravity models are then used to compute the observation residuals within orbital solutions for the omitted satellite and the results are compared to their predicted values based on the error covariance of these models. To ensure meaningful results, the tests were designed so that the observation residuals are dominated by geopotential modeling errors. This yields a reliable test of the error estimates of the subset solutions and hence tests the data weighting used in the construction of these models (GEM‐T3 and subset solutions alike). The error estimates for GEM‐T3 are based upon an optimal data weighting method and have been obtained in a separate calibration process. The test results shown here indicate that the GEM‐T3 error estimates for the gravity parameters are calibrated and that the predicted orbit errors correspond well with actual orbit accuracies. Test results of the complete GEM‐T3 model with totally independent high precision DORIS Doppler tracking data acquired on the French SPOT‐2 satellite confirms these conclusions.

High‐resolution gravity model of Venus

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter (PVO) by means of a two‐step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter‐smoother. The Kalman filter has been evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography‐gravity correlation previously reported. The topography‐gravity scatter plots show two distinct trends.

The masses of Uranus and its major satellites from Voyager tracking data and earth-based Uranian satellite data

Improved values for the masses of the Uranian system and the satellites Ariel, Umbriel, Titania, Oberon, and Miranda are obtained on the basis of an analysis of the Doppler-tracking data and star-satellite imaging from the Voyager 2 spacecraft combined with earth-based astrometric satellite observations. Masses are expressed as the product, the universal gravitational constant times the mass of the body, in units of (cu km/sq s). The satellite masses are (4.4 +/- 0.5) for Miranda, (90.3 +/- 8.0) for Ariel, (78.2 +/- 9.0) for Umbriel, (235.3 +/- 6.0) for Titania, and (201.1 +/- 5.0) for Oberon. Quoted errors are standard errors and are the present assessment of the true rather than the formal errors. The Uranus rotational pole orientation angles and gravity harmonic coefficients were fixed at the values determined by French et al. (1988) from stellar occultations of the Uranian rings observed from both the earth and Voyager 2 and from the occultation of the spacecraft radio signal.

Mars gravity field error analysis from simulated radio tracking of Mars Observer

The Mars Observer (MO) Mission, in a near‐polar orbit at 360–410 km altitude for nearly a 2‐year observing period, will greatly improve our understanding of the geophysics of Mars including its gravity field. To assess the expected improvement of the gravity field, we have conducted an error analysis based upon the mission plan for the Mars Observer radio tracking data from the Deep Space Network. Our results indicate that it should be possible to obtain a high‐resolution model (spherical harmonics complete to degree and order 50 corresponding to a 200‐km horizontal resolution) for the gravitational field of the planet. This model, in combination with topography from MO altimetry, should provide for an improved determination of the broad scale density structure and stress state of the Martian crust and upper mantle. The mathematical model for the error analysis is based on the representation of doppler tracking data as a function of the Martian gravity field in spherical harmonics, solar radiation pressure, atmospheric drag, angular momentum desaturation residual acceleration (AMDRA) effects, tracking station biases, and the MO orbit parameters. Two approaches are employed. In the first case, the error covariance matrix of the gravity model is estimated including the effects from all the nongravitational parameters (noise‐only case). In the second case, the gravity recovery error is computed as above but includes unmodelled systematic effects from atmospheric drag, AMDRA, and solar radiation pressure (biased case). The error spectrum of gravity shows an order of magnitude of improvement over current knowledge based on doppler data precision from a single station of 0.3 mm s−1 noise for 1‐min integration intervals during three 60‐day periods. This first approach of noise only yielded an estimated total accuracy (omission plus commission) for a 200 km block size of 5.4 m for geoid undulations and 31 mGal for gravity anomalies. For the second case, corresponding to the unmodelled systematic effects, an additional error of 5% in the above statistics was obtained. Although the degradation in the accuracy of the mean gravity anomalies and mean geoid undulations is not very pronounced, significant degradation in the recovery of the harmonic coefficients was observed due to the unmodelled systematic nongravitational effects (mainly atmospheric drag). A worst result occurred for an individual 60‐day period, corresponding to maximum atmospheric drag, which gave significant degradation for the low‐degree terms out through degree 20. However, the overall accuracy for the combined solution of the three 60‐day periods for the second case of systematic effects gave only a small difference from the noise‐only solution. The results suggest that the spacecraft orbit could possibly be raised in altitude without significant loss of gravitational signal, because the atmospheric drag is the dominant error source. A change in altitude could also alleviate the large effects seen in the spectrum of the satellite resonant orders. A conservative error estimate for the gravity recovery, corresponding to the complete mapping period, was made based upon a simplified approach of scaling systematic and random effects so as to correspond to each orbit orientation period. These contributions of each orbit orientation were combined throughout the entire mapping mission to obtain the overall accuracy estimate of the gravity field.

IMA-4A pulsed magnetic analyzer: 37410 Mel'gui, M.A.; Piunov, V.D.; Tsukerman, V.L. Soviet Journal of Nondestructive Testing, Vol. 22, No. 11, pp. 767–771 (Jul. 1987)

A new analysis of the Doppler tracking data from the Lunar Prospector mission in 1999 revealed a number of previously-unseen gravity anomalies at spatial scales as small as 27 km over the nearside. The tracking data at low altitudes (50 km or below) were better analyzed to resolve the nearside features without dampening from a power law constraint, by partitioning the gravity parameters concentrated on either the nearside or farside. The resulting model presents gravity anomalies correlated with topography with a correlation coefficient of 0.7 or higher from degree 50 to 150, the widest bandwidth yet. The gravity-topography admittance of ∼70 mGal/km is found from numerous craters of which diameters are 60 km or less. In addition, the new model produces orbits that fit to independent radio tracking data from the Lunar Reconnaissance Orbiter and Kaguya (SELENE) better than previous gravity models. This high-resolution model can be of immediate use to geophysical analysis of small craters. Our technique could be applied to an upcoming mission, the Gravity Recovery And Interior Laboratory and useful to extract short wavelength signals from the MESSENGER Doppler data.

A new constraint on Saturn's zonal gravity harmonics from Voyager observations of an eccentric ringlet

The first experimental determination of Saturn's J6 is derived from the simultaneous solution of three linear relations involving Saturn's zonal gravity harmonics. Two of these relations arise from the combined analysis of Pioneer 11 Doppler tracking and satellite secular rate data by Null et al. (1981). The third is the result of the analysis of Voyager 1 and 2 observations of the narrow eccentric ringlet at 1.2908Rs by Porco et al. (1984). On the assumption that the eccentricity of this ringlet is forced by the satellite Titan, we redetermine the location of the Titan apsidal resonance to an accuracy of ±13 km, which in turn provides a strong constraint on Saturn's zonal gravity harmonics. Combining this constraint with the results of Null et al. and adopting a priori values for J8, J10, and J12 based on interior models, we obtain new estimates for the first three zonal gravity coefficients: J2 = (16,297±18) × 10−6, J4 = (−910±6l) × 10−6, and J6 = (107 ± 50) × 10−6, all normalized to an equatorial reference radius, Rs = 60,330 km. Linearized about these nominal values, the Titan ringlet constraint alone may be written in the form J2 − 1.507 (J4 + 910 × 10−6) + 1.586 (J6 − 107 × 10−6) − 1.430 (J8 + 10 × 10−6) + 1.181 (J10 − 2 × 10−6) − 0.922 (J12 + 0.5 × 10−6) + 0.692J14 − 0.505 J16 = (16,297 ±12) × 10−6.

GEOSAT data available soon

GEOSAT altimeter data collected after November 8, 1986, will be made available to the general research community by the National Oceanic and Atmospheric Administration (NOAA) beginning in early 1987. Although GEOSAT has been operating since April 1985, observations from the first 18 months are classified. In October 1986 the satellite was maneuvered into a 17‐day exact repeat orbit whose ground track coincides with the previous Seasat altimeter tracks, allowing new GEOSAT data to be unclassified. Under agreement reached with the U.S. Navy and the Johns Hopkins University Applied Physics Laboratory (Laurel, Md.), NOAA will assume responsibility for generating the unclassified data sets from this Exact Repeat Mission (ERM). Doppler tracking data will first be evaluated by the Naval Astronautics Group (NAG) to ensure that the GEOSAT ground track has deviated by no more than 1 km (cross track) from the exactrepeat orbit. On‐board thrusters will be fired when necessary (approximately monthly) to maintain colinearity. Raw data in, the form of sensor data records (SDRs) will then be transmitted to a NOAA processing facility in Rockville, Md., where they will be converted to finished geophysical data records (GDRs). SDR‐to‐GDR production consists of merging the altimeter data with an ephemeris provided by NAG and adding correctionfields for tides, troposphere (wet and dry components), and ionosphere. Completed GDRs will be sent to NOAA National Environmental Satellite Data and Information Service (NESDIS) in Washington, D.C., where they will be made avilable to the public. (GEOSAT data will initially be distributed to U.S. institutions only; foreign institutions are advised to seek access through formal embassy channels.)

Filtering of spacecraft Doppler tracking data and detection of gravitational radiation.

A gravitational-radiation pulse leaves a unique trace on the Doppler tracking record of a spacecraft. In a one-way microwave link the signal appears twice in the Doppler records. In a link that is transponded (or reflected) from the spacecraft the signal is repeated three times. Similarly some of the sources of Doppler system noise also have a unique, repeated signature. These features provide a meaningful way to improve the sensitivity of proposed spacecraft tracking experiments by using an on-board clock of extremely high stability where the spacecraft and Earth stations each obtain Doppler data. We construct software filters for data from this type of experiment, and using numerical simulations we compare the sensitivity of the proposed new experiments to current ones, where two-way Doppler data are obtained.

Orbit determination singularities in the Doppler tracking of a planetary orbiter

On a number of occasions, spacecraft launched by the U.S. have been placed into orbit about the moon, Venus, or Mars. It is pointed out that, in particular, in planetary orbiter missions two-way coherent Doppler data have provided the principal data type for orbit determination applications. The present investigation is concerned with the problem of orbit determination on the basis of Doppler tracking data in the case of a spacecraft in orbit about a natural body other than the earth or the sun. Attention is given to Doppler shift associated with a planetary orbiter, orbit determination using a zeroth-order model for the Doppler shift, and orbit determination using a first-order model for the Doppler shift.

Venus gravity west of Beta Regio

Doppler tracking data from the Pioneer Venus Orbiter (PVO) have been used to estimate the anomalous gravity field in the region of Venus west of Beta Regio. The analysis invokes a Kalman filter-smoother to solve the nonlinear spacecraft state estimation problem and a linear Bayesian estimator to perform the geophysical inversion. The topographic map for this region, derived from the PVO radar, has been filtered to have the same distortions and degree of smoothing as the gravity map. The undulations of the gravity are about 0.2 times as large as expected from the topography on the assumption that the latter is uncompensated. A comparison of the gravity and topography by means of the spectral admittance is consistent with Airy compensation at a depth of 50 km if the surface material has a density of 2.6 g/cm 3. However, this is not a unique interpretation.

Venus gravity: A harmonic analysis and geophysical implications

An improved model of Venusian global gravity has been obtained by fitting a tenth degree and order spherical harmonic series to 78 orbital arcs of Doppler tracking data from Pioneer Venus Orbiter. Maps of the free‐air anomaly and its formal error are presented, as are “geoid” and isostatic anomaly maps. The gravitational variance spectrum of Venus has a form very similar to that observed previously on the earth, moon, and Mars. In contrast to the earth, Venus exhibits a significant positive correlation between topography and gravity. The gravity/topography admittance function is consistent with a global average effective depth of isostatic compensation of 200 ± 40 km. The second‐degree harmonics determine the orientation of the principal inertial axes and thereby reveal two unusual features. First, the axis of greatest inertia departs from the rotation axis by 3°. However, the extremely slow rotation of Venus makes the resulting large amplitude wobble energetically comparable to the 0.3 arc sec Chandler wobble of the earth. Second, the orientation of the axis of least inertia relative to the sub‐earth point at times of particularly close inferior conjunctions is strongly suggestive of a spin‐orbit resonance with earth, albeit not the resonance that has usually been considered in the past.

Constants related to the Moon

Determinations of constants related to the Moon obtained from Doppler tracking data from Lunar Orbiter 4 combined with laser ranging data from lunar retroreflectors are compared with those obtained previously by classical methods.

Venus: Comparison of gravity and topography in the vicinity of Beta Regio

The Doppler tracking data obtained from the Pioneer Venus Orbiter when it passed near Beta Regio yielded a peak vertical anomaly of 150 mGal when analyzed by our two stage procedure. A comparison of maps of the gravity and topography at comparable resolution shows a striking correlation. A scatter plot shows that the observed gravity anomaly is approximately 0.4 of that expected from uncompensated topography of half the mean density of Venus. However, the spectral admittance shows that the gravity anomalies can not be explained either by Airy compensation at fixed depth or by a model comprising an elastic plate atop an inviscid fluid. The gravity and topography variations may signify deep compensation or dynamic support for Beta Regio and more shallow compensation for other features.

Gravity field model of mars in spherical harmonics up to degree and order eighteen

A new model of Mars gravity field in spherical harmonics up to eighteenth degree and order has been computed from all available Doppler tracking data of Mariner 9 and Viking 1 and 2 orbiters. It represents an achievement in the knowledge of Mars global gravitational potential, since no more data will be available for such a derivation before the next mission to the planet. The model has been extensively tested from the point of view of orbit representation over periods of time ranging from a few hours to 12 days, and it is currently used for geophysical studies of the Martian lithosphere.

Saturn gravity results obtained from Pioneer 11 tracking data and earth-based Saturn satellite data

Improved gravity coefficients for Saturn, its satellites and rings are calculated on the basis of a combination of Pioneer 11 spacecraft Doppler tracking data and earth-based determinations of Saturn natural satellite apse and node rates. Solutions are first obtained separately from the coherent Doppler tracking data obtained for the interval from August 20 to September 4, surrounding the time of closest approach, with the effects of solar plasma on radio signal propagation taken into account, and from secular rates for Mimas, Enceladus, Tethys, Dione, Rhea and Titan determined from astrometric data by Kozai (1957, 1976) and Garcia (1972). Combination of the data by the use of the Pioneer solution and corresponding unadjusted covariance matrix as a priori information for a secular rate analysis results in values for the total ring mass of essentially zero at a standard error level of 1.7 x 10 to the -6th Saturn masses, a ratio of solar mass to that of the Saturn system of 3498.09 + or - 0.22, masses of Rhea, Titan and Iapetus of 4.0 + or - 0.9, 238.8 + or - 3, and 3.4 + or - 1.3 x 10 to the -6th Saturn masses, respectively, and second and fourth zonal harmonics of 16,479 + or - 18 and -937 + or - 38, respectively. The harmonic coefficients are noted to be important as boundary conditions in the modeling of the Saturn interior.

Dynamical Constants and Reference Parameters for Mars

AbstractDynamical constants and other fundamental reference parameters for Mars have been derived from analyses of Viking lander ranging and Doppler tracking data covering a time span of nearly four years. Precise values have been obtained for the coordinates of the spin axis and for the rotation rate, suggesting that these Viking-derived values are definitive and are suitable for adoption by the IAU. Preliminary results have been obtained for a small seasonal variation in the rotation rate, and progress has been made toward a direct determination of the precession constant.