Mars gravity field error analysis from simulated radio tracking of Mars Observer
Authors: Smith D. E. , Lerch F. J. , Chan J. C. , Chinn D. S. , Iz H. B. , Mallama A. , Patel G. B. 
Published: February 2008

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.