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Gravity and Macro-Model Tuning for the Geosat Follow-on Spacecraft

The US Navy's GEOSAT Follow-On (GFO) spacecraft was launched on February 10, 1998 and the primary objective of the mission was to map the oceans using a radar altimeter. The spacecraft tracking complement consisted of GPS receivers, a laser retroreflector and Doppler beacons. Since the GPS receivers have not yet returned reliable data, the only means of providing high-quality precise orbits has been though satellite laser ranging (SLR). The spacecraft has been tracked by the international satellite laser ranging network since April 22, 1998, and an average of 7.4 passes per day have been obtained from US and participating foreign stations. Since the predicted radial orbit error due to the gravity field is two to three cm, the largest contributor to the high SLR residuals (7-10 cm RMS for five day arcs) is the mismodelling of the non-conservative forces, not withstanding the development of a three-dimensional eight-panel model and an analytical attitude model for the GFO spacecraft. The SLR residuals show a clear correlation with beta-prime (solar elevation) angle, peaking in mid-August 1998 when the beta-prime angle reached -80 to -90 degrees. In this paper we discuss the tuning of the non-conservative force model, for GFO and report the subsequent addition of the GFO tracking data to the Earth gravity model solutions.

Lemoine, Frank G.↗

The Cassini Gravitational Wave Experiment

Doppler tracking experiments using the earth and a distant spacecraft as separated test masses have been used for gravitational wave searches in the low-frequency band. Here we describe the experiment, including the transfer functions of the signals and noises to the Doppler observable, and present the noise statistics and compare them with the pre-experiment noise budget.

gravitational↗

Earth-moon mass ratio from Mariner 9 radio tracking data.

The phase-coherent range and Doppler tracking data obtained as a basis for the navigation of the Mariner 9 spacecraft from earth to Mars determine also the earth-moon mass ratio. As the earth revolves about the center of mass of the earth-moon system, a sinusoidal curve is impressed on the range and Doppler tracking data with a frequency equal to the sidereal mean motion of the moon. The mass ratio was determined from range and Doppler data obtained over a period of 15 weeks. The results from the Mariner Mars 1971 data are presented in a table together with previous results obtained in connection with other spacecraft.

Wong, S. K.↗

Estimating Geophysical Parameters From Gravity Data

ORBSIM program developed for accurate extraction of parameters of geophysical models from Doppler-radio-tracking data acquired from orbiting planetary spacecraft. Model of proposed planetary structure used in numerical integration along simulated trajectories of spacecraft around primary body. Written in FORTRAN 77.

Sjogren, William L.↗

Investigations of Mars dynamics and geodesy via the Viking spacecraft

Results are reported for analyses of Doppler, ranging, and tracking data from the Viking landers and orbiters of relevance to the dynamics and geodesy of Mars. Highly improved numerical results are given for the orientation of the spin axis of Mars, the planet's sidereal rotation rate, and the earth-Mars ephemeris. A refined definition of the global gravitational field of Mars is discussed, a local gravitational survey based on Viking Orbiter 2 tracking data is described, and a mass anomaly near Olympus Mons is noted. Radius data are examined which suggest an asymmetry in the figure of Mars characterized by generally higher topography in the southern than in the northern hemisphere. The mass of Phobos is determined on the basis of Orbiter 1 orbital perturbations, and the mean density of this Martian satellite is found to be approximately 2.0 g/cu cm, which is suggestive of primitive carbonaceous chondrites and, if true, implies that Phobos was formed in the asteroid belt.

Michael, W. H., Jr.↗

Determination of normal points for the relativity test of the celestial mechanics experiment

The relativity test is based on Mariner 9 tracking data acquired by the Deep Space Network. These data consist of two types of measurements: (1) two-way frequency difference (Doppler) measurements that are proportional to the tracking station-spacecraft range rate, and (2) signal round trip time-delay measurements that are proportional to the station-spacecraft range. A data compression scheme has been employed to alleviate accuracy and cost difficulties by (1) using the Doppler data to solve for the spacecraft orbit and to relate spacecraft position to the center of mass of Mars; and (2) combining this result with the station-spacecraft range measurements to obtain measurements of the Earth-Mars distance, called normal points, that contain all of the information pertinent to a detailed knowledge of the Earth-Mars motion.

Jordan, J. F.↗

GEOS-3 Doppler difference tracking

The Doppler difference method as applied to track the GEOS 3 spacecraft is discussed. In this method a pair of 2 GHz ground tracking stations simultaneously track a spacecraft beacon to generate an observable signal in which bias and instability of the carrier frequency cancel. The baselines are formed by the tracking sites at Bermuda, Rosman, and Merritt Island. Measurements were made to evaluate the effectiveness of the Doppler differencing procedure in tracking a beacon target with the high dynamic rate of the GEOS 3 orbit. Results indicate the precision of the differenced data to be at a level comparable to the conventional precise two way Doppler tracking.

Rosenbaum, B.↗

The gravity field in the central Pacific from satellite-to-satellite tracking

Satellite-to-satellite Doppler tracking between the ATS 6 and the GEOS 3 spacecraft was used to measure the high-degree and high-order gravity field over an 80-deg region in the central Pacific Ocean. Forty passes of GEOS 3/ATS 6 Doppler data have been analyzed. The precision of these range rate data is about 0.3 mm/s, and the line-of-sight gravity anomalies recovered from these data have a precision of about 0.2 mGal at the GEOS 3 altitude of about 840 km. In general, the agreement between the SST-derived map and the conventional GEM method and an altimeter-derived geoid is good. Eight significant positive gravity anomalies were exposed in the central Pacific. Generally speaking, the anomalies form a roughly east-west pattern of alternating sign in the central region, and near the East Pacific they strike about north and south.

Marsh, J. G.↗

Precise Orbit Determination for the GEOSAT Follow-On Spacecraft

The US Navy's GEOSAT Follow-On spacecraft was launched on February 10, 1998 with its primary mission objective to map the oceans using a radar altimeter. The spacecraft tracking complement consists of GPS receivers, a laser retroreflector and Doppler beacons. Since the GPS receivers have not yet returned reliable data, the only means of providing high-quality precise orbits has been though satellite laser ranging (SLR). SLR has tracked the spacecraft since April 22, 1998, and an average of 7 passes per day have been obtained from US and foreign stations. Since the predicted radial orbit error due to the gravity field is only two to three cm, the largest contributor to the high SLR residuals (10 cm) is the mismodelling of the non-conservative forces. The SLR residuals show a clear correlation with beta prime (solar elevation) angle, peaking in mid-August 1998 when the beta prime angle reached -80 to -90 degrees. We report in this paper on the analysis of the GFO tracking data (SLR, Doppler, and if available GPS) using GEODYN, and on the tuning of the non-conservative force model and the gravity model using these data.

Lemoine, Frank G.↗

Comparison of Type 2 versus Type 3 Carrier Tracking Loops under High Dynamic Signal Conditions

Virtually all deep-space missions today and in the past employed Type 2 tracking loops in their spacecraft receivers. This was acceptable since the uplink from a single ground antenna makes use of very accurate trajectory information where the radiated frequency is Doppler compensated. However, in the desire to conserve ground resources, the technique of Multiple Uplinks per Antenna (MUPA) is being considered when using a single ground antenna to uplink to a constellation of spacecraft within its beam. This single frequency technique requires the use of non-standard signal acquisition techniques since the constellation may realize different orbits and trajectories around a planetary body leading to varying Doppler offsets and dynamics at each member spacecraft. In such a case, a Type 2 tracking loop may not suffice. An earlier study discussed the various methods for acquiring signals in spacecraft receivers with uncompensated Doppler at the uplink station. In the earlier study, three methods of achieving acquisition and lock were discussed for signals with large Doppler frequency offsets as well as high dynamics; 1) a step-and-sweep signal search algorithm, 2) an FFT signal search algorithm, and, 3) on-board tuning of the signal using uploaded trajectory information or lookup tables. On-board tuning appeared a feasible solution given the trend towards utilizing software-defined radios (SDRs). In the absence of on-board tuning, a search algorithm (e.g., step-and-sweep or FFT) could be utilized in the SDR. One such consideration is in the design of the tracking loop filter, where a Type 3 loop may be more amenable to handling large uncompensated Doppler effects. This report presents an analysis of comparing performance of Type 2 versus Type 3 carrier tracking loops when acquiring and tracking signals with large Doppler dynamics.

Abraham, Douglas↗

Recent results on the mass, gravitational field and moments of inertia of the moon.

Use of Doppler tracking data from the Lunar Orbiter series of spacecraft in an analysis of the spherical harmonic coefficients of the lunar gravitational field through thirteenth degree and order. The value obtained for the mass of the moon, GM = 4902.84 cu km/sec/sec, is in good agreement with previous results and with results obtained by alternate procedures. Acceleration contour plots, derived from the gravitational coefficients, show correlations with surface features on the near side of the moon, but are of questionable validity for the far side because of the lack of direct tracking data on the far side. Based on the most recent gravitational field data, the current estimate for the polar moment of inertia of the moon is C/Ma squared = 0.4019 super + 0.004 sub - 0.002. This value indicates that the interior of the moon can be homogeneous, but some results presented strongly suggest that the moon is differentiated, with an excess of mass in the direction toward the earth.

Michael, W. H., Jr.↗

Gravity and Nonconservative Force Model Tuning for the GEOSAT Follow-On Spacecraft

The US Navy's GEOSAT Follow-On spacecraft was launched on February 10, 1998 and the primary objective of the mission was to map the oceans using a radar altimeter. Three radar altimeter calibration campaigns have been conducted in 1999 and 2000. The spacecraft is tracked by satellite laser ranging (SLR) and Doppler beacons and a limited amount of data have been obtained from the Global Positioning Receiver (GPS) on board the satellite. Even with EGM96, the predicted radial orbit error due to gravity field mismodelling (to 70x70) remains high at 2.61 cm (compared to 0.88 cm for TOPEX). We report on the preliminary gravity model tuning for GFO using SLR, and altimeter crossover data. Preliminary solutions using SLR and GFO/GFO crossover data from CalVal campaigns I and II in June-August 1999, and January-February 2000 have reduced the predicted radial orbit error to 1.9 cm and further reduction will be possible when additional data are added to the solutions. The gravity model tuning has improved principally the low order m-daily terms and has reduced significantly the geographically correlated error present in this satellite orbit. In addition to gravity field mismodelling, the largest contributor to the orbit error is the non-conservative force mismodelling. We report on further nonconservative force model tuning results using available data from over one cycle in beta prime.

Lemoine, Frank G.↗