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Accuracy of the determination of mean anomalies and mean geoid undulations from a satellite gravity field mapping mission

Improved knowledge of the Earth's gravity field was obtained from new and improved satellite measurements such as satellite to satellite tracking and gradiometry. This improvement was examined by estimating the accuracy of the determination of mean anomalies and mean undulations in various size blocks based on an assumed mission. In this report the accuracy is considered through a commission error due to measurement noise propagation and a truncation error due to unobservable higher degree terms in the geopotential. To do this the spectrum of the measurement was related to the spectrum of the disturbing potential of the Earth's gravity field. Equations were derived for a low-low (radial or horizontal separation) mission and a gradiometer mission. For a low-low mission of six month's duration, at an altitude of 160 km, with a data noise of plus or minus 1 micrometers sec for a four second integration time, we would expect to determine 1 deg x 1 deg mean anomalies to an accuracy of plus or minus 2.3 mgals and 1 deg x 1 deg mean geoid undulations to plus or minus 4.3 cm. A very fast Fortran program is available to study various mission configurations and block sizes.

Jekeli, C.

Earth's gravity field mapping requirements and concept

A future sensor is considered for mapping the Earth's gravity field to meet future scientific and practical requirements for earth and oceanic dynamics. These are approximately + or - 0.1 to 10 mgal over a block size of about 50 km and over land and an ocean geoid to 1 to 2 cm over a distance of about 50 km. To achieve these values requires a gravity gradiometer with a sensitivity of approximately 10 to the -4 power EU in a circular polar orbiting spacecraft with an orbital altitude ranging 160 km to 180 km.

Vonbun, F. O.

Satellite-to-satellite tracking experiment for global gravity field mapping

The satellite-to-satellite (STS) tracking concept for estimating gravitational parameters offers an attractive means to improve on regional and global gravity models in areas where data availability is limited. The extent to which the STS tracking measurements can be effectively utilized in global field models depends primarily on the satellite's altitude, number of satellites, and their orbit constellation. The estimation accuracy of the gravity field recovery also depends on the measurement accuracy of the sensors employed in the STS tracking concept. A comparison of the obtainable accuracies in the gravity field recovery using various STS tracking concepts was presented by Jekeli. The results of a feasibility study for a specific realization of the STS high-low tracking concept are summarized. In this realization, the high altitude satellites are the GPS satellites, and the low orbit satellite is the space shuttle. The GPS satellite constellation consists of 18 satellites in 6 orbital planes inclined at 55 deg. The shuttle orbit is at approximately 300 km, with an inclination of 30 deg. This specific configuration of high-low satellites for measuring perturbation in the gravity field is named the Air Foce STAGE (Shuttle GPS Tracking for Anomalous Gravitation Estimation) mission. The STAGE mission objective is to estimate the perturbations in gravity vector at the shuttle altitude to an accuracy of 1 mgal or better. Recent simulation studies have confirmed that the 1 mgal accuracy objective is near optimum for the STAGE mission.

Upadhyay, Triveni N.

Gravity Field Mapping of Mars with MGS

Tracking of the MGS spacecraft in orbit at Mars by the Deep Space Network since last September has provided doppler and range measurements that are being used to improve the model of the Mars gravity field. During most of October 1997, April 1998, and June thru August 1998 high quality tracking data were obtained while the periapse was in the northern hemisphere at altitudes in the 170 to 190 km range. The eccentric orbit had a period of about 11.5 hrs and an inclination of about 96.2 degrees so that low altitude tracking was obtained over most of the northern hemisphere, including the north polar icecap. Data from the earlier Mariner 9 and Viking missions have been added to the MGS data and a series of experimental gravity models developed from the combined datasets. These models have generally been of degree and order 70 and are a significant improvement over earlier models that did not include the MGS data. Gravity anomalies over the north polar cap region of Mars are generally less than 50 to 100 mgals and show no obvious correlation with the topography. Successive MGS orbits derived using these new models are showing agreement at the 100 meter level, and this has been confirmed with the laser altimeter (MOLA) on MGS These comparisons are expected to improve significantly as more tracking data get included in the solution and the MGS orbit becomes more circular giving a more balanced geographical distribution of data at low altitude. This will happen early in 1999 as the orbit approaches the mapping configuration of a circular orbit at about 400 Km.

Smith, David E.

Twinsat earth gravity field mapping

Results of a sensitivity study on the proposed Lo-Lo (Twinsat) satellite-to-satellite tracking mission are described. The relative range-rate signal due to a local gravitational anomaly is investigated as a function of height and satellite separation. It is shown that the signal strength is weak and that an optimal combination of signal strength and resolution is achieved when the satellites are separated by 3 deg along-track. The signal does not resolve point masses closer than 5 deg apart when the satellites are at 300 km altitude. The influence of other factors on the system is evaluated, including the low frequency gravitation field effect on the orbit and the dependence of the noise of the data type on (electronic) integration time.

Lowrey, B. E.

Lunar Scout Two spacecraft gravity experiment

Measurement of the gravity field of the Moon has a high science priority because of its implications for the internal structure and thermal history of the Moon, and it has a high priority for future exploration activities because of the influence of lunar gravity on spacecraft navigation and orbit maintenance. The current state of knowledge in the lunar gravity field (and the uncertainty in the knowledge) is based primarily on data accumulated from the Lunar Orbiter and Apollo programs. Data are sparse and emphasize the equatorial band (+/- 30 deg) on the near side of the Moon. There are no tracking data on the far side and only the Lunar Orbiter 5 provides a small amount of high inclination data. A host of gravity models developed from different combinations of tracking data have large discrepancies in their predictions of spacecraft motion and orbit lifetimes. There are also large disagreements in the Mercator projections of the gravity acceleration from each model, especially on the far side, where the contours tend to have no obvious relationship with the local topography. The science and engineering requirements for global gravity field mapping will be satisfied with continuous radio metric tracking of Lunar Scout 1 in a low polar orbit using the Deep Space Network and Lunar Scout 2 in a high elliptical orbit. The gravity field of the Moon will be mapped during the Scout Program using a two spacecraft concept. In the two spacecraft concept, one spacecraft is placed in a high altitude eccentric orbit while the second spacecraft is in a low altitude polar orbit. The gravity experiment requires a radio frequency that will permit two-way Doppler tracking between the spacecraft and the Deep Space Network (DSN). Both spacecraft carry NASA standard transponder systems for data transmission to Earth as well as for tracking and orbit determination. Data sufficient to produce a gravity field map could be acquired within one month with this system.

Cheng, Andrew F.

Improvements of the gravity field from satellite techniques as proposed to the European Space Agency

A summary of the European Earth Sciences Space Programme and the requirements for each gravity field mapping resulting from this programme are given. Three satellite experiments for gravity field improvement proposed to the European Space Agency in the last years are shortly characterized. One of these experiments, the low-low-SST-SLALOM experiment, based on laser interferometry for a "two target-one Spacelab telescope" configuration, is discussed in more detail. Reasons for the low-low concept selection are given and some mission aspects and a possible system concept for a compact ranging, acquisition and tracking system are presented.

Reigber, C.

Geodynamics and temporal variations in the gravity field

Just as the Earth's surface deforms tectonically, so too does the gravity field evolve with time. Now that precise geodesy is yielding observations of these deformations it is important that concomitant, temporal changes in the gravity field be monitored. Although these temporal changes are minute they are observable: changes in the J2 component of the gravity field were inferred from satellite (LAGEOS) tracking data; changes in other components of the gravity field would likely be detected by Geopotential Research Mission (GRM), a proposed but unapproved NASA gravity field mission. Satellite gradiometers were also proposed for high-precision gravity field mapping. Using simple models of geodynamic processes such as viscous postglacial rebound of the solid Earth, great subduction zone earthquakes and seasonal glacial mass fluctuations, we predict temporal changes in gravity gradients at spacecraft altitudes. It was found that these proposed gravity gradient satellite missions should have sensitivities equal to or better than 10(exp -4) E in order to reliably detect these changes. It was also found that satellite altimetry yields little promise of useful detection of time variations in gravity.

Mcadoo, D. C.

Arctic geodynamics: Arctic science and ERS-1 satellite altimetry

A detailed gravity field map of the mid Arctic Ocean, spreading ridge system was produced on the basis of ERS-1 satellite altimetry data. Areas of special concern, the Barents and Kara Seas, and areas surrounding the islands of Svalbard, Frans Josef Land and Novoya Zemlya are reviewed. ERS-1 altimetry covers unique Arctic and Antarctic latitudes above 72 degrees. Before ERS-1 it was not possible to study these areas with satellite altimetry. Gravity field solutions for the Barents Sea, portions of the Arctic Ocean and the Norwegian sea are shown. The largest gravity anomalies occur along the Greenland fracture zone as well as along transform faults near Svalbard.

Anderson, Allen Joel

Terrestrial gravity data and comparisons with satellite data

Figures that demonstrate the state of terrestrial gravity coverage, and comparisons between satellite derived gravity field and terrestrial gravity data are presented. It is shown that only a few areas of the world have information accurate enough for geodesy and geophysics. A gravity field mapping space mission is recommended.

Rapp, R. H.

GRAIL - A Microwave Ranging Instrument to Map Out the Lunar Gravity Field

Gravity Recovery and Interior Laboratory, or GRAIL, is a NASA mission to map out the gravity field of the moon to an unprecedented level of detail. The instrument for this mission is based on GRACE (Gravity Recovery and Climate Experiment), an earth-orbiting mission currently mapping out the gravity field of the earth. This paper will describe the similarities and differences between these two instruments with a focus on the microwave ranging measurements used to determine the gravity parameters and the testbed built at Jet Propulsion Laboratory to demonstrate micron level ranging capability. The onboard ultrastable oscillator and RF instruments will be described and noise contributions discussed.

Enzer, Daphna G.

Gravity Recovery and Interior Laboratory (GRAIL) Mission: Mission Status and Initial Science Results

The Gravity Recovery and Interior Laboratory (GRAIL) Mission is a component of the NASA Discovery Program. GRAIL is a twin-spacecraft lunar gravity mission that has two primary objectives: to determine the structure of the lunar interior, from crust to core; and to advance understanding of the thermal evolution of the Moon. GRAIL launched successfully from the Cape Canaveral Air Force Station on September 10, 2011, executed a low-energy trajectory to the Moon, and inserted the twin spacecraft into lunar orbit on December 31, 2011 and January 1, 2012. A series of maneuvers brought both spacecraft into low-altitude (55-km), near-circular, polar lunar orbits, from which they perform high-precision satellite-to-satellite ranging using a Ka-band payload along with an S-band link for time synchronization. Precise measurements of distance changes between the spacecraft are used to map the lunar gravity field. GRAIL completed its primary mapping mission on May 29, 2012, collecting and transmitting to Earth >99.99% of the possible data. Spacecraft and instrument performance were nominal and has led to the production of a high-resolution and high-accuracy global gravity field, improved over all previous models by two orders of magnitude on the nearside and nearly three orders of magnitude over the farside. The field is being used to understand the thickness, density and porosity of the lunar crust, the mechanics of formation and compensation states of lunar impact basins, and the structure of the mantle and core. GRAIL s three month-long-extended mission will initiate on August 30, 2012 and will consist of global gravity field mapping from an average altitude of 22 km.

Neumann, Gregory A.

Accuracy of mapping the Earth's gravity field fine structure with a spaceborne gravity gradiometer mission

The spaceborne gravity gradiometer is a potential sensor for mapping the fine structure of the Earth's gravity field. Error analyses were performed to investigate the accuracy of the determination of the Earth's gravity field from a gravity field satellite mission. The orbital height of the spacecraft is the dominating parameter as far as gravity field resolution and accuracies are concerned.

Kahn, W. D.

Magellan mission to Venus

The Magellan spacecraft arrived at Venus on August 10, 1990 to begin global high-resolution radar image and altimeter mapping and gravity field determination of the planet. Mapping of this cloud covered planet is done from an elliptical orbit with a 3.15 hour period and a 275 km periapsis. After the initial checkout of the spacecraft, the primary missions lasts for 243 days (one Venus day); the time it takes for Venus to make one revolution beneath the spacecraft. The data collected by Magellan is expected to provide an understanding of the geological and geophysical nature of the planet Venus, and the general processes that control planetary evolution.

Boyce, Joseph M.

A spaceborne superconducting gravity gradiometer for mapping the earth's gravity field

The principles of a satellite gravity gradiometer system which measures all five independent components of the gravity gradient tensor with a sensitivity of 0.001 E/Hz to the 1/2 power or better, are analyzed, and the status of development of the system is reviewed. The superconducting gravity gradiometer uses sensitive superconducting accelerometers, each of which are composed of a weakly suspended superconducting proof mass, a superconducting magnetic transducer, and a low-noise superconducting magnetometer. The magnetic field produced by the transducer coils is modulated by the motion of the proof mass and detected by the magnetometer. A combination of two or four of such accelerometers with proper relative orientation of sensitive axes results in an in-line or a cross component gravity gradiometer.

Paik, H. J.

NASA's geodynamics program

The NASA geodynamics program covers dynamics of the core; dynamics and structure of the mantle; dynamics and structure of the lithosphere; evolution and composition of the Earth; and comparative planetology. Projects include crustal dynamics/Earth observations; gravity field modelling; and magnetic field studies. Planned space flights include global gravity and magnetic field mapping; magnetic field secular changes; gravity gradiometer mission; LAGEOS-2; and Earth Observing System.

Mcadoo, D. C.