Gravity Field Model Determination Based on GOCE Satellite Point-Wise Accelerations Estimated from Onboard Carrier Phase Observations

GPS-based, satellite-to-satellite tracking observations have been extensively used to elaborate the long-scale features of the Earth’s gravity field from dedicated satellite gravity missions. We proposed compiling a satellite gravity field model from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite accelerations directly estimated from the onboard GPS data using the point-wise acceleration approach, known as the carrier phase differentiation method. First, we composed the phase accelerations from the onboard carrier phase observations based on the sixth-order seven-point differentiator, which can eliminate the carrier phase ambiguity for Low Earth Orbiter (LEO). Next, the three-dimensional (3D) accelerations of the GOCE satellite were estimated from the derived phase accelerations as well as GPS satellite ephemeris and precise clock products. Finally, a global gravity field model up to the degree and order (d/o) 130 was compiled from the 71 days and nearly 2.5 years of 3D satellite accelerations. We also recovered three gravity field models up to d/o 130 from the accelerations derived by differentiating the kinematic orbits of European Space Agency (ESA), Graz, and School of Geodesy and Geomatics (SGG), which was the orbit differentiation method. We analyzed the accuracies of the derived accelerations and the recovered gravity field models based on the carrier phase differentiation method and orbit differentiation method in time, frequency, and spatial domain. The results showed that the carrier phase derived acceleration observations had better accuracy than those derived from kinematic orbits. The accuracy of the recovered gravity field model based on the carrier phase differentiation method using 2.5 years observations was higher than that of the orbit differentiation solutions for degrees greater than 70, and worse than Graz-orbit solution for degrees less than 70. The cumulative geoid height errors of carrier phase, ESA-orbit, and Graz-orbit solutions up to degree and order 130 were 17.70cm, 21.43 cm, and 22.11 cm, respectively.

From Tensor to Vector of Gravitation

ABSTRACTDifferent gravitational force models are used for determining the satellites’ orbits. The satellite gravity gradiometry (SGG) data contain this gravitational information and the satellite accelerations can be determined from them. In this study, we present that amongst the elements of the gravitational tensor in the local north-oriented frame, all of the elements are suitable for this purpose except Txy. Three integral formulae with the same kernel function are presented for recovering the accelerations from the SGG data. The kernel of these integrals is well-behaving which means that the contribution of the far-zone data is not very significant to their integration results; but this contribution is also dependent on the type of the data being integrated. Our numerical studies show that the standard deviations of the differences between the accelerations recovered from Tzz, Txzand Tzyand those computed by an existing Earth´s gravity model reduce by increasing the cap size of integration. However, their root mean squared errors increase for recovering Tyfrom Tyz. Larger cap sizes than 5 on is recommended for recovering Txand Tzbut smaller ones for Ty.

A discussion on orbital analysis - Satellite accelerations and air densities at extreme altitudes

Since 1962 observational studies on very high satellites have been made by means of the 24 in. reflecting telescope of the University of London Observatory. Analysis of the observations involves use of orbit elements specially provided by the Smithsonian Astrophysical Observatory (S.A.O.). Initially our attention was concentrated on the Midas type objects; these are Agena vehicles in nearly polar and nearly circular orbits, at heights of 3000 to 4000 km. It was hoped that precise observations might show small accelerations due to air drag, though it would be necessary to resolve P to better than 1 x 10~10 for this purpose. Observations are confined to the times when the orbit does not contain shadow; for the Midas orbits these periods last roughly 3 months. The acceleration due to solar radiation pressure when the orbit includes shadow is in principle calculable—and is indeed included in routine analyses for the higher satellites, by for example the S.A.O. It is important to realize, though, that for the very high satellites this acceleration due to solar radiation pressure (s.r.p.) may greatly exceed the acceleration due to air drag. For example, even in the case of Echo 2 at a height of about 1200 km, presently (1966) i r.p. may at times equal Pdrag. (see Cook & Scott 1966). In the case of the small balloon satellite 1963- 30D, with a mean altitude of about 3500 km and an orbital eccentricity of nearly 0.1 presently, Ps.r.p. may exceed pdrag by a factor of 100 on occasion. Consequently one cannot extract the air drag effect from the total observed acceleration; the value of Ps.r.p. is not known to an accuracy of 1 % for various reasons—neither the area/mass ratio for the satellite is known to this accuracy, nor is the reflexion coefficient. Therefore, one must confine the investigations of air drag effects to the all-in-sunlight phases (or, possibly, use very nearly circular orbits, for which Psrp is much reduced; but unfortunately the balloon satellites’ orbits rapidly depart from initially small eccentricities through s.r.p. perturbations).