On the Measurement of the Lense-Thirring effect Using the Nodes of the LAGEOS Satellites in reply to "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio

In this paper, we provide a detailed description of our recent analysis and determination of the frame-dragging effect obtained using the nodes of the satellites LAGEOS and LAGEOS 2, in reply to the paper "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. IorioComment: Added: the precise references to the the ArXiv papers of L. Iorio: gr-qc/0411024 v9 19 Apr 2005 and gr-qc/0411084 v5 19 Apr 2005, explicitly containing his proposal to use the mean anomal

Error analysis for a spaceborne laser ranging system

The dependence (or independence) of baseline accuracies, obtained from a typical mission of a spaceborne ranging system, on several factors is investigated. The emphasis is placed on a priori station information, but factors such as the elevation cut-off angle, the geometry of the network, the mean orbital height, and to a limited extent geopotential modeling are also examined. The results are obtained through simulations, but some theoretical justification is also given. Guidelines for freeing the results from these dependencies are suggested for most of the factors

Laser retroreflector experiment on NAVSTAR 35 and 36

In GPS one of the primary errors contributing to positioning inaccuracy is the performance of the on-board atomic clock. To determine and predict the performance of this atomic clock has been a problem due to the ambiguity of the orbital position error and clock uncertainty in the Radio Frequency (RF) tracking of the navigation signals. The Laser Retroreflector Experiment (LRE) on-board NAVSTAR 35 and 36 provides a means of separating these ambiguous errors by enabling highly precise and accurate satellite positions to be determined independently of the RF signals. The results of examining onboard clock behavior after removing the orbital position signatures will be discussed. GPS RF tracking data from various DOD and other sites are used to reconstruct the onboard clock data and examine the clock behavior. From these data, the effects of clock performance on GPS positioning performance can examined

Measuring the relativistic perigee advance with Satellite Laser Ranging

One of the most famous classical tests of General Relativity is the gravitoelectric secular advance of the pericenter of a test body in the gravitational field of a central mass. In this paper we explore the possibility of performing a measurement of the gravitoelectric pericenter advance in the gravitational field of the Earth by analyzing the laser-ranged data to some existing, or proposed, laser-ranged geodetic satellites. At the present level of knowledge of various error sources, the relative precision obtainable with the data from LAGEOS and LAGEOS II, suitably combined, is of the order of $10^{\rm -3}$. Nevertheless, these accuracies could sensibly be improved in the near future when the new data on the terrestrial gravitational field from the CHAMP and GRACE missions will be available. The use of the perigee of LARES (LAser RElativity Satellite), in the context of a suitable combination of orbital residuals including also LAGEOS II, should further raise the precision of the measurement. As a secondary outcome of the proposed experiment, with the so obtained value of \ppn and with \et=4\beta-\gamma-3 from Lunar Laser Ranging it could be possible to obtain an estimate of the PPN parameters $\gamma$ and $\beta$ at the $10^{-2}-10^{-3}$ level.Comment: LaTex2e, 14 pages, no figures, 2 tables. To appear in Classical and Quantum Gravit

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the GEM-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient by coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment

Status of Precise Orbit Determination for Jason-2 Using GPS

The JASON-2 satellite, launched in June 2008, is the latest follow-on to the successful TOPEX/Poseidon (T/P) and JASON-I altimetry missions. JASON-2 is equipped with a TRSR Blackjack GPS dual-frequency receiver, a laser retroreflector array, and a DORIS receiver for precise orbit determination (POD). The most recent time series of orbits computed at NASA GSFC, based on SLR/DORIS data have been completed using both ITRF2005 and ITRF2008. These orbits have been shown to agree radially at 1 cm RMS for dynamic vs SLRlDORIS reduced-dynamic orbits and in comparison with orbits produced by other analysis centers (Lemoine et al., 2010; Zelensky et al., 2010; Cerri et al., 2010). We have recently upgraded the GEODYN software to implement model improvements for GPS processing. We describe the implementation of IGS standards to the Jason2 GEODYN GPS processing, and other dynamical and measurement model improvements. Our GPS-only JASON-2 orbit accuracy is assessed using a number of tests including analysis of independent SLR and altimeter crossover residuals, orbit overlap differences, and direct comparison to orbits generated at GSFC using SLR and DORIS tracking, and to orbits generated externally at other centers. Tests based on SLR and the altimeter crossover residuals provide the best performance indicator for independent validation of the NASAlGSFC GPS-only reduced dynamic orbits. For the ITRF2005 and ITRF2008 implementation of our GPS-only obits we are using the IGS05 and IGS08 standards. Reduced dynamic versus dynamic orbit differences are used to characterize the remaining force model error and TRF instability. We evaluate the GPS vs SLR & DORIS orbits produced using the GEODYN software and assess in particular their consistency radially and the stability of the altimeter satellite reference frame in the Z direction for both ITRF2005 and ITRF2008 as a proxy to assess the consistency of the reference frame for altimeter satellite POD

An improved model of the Earth's gravitational field: GEM-T1

Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested

Gravitational model improvement at the Goddard Space Flight Center

Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment