R. Noomen

Global lunar gravity recovery from satellite-to-satellite tracking

Abstract A feasibility study is presented of high resolution and accuracy determination of the global grayity field of the Moon from a combination of low-low satellite-to-satellite range-rate observations and conventional tracking from stations on Earth. The European Moon ORbiting Observatory (MORO) mission, studied as a candidate for the third mediumsized science mission (M3) under the European Space Agencys Horizon 2000 scientific programme, is adopted for the simulation purposes. Global coverage and mapping of the fine details of the gravity field is achieved by satellite-to-satellite tracking (SST) of a small sub-satellite deployed by MORO in its 100 km polar orbit, whereas the long-wavelength features are obtained from Earth-based tracking. The combination of SST and Earth-based tracking therefore represents a powerful tool over a wide range of wavelengths. Moreover, tracking from Earth provides a clear reference for the satellite orbits, which are hard to determine from SST data only. The baseline mission proposal foresees a co-orbiting satellite pair in which the two satellites follow each other in essentially the same orbital plane with only a small spacing in time. The MORO gravimetry experiment requirements prescribe a surface level radial acceleration accuracy of a few mGal with a surface resolution of 50–100km. A number of satellite tracking configurations has been investigated and the influence of noise and systematic errors has been studied. Using perfect measurements and in the absence of systematic model errors the gravity field of the Moon, assumed to be pertectly represented by the 60 × 60 Lun60d model of Konopliv et al. (1993) with a surface resolution of 91 km, has been recovered with a radial acceleration accuracy better than 0.003 mGal using a 3° in-plane satellite spacing. Introducing uncorrelated random noise to the tracking links and a 10% model error in the direct solar radiation pressure model, still an accuracy better than 5 mGal can be achieved. Finally, it is shown that a small angular separation in right ascension of the ascending node of the orbital planes of MORO and its sub-satellite adds extra cross-track information to the SST range-rate signal and thus enables better determination of high sectorial and near-sectorial terms of the gravity field.

Numerical simulation of the LAGEOS thermal behavior and thermal accelerations

The temperature distribution throughout the LAGEOS satellites is simulated numerically with the objective to determine the resulting thermal force. The different elements and materials comprising the spacecraft, with their energy transfer, have been modeled with unprecedented detail. The radiation inputs on the satellites are direct solar (eclipse modulated), Earth albedo, and Earth infrared radiations. For each satellite the lifetime temperature (behavior) of 2133 nodes is computed. On the basis of this distribution, individual forces and the net instantaneous accelerations are obtained. Simulations yield typical temperature variations ranging between 30 and 100 K for different elements and materials, whereas the net instantaneous accelerations are on the order of 70 pm s?2, in good agreement with previous results. Simulations also show the importance of the consideration of a proper orientation of the satellite: LOSSAM yields acceleration differences of up to three times the acceleration obtained with a constant spin axis orientation. The temperature of the four germanium retroreflectors deviates up to 70 and 100 K with respect to their silica counterparts for LAGEOS I and II, respectively. This generates thermal acceleration differences of several pm s?2, up to 25% of the postulated difference in reflectivity between hemispheres. Two factors play a major role: the spin rate and the Sun aspect angle with respect to the spin axis. On the basis of the latter, two characteristic periods can be distinguished: a rapid spin, slow drift period (until 13 and 8 years after launch for LAGEOS I and II, respectively) and a slow spin, rapid wobbling afterward. The acceleration results will be used in a refined orbit computation in a subsequent investigation.

Space-time dynamics estimation from space mission tracking data

Many physical parameters that can be estimated from space mission tracking data influence both the translational dynamics and proper time rates of observers. These different proper time rates cause a variability of the time transfer observable beyond that caused by their translational (and rotational) dynamics. With the near-future implementation of (interplanetary) transponder laser ranging, these effects will become increasingly important, requiring a re-evaluation of the common data analysis practice of using a priori time ephemerides, which is the goal of this paper. We develop a framework for the simultaneous estimation of the initial translational state and the initial proper time of an observer, with the goal of facilitating robust tracking data analysis from next-generation space missions carrying highly accurate clocks and tracking equipment. Using our approach, the influence of physical parameters on both translational and time dynamics are considered at the same level in the analysis, and mutual correlations between the signatures of the two are automatically identified. We perform a covariance analysis using our proposed method with simulated laser data from Earth-based stations to both a Mars and Mercury lander. Using four years of tracking data for the Mars lander simulations, we find a difference between our results using the simultaneous space-time dynamics estimation and the classical analysis technique (with an ta priori time ephemeris) of around 0.1 % in formal errors and correlation coefficients. For a Mercury lander this rises to around 1% for a 1-month mission and 10 % for a 4-year mission. By means of Monte Carlo simulation, we find that using an a priori time ephemeris of representative accuracy will result in estimation errors that are orders of magnitude above the formal error when processing highly accurate laser time transfer data.

Satellite laser ranging, status and impact for WEGENER

Abstract The principles of the technique of Satellite Laser Ranging are briefly explained and the current status and outlook for further development are described. Results for the application of this technique in the WEGENER program are reviewed and strategies for continued contributions to this program from stationary and transportable laser ranging systems are presented.

Orbit analysis of the satellite westpac

Abstract This paper addresses the computation of the orbit of the satellite WESTPAC, which was launched on July 10, 1998, into a circular orbit at an altitude of 835 km and with an inclination of 98 degrees. To obtain a high-quality orbit solution, all forces acting on the satellite need to be modelled as accurately as possible. This paper discusses the influence of the modelling of different physical effects on the motion of WESTPAC, in particular in terms of orbit quality. The study is based on observations taken by the global network of laser stations during the period from August 1, 1998, until March 30, 1999. In this study, a number of test cases are defined and investigated, focussing on optimum orbit quality. The latter is assessed by looking at the (weighted) rms-of-fit, the orbit overlaps of successive data arcs and the stability of independent solve-for parameters. The investigation has resulted in a “best” scenario which includes the following elements: the GRIM-5S1 gravity field solution, the MSIS86 model for atmospheric density, the GOT99.2 ocean tides model, drag coefficients solved-for at 12-hour intervals, and one set of 1-cpr accelerations in the along-track and cross-track directions. This scenario gives a fit of the laser range observations of 3.7 cm and an orbit quality of about 5, 10 and 20 cm in the radial, cross-track and along-track directions, respectively.

Navigation and orbit computation aspects of the ESA NAVSAT system concept

The European Space Agency (ESA) presently studies a NAVSAT satellite navigation system concept, which may be considered a civil variant of the U.S. NAVSTAR Global Positioning System (GPS). A user of the NAVSAT system will be able to determine his 3-dimensional position in realtime with an absolute accuracy of better than 10 m, and his velocity with an accuracy of about 10 cm/s. Since 1983 the National Aerospace Laboratory (NLR) and Delft University of Technology (DUT) in The Netherlands are involved in the NAVSAT studies. This paper presents some results of a Study of NAVSAT Control Segment Characteristics. It starts with an introduction of the general concept. Then, the satellite orbit and tracking aspects are discussed and the ranging error budgets and the achievable user positioning accuracy are estimated. Subsequently, a proposed tracking data compression technique is described. The orbit determination of the satellites from the compressed tracking data is discussed in some detail and results are presented of orbit determination and orbit prediction error analyses. The paper concludes with an analysis of a realtime Kalman filter process to improve the orbit information during a satellite pass over a ground station.

Analysis of Uncertainties and Modeling in Short-Term Reentry Predictions

Satellite reentry predictions are used to determine the time and location of impacts of decaying objects. These predictions are complicated by uncertainties in the initial state and environment models, and the complex evolution of the attitude. Typically, the aerodynamic and error propagation are done in a simplistic fashion. Full six–degrees-of-freedom modeling and attitude control is proposed for studying the historic reentry case of the Gravity Field and Steady-State Ocean Circulation Explorer satellite. Improved error modeling and estimation of the initial state and atmospheric density are introduced for both Global Positioning System and two-line elements states. A sensitivity analysis is performed to identify the driving parameters for several models and epochs. The predictions are compared against Tracking And Impact Predictions, and predictions by the European Space Agency Space Debris Office. The performed predictions are consistently closer to the true decay epoch for several starting epochs, wh...

Third-order Analytical Solutions around Non-collinear Equilibrium Points of a Contact Binary Asteroid

The third-order analytical solution for orbital motion around the non-collinear equilibrium points (EPs) of a contact binary asteroid is constructed in this paper. A contact binary asteroid is an asteroid consisting of two lobes that are in physical contact. It is represented by the combination of an ellipsoid and a sphere. The gravity field of the ellipsoid is approximated by a spherical harmonic expansion with terms and , and the sphere by a straightforward point mass model. The non-collinear EPs are linearly stable for the asteroids with slow rotation rates, and become unstable as the rotation rates goes up. To study the motion around the stable EPs, a third-order analytical solution is constructed, by the Lindstedt-Poincare (LP) method. A good agreement is found between this analytical solution and numerical integrations for the motion in the vicinity of the stable EPs. Its accuracy decreases when the orbit goes further away from the EPs and the asteroid rotates faster.

First Results of WEGENER/MEDLAS Data Analysis

The WEGENER/MEDLAS project is aimed at the determination of crustal deformations in the Mediterranean area, the region where the Eurasian, the African and the Arabic tectonic plates meet (Reinhart, 1985). The deformations are to be derived from the very precise distance measurements to the geodetic satellite LAGEOS (Cohen, 1985), that are obtained by mobile satellite laser ranging (SLR) systems. Participating mobile laser systems are MTLRS-1 from Germany, MTLRS-2 from the Netherlands and the US TLRS-1 system. From 1985, they are being deployed at about 15 carefully selected locations in this region, occupying each site at intervals of about one or two years. From the SLR tracking data acquired at these sites, successive and very precise solutions for the positions of the mobile laser systems are computed. The small differences between these solutions are assumed to be related to the tectonic deformations in the region. This paper will mainly discuss the analysis results that have been computed from full-rate laser range observations. These results are based on the measurements taken during the first two observation campaigns, that were organized in 1986 and 1987. In addition, a preliminary result from the analysis of quick-look data of the 1989 campaign will also be presented.

Precise orbit computations of Lageos for Wegener-Medlas

Abstract The WEGENER-MEDLAS project was conceived to investigate crustal motions in the Eastern Mediterranean using highly accurate laser tracking of the LAGEOS satellite. The tracking data are processed to produce accurate point positions of the laser tracking systems. By repeating these position determinations at regular time intervals, changes in the relative positions may be observed, providing quantitative data on the crustal motions which are expected to be of the order of 1 – 5 cm/year. Initial tracking started in January 1986. This paper discusses some of the data analysis techniques applied by the Section Orbital Mechanics of Delft University of Technology. These techniques are based on one-week data arcs and on a data arc with a length of one year, and involve the accurate modeling of the trajectory of LAGEOS. The effects of various perturbations on the motion of this satellite are discussed including the earths gravity field, solar radiation pressure and third-body perturbations. Recent improvements in the modeling of some of these effects are highlighted and results are given for the evolution of some parameters recovered from one-week data arcs. To demonstrate the overall accuracy of the orbit modeling for one-week data periods, some examples of the results obtained for the relative motions between various global stations are presented. They are compared with results derived from independent geophysical data.