Search

For almost 10 years, the Gravity Recovery and Climate Experiment (GRACE) has provided information about the Earth gravity field with unprecedented accuracy. Efforts are ongoing to approach the GRACE baseline accuracy as there still remains an order of magnitude between the present error level of the gravity field solutions and the GRACE baseline. At the current level of accuracy, thorough investigation of sensor related effects is necessary as they are one of the potential contributors to the error budget. In the science mode operations, the twin satellites are kept precisely pointed with their KBR antennas towards each other. It is the task of the onboard attitude and orbit control system (AOCS) to keep the satellites in the required formation. We analyzed long time series of the inter-satellite pointing variations as they reflect the AOCS performance and characteristics. We present significant systematic effects in the inter-satellite pointing and discuss their possible sources. Prominent features are especially related to the magnetic torquer characteristics, star cameras’ performance and KBR antenna calibration parameters. The relation between the magnetic torquer attitude control and the Earth magnetic field, impact of the different performance of the two star camera heads on the attitude control and the features due to uncertainties in the calibration parameters relating the star camera frame to K-frame are discussed in detail. Proper understanding of these effects will help to reduce their impact on the science data and subsequently increase the accuracy of the gravity field solutions. Moreover, understanding the complexity of the onboard system is essential not only for increasing the accuracy of the GRACE data but also for the development of the future gravity field satellite missions.

Inner-Formation Gravity Measurement Satellite System (IFGMSS) is used to map the gravity field of Earth. The IFGMSS consists of two satellites in which one is called “inner satellite” and the other one is named as “outer satellite”. To measure the pure Earth gravity, the inner satellite is located in the cavity of the outer satellite. Because of the shield effect of the cavity, the inner satellite is affected only by the gravitational force, so it can sense Earth gravity precisely. To avoid the collision between the inner satellite and the outer satellite, it is best to perform a real-time control on the outer satellite. In orbit, the mass of the outer satellite decreases with the consumption of its propellant. The orbit angular rate of the inner satellite varies with time due to various disturbing forces. These two parameters’ uncertainties make the C–W function be not so accurate to describe the formation behavior of these two satellites. Furthermore, the thrusters also have some uncertainties due to the unmodelled dynamics. To cancel the effects caused by the above uncertainties, we have studied the robust control method based on the μ -synthesis. This μ -synthesis eliminates the conservativeness and improves the control efficiency comparing with the H ∞ method. Finally, to test the control method, we simulate an IFGMSS mission in which the satellite runs in a sun synchronous circular orbit with an altitude of 300 km. The simulation results show the effectiveness of the robust control method. The performances of the closed-loop system with the μ -controller are tested by the μ -analysis. It has found that the nominal performance, the robust stability and the robust performance are all achieved. The transient simulation results further prove the control response is fast and the accuracy of the relative position meets the demand of the gravity measurement.

The Earth’s gravity field modelling is an ill-posed problem having a sensitive solution to the error of data. Satellite gravity gradiometry (SGG) is a space technique to measure the second-order derivatives of geopotential for modelling this field, but the measurements should be validated prior to use. The existing terrestrial gravity anomalies and Earth gravity models can be used for this purpose. In this paper, the second-order vertical–horizontal (VH) and horizontal–horizontal (HH) derivatives of the extended Stokes formula in the local north-oriented frame are modified using biased, unbiased and optimum types of least-squares modification. These modified integral estimators are used to generate the VH and HH gradients at 250 km level for validation purpose of the SGG data. It is shown that, unlike the integral estimator for generating the second-order radial derivative of geopotential, the system of equations from which the modification parameters are obtained is unstable for all types of modification, with large cap size and high degree, and regularization is strongly required for solving the system. Numerical studies in Fennoscandia show that the SGG data can be estimated with an accuracy of 1 mE using an integral estimator modified by a biased type least-squares modification. In this case an integration cap size of 2.5° and a degree of modification of 100 for integrating 30′ × 30′ gravity anomalies are required.

International audience; This paper provides a hamiltonian formulation of the equations of motion of an artificial satellite or space debris orbiting the geostationary ring. This theory of order 1 has been formulated using canonical and non-singular elements for eccentricity and inclination. The analysis is based on an expansion in powers of the eccentricity and of the inclination. The theory accounts for the influence of the Earth gravity field expanded in spherical harmonics, paying a particular attention to the resonance occurring for geosynchronous objects. The luni-solar perturbations are also taken into account. We present the resonant motion and its main characteristics: equilibria, stability, fundamental frequencies and width of the resonant area by comparison with a basic analytical model. Finally, we show some results concerning the long term dynamics of a typical space debris under the influence of the gravitational field of the Earth and the luni-solar interactions.

The German small geoscientific satellite CHAMP flies around the Earth since July 2000 in a highly inclined orbit with an altitude of initially 450 km and meanwhile at about 400 km. From the gravitational orbit perturbations, exploiting GPS-CHAMP satellite-to-satellite tracking and on-board accelerometer data over a time span of altogether six months, a new long-wavelength global gravity field model, called EIGEN-2, has been derived in a German/French effort. Thanks to CHAMP's dedicated orbit configuration, continuous GPS tracking and in-orbit measurement of non-gravitational satellite accelerations, the new CHAMP-only solution provides the geoid and gravity with an accuracy of 10 cm and 0.5 mGal, respectively, at a half wavelength resolution of 550 km. This is an improvement by almost one order of magnitude compared to any multi-satellite pre-CHAMP satellite-only gravity field model.

In this work the problem of a spacecraft bi-impulsive transfer between two given non coplanar elliptical orbits, with minimum fuel consumption, is solved considering a non-Keplerian force field (the perturbing forces include Earth gravity harmonics and atmospheric drag). The problem is transformed in the Two Point Boundary Value Problem. It is developed and implemented a new algorithm, that uses the analytical expressions developed here. A dynamics that considered a Keplerian force field was used to produce an initial guess to solve the Two Point Boundary Value Problem. Several simulations were performed to observe the spacecraft orbital behaviour by different kind of perturbations and constraints, on a fuel consumption optimization point of view.

The paper presents the Comet Nucleus Sample and Return (CNSR) Mission strategy using electric propulsion. The mission objective is very clear and may provide clues to the understanding of the origin of the solar system and of life. The target comet here is an extinct comet, to which a concrete and promising sample collection scenario was constructed. The essence of this paper lies in the use of its novel energy accumulation ring located around the Earth trajectory that gains the angular momentum that results in the high speed Earth swing-by after one or one and a half year quasi-synchronous flight. The spacecraft returns back to the Earth at a specific period regardless of how large the relative excess velocity is gained. This is the essence of the scheme. While the targets accessed via the scheme shown are limited, this strategy enables even a NASA DISCOVERY class, small spacecraft to perform the valuable CNSR mission. The plan is found feasible, and the launch window is open in 2005 and the spacecraft can return the sample back to the Earth in only eight years. Another window in 2009–2010 is also provided. A concrete proposal is shown for the comet Wilson-Harrington (W.H.) here. The ISAS of Japan opens the window to the international organizations for collaboration in this mission.

A development of an analytical solution for the motion of an artificial Earth satellite subject to the combined effects of Earth gravity and air drag is presented. The atmospheric model takes into account a linear variation of the density scale height with altitude, the rotation and the oblateness of the atmosphere. The perturbation theory is based upon Lie transforms. The secular and long-periodic terms as well as the short-periodic effects are included in the theory which is valid for small to moderate eccentricities and for all values of the inclination.

The navigation of the ESA spacecraft Giotto to its encounter with comet P/Halley on 14 March 1986 required just 10% of the fuel available. Although the spacecraft was damaged by dust impacts during its close flyby at the nucleus of P/Halley it was retargeted to return close to Earth to maintain the option to extend the mission to encounter another comet, P/Grigg-Skjellerup on 10 July 1992. On 2 April 1986 the spacecraft was put into hibernation configuration and had been orbiting the Sun in the ecliptic with an orbital period of 10 months. On 19 February 1990 it was reactivated, spacecraft subsystems and the payload checked out to determine its health status. On 2 July 1990 Giotto performed succesfully the first-ever Earth gravity assist manoeuvre of a spacecraft approaching the Earth from deep space and was retargeted for comet P/Grigg--Skjellerup. It was concluded that the spacecraft is ready to provide valuable data during a potential encounter with a second comet.

An analytical metod for calculating precise orbits of very low satellites in the Earth gravity field is presented. New formulae for effective calculation of tesseral harmonic perturbations due to arbitrary high order and degree harmonics have been obtained and applied. These formulae are based on generalised lumped coefficients and they give the perturbations in nonsingular orbital elements: l + g, e cos g, e sin g, h, L and H. A new third-order solution of a satellite theory including all zonal harmonics has been obtained and used. The perturbations in orbits of GRM satellites have been computed by using the presented methods. Significant values of perturbations for high orders and degrees as well as resonant effects are obtained.

A new method of Earth gravity model improvement based on an analytical formulation of Doppler residuals is presented here in prospect of future geodetic and altimetric missions (DORIS, TOPEX/POSEIDON, ERS1). After an intermediate step of orbit improvement, disturbing forces due to gravity field mismodeling are recovered above tracking stations at satellite altitude. Some significant simulation results for SEASAT and DORIS are presented.

A method for assessing worst case errors in the orbital elements or a combination of them due to the errors (formal or calibrated standard deviations) in the harmonic coefficients is reviewed. The errors of the harmonics are transformed to the errors of the lumped geopotential coefficients and these are then used for the orbital inaccuracy estimates. The method is found to be effective mainly for circular and low orbits. Only approximate or preliminary values of inclination and semimajor axis are necessary to make the estimate. Numerical results — the radial inaccuracy — for altimetry satellites (SEASAT, TOPEX, ERS-1), for a few geodynamic satellites and for GRM are presented. The examples for altimetry missions show — in good accord with independent analysis of other authors — that an improvement of at least one order in the accuracy of recent Earth gravity models (such as GEM 10B,C,L2, OSU 81,84, GRIM 3L1) is needed to exploit the present and planned altimeter measuring accuracy in full.