Modern scientific space missions pose high requirements on the accuracy of the prediction and the analysis of satellite motion. On the one hand, accurate orbit propagation models are needed for the ...design and the preparation of a mission. On the other hand, these models are needed for the mission data analysis itself, thus allowing for the identification of unexpected disturbances, couplings, and noises which may affect the scientific signals. We present a numerical approach for Solar Radiation Pressure modelling, which is one of the main contributors for nongravitational disturbances for Earth orbiting satellites. The here introduced modelling approach allows for the inclusion of detailed spacecraft geometries, optical surface properties, and the variation of these optical surface properties (material degradation) during the mission lifetime. By using the geometry definition, surface property definitions, and mission definition of the French MICROSCOPE mission we highlight the benefit of an accurate Solar Radiation Pressure modelling versus conventional methods such as the Cannonball model or a Wing-Box approach. Our analysis shows that the implementation of a detailed satellite geometry and the consideration of changing surface properties allow for the detection of systematics which are not detectable by conventional models.
ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving ...our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals.For this mission, accurate pulse timing with an ultra-stable clock, and a drag-free spacecraft with reliable inertial sensor are required. T2L2 has demonstrated the required accurate pulse timing; rubidium clock on board Galileo has mostly demonstrated the required clock stability; the accelerometer on board GOCE has paved the way for achieving the reliable inertial sensor; the demonstration of LISA Pathfinder will provide an excellent platform for the implementation of the ASTROD I drag-free spacecraft. These European activities comprise the pillars for building up the mission and make the technologies needed ready. A second mission, ASTROD or ASTROD-GW (depending on the results of ASTROD I), is envisaged as a three-spacecraft mission which, in the case of ASTROD, would test General Relativity to one part per billion, enable detection of solar g-modes, measure the solar Lense-Thirring effect to 10 parts per million, and probe gravitational waves at frequencies below the LISA bandwidth, or in the case of ASTROD-GW, would be dedicated to probe gravitational waves at frequencies below the LISA bandwidth to 100 nHz and to detect solar g-mode oscillations. In the third phase (Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD bandwidth. This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper (Appouchaux et al., Exp Astron 23:491–527,
2009
; designated as Paper I) which was based on our last proposal submitted for the 2007 ESA call. In this paper, we present our orbit selection with one Venus swing-by together with orbit simulation. In Paper I, our orbit choice is with two Venus swing-bys. The present choice takes shorter time (about 250 days) to reach the opposite side of the Sun. We also present a preliminary design of the optical bench, and elaborate on the solar physics goals with the radiation monitor payload. We discuss telescope size, trade-offs of drag-free sensitivities, thermal issues and present an outlook.
The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) satellites are equipped with high-precision three-axis accelerometers to measure all non-gravitational accelerations acting on the ...satellites. Precise knowledge of these perturbations is a major prerequisite for successful Gravity Field Recovery (GFR). Unfortunately, after only one month in orbit the accelerometer on one of the two satellites produced decreasingly accurate measurements. Due to this, the GRACE-D accelerometer data has to be replaced by artificial data for the use in the GFR process. In most existing approaches, which are called transplants, this data is constructed from GRACE-C measurements.
We are developing a GRACE-D accelerometer product that relies mainly on modelled acceleration data instead of a full transplant. By using physical models to generate acceleration data, we are able to better understand the accelerometer signal and its characteristics, which is beneficial for subsequent processes involving accelerometer data. We present the evaluation of our modelled data in terms of comparison to the official Science Data System (SDS) accelerometer data. For the first GRACE-FO satellite real accelerometer is used as a reference, but for the second satellite the main comparisons are done with respect to the ACH1B transplant data product. To get information about environmental changes and long-term effects data sets covering one year and nearly the whole mission duration are presented. In terms of gravity field solutions the performance of purely modelled accelerometer data for GRACE-D and a minimalistic transplant approach of estimated density values is compared to transplant products of other processing centres for the year 2019 as well as one month of 2023. Through this, the modelled solution can act as a cross-reference to the transplant, contributing to an improved implementation of the external perturbation characteristics and the influence of higher solar activity on our models and the subsequent gravity field solutions can be determined.
Comparison of the artificial acceleration data to the real ACT1B data for GRACE-C showed that models related to the atmospheric drag are the limiting factors in our high-precision environment modelling approach. Nevertheless, it was still possible to generate monthly gravity field solutions with a combination of ACT1B data for GRACE-C and artificial data for GRACE-D that showed hydrological signals. Application of the transplant that substitutes the limiting modelled thermospheric density with estimated values obtained at GRACE-C positions reduces the residuals between artificial and real acceleration data significantly.
Estimation of gravity fields showed that the improvements due to the transplant directly transfer into the gravity field solutions. Our minimalistic and physically motivated transplant is shown to be a valuable alternative to the transplant data from TUG and JPL. The GROOPS software is utilized to generate monthly gravity field solution to guarantee comparability of the presented solutions for the geodesy community. The presented results not only show the quality of our transplant product but also enabled us to identify potential areas of improvement in the data generation process and our in–house gravity field recovery tool.
The ZARM GRACE-D transplant product, all radiation accelerations and estimated density is available for download at: https://www.zarm.uni-bremen.de/zarm_daten/.
The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these ...forces in a low Earth orbit with highly precise accelerometers, for about 15 years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.
In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.
We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.
For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3 nm/s2 for total accelerations around ±50 nm/s2). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10 nm/s2 for total accelerations around ±70 nm/s2 for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.
According to the weak equivalence principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the ...10^{-15} precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A nonvanishing result would correspond to a violation of the equivalence principle, or to the discovery of a new long-range force. Analysis of the first data gives δ(Ti,Pt)=-1±9(stat)±9(syst)×10^{-15} (1σ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.
On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific ...opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter, we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these, we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976.
This work proposes a new cooperative architecture that using Global Navigation Satellite System (GNSS), Inertial Measurement Unit (IMU) and vehicle-to-vehicle (V2V) observations to obtain robust and ...accurate inter-vehicle state estimation. A new cascade structure of relative filter which consists of float estimator and fixed estimator is presented that can take advantage of both the multi-sensor data and the information from Least-squares ambiguity decorrelation adjustment (LAMBDA). Also, a cooperative baseline estimation method based on multidimensional scaling (MDS) is proposed to further exploit the relative estimation from many other collaborators. Lastly, we combine the cascade relative filter (CRF) with MDS to estimate the relative states cooperatively using a feedback scheme. In the verification part, we use realistic sensor noise and a GNSS signal simulator to obtain inter-vehicle and GNSS measurements for a multiple-vehicle network. In a harsh GNSS scenario, only 51.20% of epochs in RTKLIB software can pass the LAMBDA acceptance test, but our proposed methods can achieve 77.85% (CRF) and 85.05% (CRF/MDS). Referring to the recovery time from a float solution to fixed solution, RTKLIB needs 179.23 s in the case of 4 satellites, but only 34.88 s (CRF) and 21.39 s (CRF/MDS) for the proposed methods. Results show that the proposed CRF has good performance when fusing with IMU and V2V observations, and has a better performance than existing methods. Moreover, the proposed architecture that combines CRF and MDS can have a further improvement, which substantially increases the robustness and accuracy of relative state estimation.
The MICROSCOPE mission was designed to test the weak equivalence principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of 10-15 in terms of the ...Eötvös ratio η . Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultrasensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five months worth of science free-fall data, two-thirds with a pair of test masses of different compositions—titanium and platinum alloys—and the last third with a reference pair of test masses of the same composition—platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the titanium and platinum pair constrained to η ( Ti,Pt ) = -1.5±2.3 ( stat ) ±1.5 ( syst ) ×10-15 at 1σ in statistical errors.
The weak equivalence principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very ...foundation of general relativity. The MICROSCOPE mission aims to test its validity to a precision of 10−15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter (both 1 uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1 uncertainties leads to a current limit on of about .
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