Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery

The prospects of future satellite gravimetry missions to sustain a continuous and improved observation of the gravitational field have stimulated studies of new concepts of space inertial sensors with potentially improved precision and stability. This is in particular the case for cold-atom interferometry (CAI) gradiometry which is the object of this paper. The performance of a specific CAI gradiometer design is studied here in terms of quality of the recovered gravity field through a closed-loop numerical simulation of the measurement and processing workflow. First we show that mapping the time-variable field on a monthly basis would require a noise level below $5\text{mE}/\sqrt{\text{Hz}}$. The mission scenarios are therefore focused on the static field, like GOCE. Second, the stringent requirement on the angular velocity of a one-arm gradiometer, which must not exceed ${10}^{-6}$?rad/s, leads to two possible modes of operation of the CAI gradiometer: the nadir and the quasi-inertial mode. In the nadir mode, which corresponds to the usual Earth-pointing satellite attitude, only the gradient $V_{\mathit{yy}}$, along the cross-track direction, is measured. In the quasi-inertial mode, the satellite attitude is approximately constant in the inertial reference frame and the 3 diagonal gradients $V_{\mathit{xx}}\text{,}{V}_{\mathit{yy}}$ and $V_{\mathit{zz}}$ are measured. Both modes are successively simulated for a 239?km altitude orbit and the error on the recovered gravity models eventually compared to GOCE solutions. We conclude that for the specific CAI gradiometer design assumed in this paper, only the quasi-inertial mode scenario would be able to significantly outperform GOCE results at the cost of technically challenging requirements on the orbit and attitude control.     

Free fall tests of the accelerometers of the MICROSCOPE mission

The MICROSCOPE mission is fully dedicated to the in-orbit test of the Universality of free fall, the so-called Weak Equivalence Principle (WEP), with an expected accuracy better than 10⁻¹⁵. The test principle consists in comparing the accelerations of two proof masses of different composition in the Earth gravitational field. The payload embarks two pairs of test-masses made of Platinum Rhodium and Titanium alloys at the core of two dedicated coaxial electrostatic accelerometers. These instruments are under qualification for a launch in 2016.     

GOCE star tracker attitude quaternion calibration and combination

We analyse the inter-boresight angles (IBA) measured by the star trackers on board the GOCE satellite and find that they exhibit small offsets of 7–9″ with respect to the ones calculated from the rotation of the star tracker reference frames to the satellite reference frame. Further, we find small variations in the offsets with a peak-to-peak amplitude of up to 8″, which correlate with variations of the star trackers’ temperatures. Motivated by these findings, we present a method for combining the attitude quaternions measured by two or more star trackers that includes an estimation of relative attitude offsets between star trackers as a linear function of temperature. The method was used to correct and combine the star tracker attitude quaternions within the reprocessing of GOCE data performed in 2018. We demonstrate that the IBA calculated from the corrected star tracker attitude quaternions show no significant offsets with respect to the reference frame information. Finally, we show that neglecting the star tracker attitude offsets in the processing would result in perturbations in the gravity gradients that are visible at frequencies below 2?mHz and have a magnitude of up to 90?mE. The presented method avoids such perturbations to a large extent.     

Finding the suitable drag-free acceleration noise level for future low-low satellite-to-satellite tracking geodesy missions

This paper evaluates the impact of residual acceleration noise on the estimation of the Earth’s time-varying gravity field for future low-low satellite-to-satellite tracking missions. The goal is to determine the maximum level of residual acceleration noise that does not adversely affect the estimation error. The Gravity Recovery And Climate Experiment (GRACE) has provided monthly average gravity field solutions in spherical harmonic coefficients for more than a decade. It provides information about land and ocean mass variations with a spatial resolution of ～350?km and with an accuracy within 2?cm throughout the entire Earth. GRACE Follow-on was launched in May 2018 to advance the work of GRACE and to test a new laser ranging interferometer, which measures the range between the two satellites with higher precision than the K-Band ranging system used in GRACE. Moreover, there have been simulation studies that show, an additional pair of satellites in an inclined orbit increases the sampling frequency and reduces temporal aliasing errors. Given the fact that future missions will likely continue to use the low-low satellite-to-satellite tracking formation with laser ranging interferometry, it is expected that the residual acceleration noise will become one of the largest error contributor for the time-variable gravity field solution. We evaluate three different levels of residual acceleration noise based on demonstrated drag-free systems to find a suitable drag-free performance target for upcoming geodesy missions. We analyze both a single collinear polar pair and the optimal double collinear pair of drag-free satellites and assume the use of a laser ranging interferometer. A partitioned best linear unbiased estimator that was developed, incorporating several novel features from the ground up is used to compute the solutions in terms of spherical harmonics. It was found that the suitable residual acceleration noise level is around 2?×?10^?12?ms^?2?Hz^?1/2. Decreasing the acceleration noise below this level did not result in more accurate gravity field solutions for the chosen mission architecture.     

Quality assessment of sub-Nyquist recovery from future gravity satellite missions

Drawing on experience from Gravity Recovery and Climate Experiment (GRACE) data analysis, the scientific challenges were already identified in several studies. Any future mission should focus on improvement in both precision and resolution in space and time. For future gravity missions which use high quality sensors, aliasing of high frequency time-variable geophysical signals to the lower frequency signals is one of the most serious problems. The aliasing problem and the spatio-temporal resolution are mainly restricted by two sampling theorems describing the space-time sampling of satellite missions: (i) a Heisenberg-like uncertainty theorem which states that the product of spatial resolution and time resolution is constant, and (ii) the Colombo–Nyquist rule (CNR), which requires the number of satellite revolutions in a repeat period to be at least twice a given maximum spherical harmonic degree. The CNR holds under the assumption of equal ground-track spacing, and limits the spatial resolution of the gravity solution.     

Traverses for the ISECG-GER design reference mission for humans on the lunar surface

This study explores the Design Reference Mission (DRM) architecture developed by Hufenbach et al. (2015) as a prelude to the release of the 2018 Global Exploration Roadmap (GER) developed by the International Space Exploration Coordination Group (ISECG). The focus of this study is the exploration of the south polar region of the Moon, a region that has not been visited by any human missions, yet exhibits a multitude of scientifically important locations – the investigation of which will address long standing questions in lunar research. This DRM architecture involves five landing sites (Malapert massif, South Pole/Shackleton crater, Schrödinger basin, Antoniadi crater, and the South Pole-Aitken basin center), to be visited in sequential years by crew, beginning in 2028. Two Lunar Electric Rovers (LER) are proposed to be tele-robotically operated between sites to rendez-vous with crew at the time of the next landing. With engineering parameters in mind we explore the feasibility of tele-robotic operation of these LERs between lunar landing sites, and identify potential high interest sampling locations en-route. Additionally, in-depth sample collection and return traverses are identified for each individual landing site across key geologic terrains that also detail crew Extra-Vehicular Activity (EVA). Exploration at and between landing sites is designed to address a suite of National Research Council (2007) scientific concepts.     

Simulation study for the determination of the lunar gravity field from PRARE-L tracking onboard the German LEO mission

A simulation study has been performed at GFZ Potsdam, which shows the anticipated improvement of the lunar gravity field model with respect to current (LP150Q model) or near-future (SELENE) knowledge in the framework of the planned German Lunar Explorations Orbiter (LEO) mission, based on PRARE-L (Precise Range And Range-rate Equipment – Lunar version) Satellite-to-Satellite (SST) and Satellite-Earth-Satellite (SEST) tracking observations. It is shown that the global mean error of the lunar gravity field can be reduced to less than 0.1 mGal at a spatial resolution of 50 km. In the spectral domain, this means a factor of 10 (long wavelengths) and some 100 (mid to short wavelengths) improvement as compared to predictions for SELENE or a factor of 1000 with respect to LP150Q. Furthermore, a higher spatial resolution of up to 28 km seems feasible and would correspond to a factor of 2–3 improvement of SELENE results. Moreover, PRARE-L is expected to derive the low-degree coefficients of the lunar gravity field with unprecedented accuracy. Considering long mission duration (at least 1 year is planned) this would allow for the first time a precise direct determination of the low-degree tidal Love numbers of the Moon and, in combination with high precision SEST, would provide an experimental basis to study relativistic effects such as the periselenium advance in the Earth–Moon system.     

A glimpse at the GOCE satellite gravity gradient observations

Since 30 September 2009, following the launch and in-orbit testing of the most sophisticated gravity mission ever built, the European Space Agency (ESA) GOCE satellite is in ‘measurement mode’, providing continuous time series of satellite gravity gradient (SGG) observations and GPS satellite-to-satellite tracking (SST) observations. The availability of GPS SST observations allows the precise reconstruction of the GOCE position and thus the precise geolocation of the SGG observations. The SGG observations are based on the differences between observations taken by pairs of accelerometers, which need to be corrected first by applying a so-called calibration matrix and second by subtracting rotational terms (centrifugal and angular accelerations).     

PROBA-3 mission and the Shadow Position Sensors: Metrology measurement concept and budget

PROBA-3 is a space mission of the European Space Agency that will test, and validate metrology and control systems for autonomous formation flying of two independent satellites. PROBA-3 will operate in a High Elliptic Orbit and when approaching the apogee at 6·10⁴ Km, the two spacecraft will align to realize a giant externally occulted coronagraph named ASPIICS, with the telescope on one satellite and the external occulter on the other one, at inter-satellite distance of 144.3 m. The formation will be maintained over 6 hrs across the apogee transit and during this time different validation operations will be performed to confirm the effectiveness of the formation flying metrology concept, the metrology control systems and algorithms, and the spacecraft manoeuvring. The observation of the Sun’s Corona in the field of view [1.08;3.0]R_Sun will represent the scientific tool to confirm the formation flying alignment. In this paper, we review the mission concept and we describe the Shadow Position Sensors (SPS), one of the metrological systems designed to provide high accuracy (sub-millimetre level) absolute and relative alignment measurement of the formation flying. The metrology algorithm developed to convert the SPS measurements in lateral and longitudinal movement estimation is also described and the measurement budget summarized.     

Optimal mission planning of the reconfiguration process of satellite constellations through orbital maneuvers: A novel technical framework

In this paper, a general new methodology is presented for the orbital reconfiguration of satellite constellations on the basis of Lambert targeting theorem. In view of the cost and risk reduction, it is very important to consider the problem of satellite constellation reconfiguration with the two constraints of overall mission cost minimization and the desired final configuration. Hence, the dependent non-simultaneous deployment approach is proposed to minimize overall fuel cost. Despite the fact that the satellites deploy in a non-simultaneous manner, supplementary phasing maneuvers on the target orbital pattern to achieve the desired orbital configuration are avoided. Moreover, a novel idea is presented to optimize the flight of satellites, which plays an important role in complying with the constraint of overall fuel cost minimization as much as possible. In order to achieve the global optimal solution of the satellite constellation reconfiguration problem, the efficient hybrid Particle Swarm Optimization/Genetic Algorithm (PSO/GA) technique, is implemented. Finally, to indicate the superiority of the presented method, a comparison to the simultaneous maneuver viewpoint is made on a number of representative cases. The obtained results imply significant reduction of reconfiguration costs by employing the proposed method.     

Finite time non-singular sliding mode control for spinning tether system with prescribed performance under artificial gravity mission

In this paper, the spinning tether system (STS) is applied to produce the artificial gravity overload with a proposed spin-up scheme in elliptical transfer orbits. To improve the comfort of the astronauts during spinning, the combined control scheme with tension and thrust is designed for spin-up. Then, based on the novel performance function and sliding mode technology, a finite time prescribed performance controller is proposed to track angular velocity for the desired artificial gravity overload. Compared with the existing works, the tracking error is controlled within the preset transient performance and converged to the origin within finite time even in the presence of unknown external disturbance. The stability of closed-loop tracking system is proved by Lyapunov theorem. Finally, the numerical simulations are given to demonstrate the effectiveness and robustness of the proposed controllers in the artificial gravity mission.     

MEMORIS: a wide angle camera for the BepiColombo mission

MEMORIS (MErcury Moderate Resolution Imaging System) is a wide angle camera (WAC) concept for the ESA mission BepiColombo. The main scientific objectives consist of observing the whole surface of Mercury in the spectral range of 400–1000 nm, with a spatial resolution of 50 m per pixel at peri-Herm (400 km) and 190 m at apo-Herm (1500 km). It will obtain a map of Mercury in stereo mode allowing the determination of a digital elevation model with a panchromatic filter through two different channels. The camera will also perform multispectral imaging of the surface with a set of 8–12 different broad band filters. A third channel dedicated to limb observations will provide images of the atmosphere. MEMORIS will thus monitor the surface and the atmosphere during the entire mission, providing a unique opportunity to study the relationship between surface regions and the atmosphere, as suggested by ground-based observations and theory.     

木星系探测及行星穿越任务轨迹初步设计

基于我国未来木星系探测任务需求,初步设计了任务轨迹。以目前的发射能力,要实现木星的环绕探测必将利用行星借力,需设计借力轨迹。首先将脉冲变轨的轨迹设计问题转化为参数优化问题,在满足2029—2032年间发射并且飞行时间不超过7年的约束条件下,使用PSO算法对发射时刻、借力时刻、深空机动时刻、到达时刻等参数进行优化,使得探测器需提供的总速度增量最小。探测器进入木星系后,利用木卫3借力捕获至环木大椭圆轨道,又利用木卫4构造共振借力,最终捕获至木卫4的环绕轨道。在此基础上,还考虑了天王星飞越的拓展任务,天王星探测器在到达木星时与木星系探测器分离,利用木星借力可无消耗飞往天王星,并在2043年完成天王星的飞越探测任务。     

Validation of the in-flight calibration procedures for the MICROSCOPE space mission

The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of 10^-15${10}^{-15}$. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of several physical parameters of the instrument. These parameters are partially estimated on-ground, but with an insufficient accuracy, and an in-orbit calibration is therefore required to correct the measurements. The calibration procedures have been defined and their analytical performances have been evaluated. In addition, a simulator software including the dynamics model of the instrument, the satellite drag-free system and the perturbing environment has been developed to numerically validate the analytical results. After an overall presentation of the MICROSCOPE mission, this paper will describe the calibration procedures and focus on the simulator. Such an in-flight calibration is mandatory for similar space missions taking advantage of a drag-free system.     

Use of reduce gravity conditions for the measurements of forces acting against the displacement of liquids inside containers

A setup called Controlled Rotation of Liquids (CROL) has been developed and used to investigate rotational behavior of liquids interacting with solids under reduced gravity conditions. The CROL setup allows us to evaluate the acceleration needed to overcome the interfacial forces that hinder liquid displacement inside different size containers. The well known Wilhelmy equation is used to explain the experimental results. Comparison between experimental results and theoretical predictions are presented and discussed.     

Numerical simulation of time delay interferometry for a LISA-like mission with the simplification of having only one interferometer

In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper (Dhurandhar, S.V., Nayak, K.R., Vinet, J.-Y. Time delay interferometry for LISA with one arm dysfunctional. Class. Quantum Grav. 27, 135013, 2010), we have found a large family of second-generation analytic solutions of time delay interferometry with one arm dysfunctional, and we also estimated the laser noise due to residual time-delay semi-analytically from orbit perturbations due to Earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry (TDI), we simulate the time delay numerically in this paper for all solutions with the generation number n ? 3. We have worked out a set of 3-year optimized mission orbits of LISA spacecraft starting at January 1, 2021 using the CGC2.7 ephemeris framework. We then use this numerical solution to calculate the residual optical path differences in the second-generation solutions of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1 cm (or 30 ps). The maximum path length difference, for all configuration calculated, is below 1 m (3 ns). This is well below the limit under which the laser frequency noise is required to be suppressed. The numerical simulation in this paper can be applied to other space-borne interferometers for gravitational wave detection with the simplification of having only one interferometer.     

LISA: Heliocentric formation design for the laser interferometer space antenna mission

The LISA (Laser Interferometer Space Antenna) mission has been selected by the European Space Agency’s Science Programme Committee as the third large-class mission of the Cosmic Vision Programme, addressing the science theme of the Gravitational Universe. With a planned launch date in 2034, LISA will be the first ever space-borne Gravitational Wave observatory, relying on laser interferometry between three spacecraft orbiting the Sun in a triangular formation. Airbus is currently leading an industrial Phase A system study on behalf of the European Space Agency. The paper will address the astrodynamics challenges associated with the LISA constellation design, driven by tight requirements on the geometric quality metrics of the near equilateral formation.     

Thermally evolved gas analysis (TEGA) of hyperarid soils doped with microorganisms from the Atacama Desert in southern Peru: Implications for the Phoenix mission

TEGA, one of several instruments on board of the Phoenix Lander, performed differential scanning calorimetry and evolved gas analysis of soil samples and ice, collected from the surface and subsurface at a northern landing site on Mars. TEGA is a combination of a high temperature furnace and a mass spectrometer (MS) that was used to analyze samples delivered to the instrument via a robotic arm. The samples were heated at a programmed ramp rate up to 1000 °C. The power required for heating can be carefully and continuously monitored (scanning calorimetry). The evolved gases generated during the process can be analyzed with the evolved gas analyzer (a magnetic sector mass spectrometer) in order to determine the composition of gases released as a function of temperature. Our laboratory has developed a sample characterization method using a pyrolyzer integrated to a quadrupole mass spectrometer to support the interpretations of TEGA data. Here we examine the evolved gas properties of six types of hyperarid soils from the Pampas de La Joya in southern Peru (a possible analog to Mars), to which we have added with microorganisms (Salmonella typhimurium, Micrococcus luteus, and Candida albicans) in order to investigate the effect of the soil matrix on the TEGA response. Between 20 and 40 mg of soil, with or without ∼5 mg of lyophilized microorganism biomass (dry weight), were placed in the pyrolyzer and heated from room temperature to 1200 °C in 1 h at a heating rate of 20 °C/min. The volatiles released were transferred to a MS using helium as a carrier gas. The quadrupole MS was ran in scan mode from 10 to 200 m/z. In addition, ∼20 mg of each microorganism without a soil matrix were analyzed. As expected, there were significant differences in the gases released from microorganism samples with or without a soil matrix, under similar heating conditions. Furthermore, samples from the most arid environments had significant differences compared with less arid soils. Organic carbon released in the form of CO₂ (ion 44 m/z) from microorganisms evolved at temperatures of ∼326.0 ± 19.5 °C, showing characteristic patterns for each one. Others ions such as 41, 78 and 91 m/z were also found. Interestingly, during the thermal process, the release of CO₂ increased and ions previously found disappeared, demonstrating a high-oxidant activity in the soil matrix when it was subjected to high temperature. Finally, samples of soil show CO₂ evolved up to 650 °C consistent with thermal decomposition of carbonates. These results indicate that organics mixed with these hyperarid soils are oxidized to CO₂. Our results suggest the existence of at least two types of oxidants in these soils, a thermolabile oxidant which is highly oxidative and other thermostable oxidant which has a minor oxidative activity and that survives the heat-treatment. Furthermore, we find that the interaction of biomass added to soil samples gives a different set of breakdown gases than organics resident in the soil. The nature of oxidant(s) present in the soils from Pampas de La Joya is still unknown.