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19 pages, 12588 KiB

Open AccessArticle

Optomechanical Accelerometers for Geodesy

by Adam Hines, Andrea Nelson, Yanqi Zhang, Guillermo Valdes, Jose Sanjuan, Jeremiah Stoddart and Felipe Guzmán

Remote Sens. 2022, 14(17), 4389; https://doi.org/10.3390/rs14174389 - 3 Sep 2022

Cited by 11 | Viewed by 2243

Abstract

We present a novel optomechanical inertial sensor for low-frequency applications and corresponding acceleration measurements. This sensor has a resonant frequency of 4.715 (1) Hz, a mechanical quality factor of 4.76(3) × 10⁵, a test mass of 2.6 g, and a projected [...] Read more.

We present a novel optomechanical inertial sensor for low-frequency applications and corresponding acceleration measurements. This sensor has a resonant frequency of 4.715 (1) Hz, a mechanical quality factor of 4.76(3) × 10⁵, a test mass of 2.6 g, and a projected noise floor of approximately 5 × 10⁻¹¹ ms⁻²/

\sqrt{Hz}

at 1 Hz. Such performance, together with its small size, low weight, reduced power consumption, and low susceptibility to environmental variables such as magnetic field or drag conditions makes it an attractive technology for future space geodesy missions. In this paper, we present an experimental demonstration of low-frequency ground seismic noise detection by direct comparison with a commercial seismometer, and data analysis algorithms for the identification, characterization, and correction of several noise sources. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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17 pages, 4042 KiB

Open AccessArticle

Towards NGGM: Laser Tracking Instrument for the Next Generation of Gravity Missions

by Kolja Nicklaus, Kai Voss, Anne Feiri, Marina Kaufer, Christian Dahl, Mark Herding, Bailey Allen Curzadd, Andreas Baatzsch, Johanna Flock, Markus Weller, Vitali Müller, Gerhard Heinzel, Malte Misfeldt and Juan Jose Esteban Delgado

Remote Sens. 2022, 14(16), 4089; https://doi.org/10.3390/rs14164089 - 21 Aug 2022

Cited by 2 | Viewed by 2763

Abstract

The precise tracking of distance variations between two satellites in low Earth orbit can provide key data for the understanding of the Earth’s system, specifically on seasonal and sub-seasonal water cycles and their impact on water levels. Measured distance variations, caused by local [...] Read more.

The precise tracking of distance variations between two satellites in low Earth orbit can provide key data for the understanding of the Earth’s system, specifically on seasonal and sub-seasonal water cycles and their impact on water levels. Measured distance variations, caused by local variations in gravitational field, serve as inputs to complex gravity models with which the movement of water on the globe can be identified. Satellite missions GOCE (2009–2013) and GRACE (2002–2017) delivered a significant improvement to our understanding of spatial and temporal gravity variations. Since 2018, GRACE Follow-On has been providing data continuity and features for the first time through the use of a laser interferometer as the technology demonstrator, in addition to a microwave ranging system as the main instrument. The laser interferometer provides an orders-of-magnitude lower measurement noise, and thereby could enable a significant improvement in the measurement of geoids if combined with suitable improvements in auxiliary instrumentation and Earth system modelling. In order to exploit the improved ranging performance, the ESA is investigating the design of a ‘Next Generation Gravity Mission’, consisting of two pairs of satellites with laser interferometers, improved accelerometers and improved platform performance. In this paper, we present the current design of the laser interferometer developed by us, the development status of the individual instrument units and the options available. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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21 pages, 11297 KiB

Open AccessArticle

Using a Multiobjective Genetic Algorithm to Design Satellite Constellations for Recovering Earth System Mass Change

by Carlos M. A. Deccia, David N. Wiese and Robert S. Nerem

Remote Sens. 2022, 14(14), 3340; https://doi.org/10.3390/rs14143340 - 11 Jul 2022

Cited by 6 | Viewed by 1872

Abstract

The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) provided twenty years of data on Earth’s time-varying gravity field. Due to their design, GRACE and GRACE-FO are inherently limited in their spatiotemporal coverage, limiting their resolution to a few hundred kilometers [...] Read more.

The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) provided twenty years of data on Earth’s time-varying gravity field. Due to their design, GRACE and GRACE-FO are inherently limited in their spatiotemporal coverage, limiting their resolution to a few hundred kilometers and temporally to roughly monthly solutions. To increase the global spatiotemporal resolution and allow for the determination of submonthly time-varying gravity field signals, a constellation of GRACE-type satellite pairs is a possible path forward. Advances in small form factor instrumentation for small satellites have become progressively inexpensive, reliable, and of higher quality. This leads us to consider that a constellation of GRACE-type small satellites could be part of future gravimetric satellite missions. In this work, we investigate the viability and limitations of a genetic-algorithm-based optimization and its objective function to generate satellite constellations to recover daily Earth system mass changes. The developed approach is used to create satellite constellations that are optimally designed to recover gravity variations of sufficient resolution at a range of temporal frequencies (i.e., daily to monthly). We analyze a constellation’s performance using a combination of observability in space, accounting for directionality, and homogeneity in time. This allows us to navigate through a vast search space in a relatively short period of time and estimate the relative performance of constellations to each other. Using evolutionary theory, we converge towards a set of optimally selected orbits. The characteristics of the designed constellations have been validated using high-fidelity numerical simulations. We summarize these results and discuss their implications for possible future constellations of small GRACE-like satellite pairs. The resulting constellations have an inherently improved spatiotemporal performance, which reduces temporal aliasing errors and allows the characterization of daily mass-change effects. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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43 pages, 9861 KiB

Open AccessArticle

Hybrid Electrostatic–Atomic Accelerometer for Future Space Gravity Missions

by Nassim Zahzam, Bruno Christophe, Vincent Lebat, Emilie Hardy, Phuong-Anh Huynh, Noémie Marquet, Cédric Blanchard, Yannick Bidel, Alexandre Bresson, Petro Abrykosov, Thomas Gruber, Roland Pail, Ilias Daras and Olivier Carraz

Remote Sens. 2022, 14(14), 3273; https://doi.org/10.3390/rs14143273 - 7 Jul 2022

Cited by 13 | Viewed by 2495

Abstract

Long-term observation of Earth’s temporal gravity field with enhanced temporal and spatial resolution is a major objective for future satellite gravity missions. Improving the performance of the accelerometers present in such missions is one of the main paths to explore. In this context, [...] Read more.

Long-term observation of Earth’s temporal gravity field with enhanced temporal and spatial resolution is a major objective for future satellite gravity missions. Improving the performance of the accelerometers present in such missions is one of the main paths to explore. In this context, we propose to study an original concept of a hybrid accelerometer associating a state-of-the-art electrostatic accelerometer (EA) and a promising quantum sensor based on cold atom interferometry. To assess the performance potential of such an instrument, numerical simulations were performed to determine its impact in terms of gravity field retrieval. Taking advantage of the long-term stability of the cold atom interferometer (CAI), it is shown that the reduced drift of the hybrid sensor could lead to improved gravity field retrieval. Nevertheless, this gain vanishes once temporal variations of the gravity field and related aliasing effects are taken into account. Improved de-aliasing models or some specific satellite constellations are then required to maximize the impact of the accelerometer performance gain. To evaluate the achievable acceleration performance in-orbit, a numerical simulator of the hybrid accelerometer was developed and preliminary results are given. The instrument simulator was in part validated by reproducing the performance achieved with a hybrid lab prototype operating on the ground. The problem of satellite rotation impact on the CAI was also investigated both with instrument performance simulations and experimental demonstrations. It is shown that the proposed configuration, where the EA’s proof-mass acts as the reference mirror for the CAI, seems a promising approach to allow the mitigation of satellite rotation. To evaluate the feasibility of such an instrument for space applications, a preliminary design is elaborated along with a preliminary error, mass, volume, and electrical power consumption budget. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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18 pages, 1055 KiB

Open AccessArticle

Application of LISA Gravitational Reference Sensor Hardware to Future Intersatellite Geodesy Missions

by William Joseph Weber, Daniele Bortoluzzi, Paolo Bosetti, Gabriel Consolini, Rita Dolesi and Stefano Vitale

Remote Sens. 2022, 14(13), 3092; https://doi.org/10.3390/rs14133092 - 27 Jun 2022

Cited by 7 | Viewed by 1976

Abstract

Like gravitational wave detection, inter-spacecraft geodesy is a measurement of gravitational tidal accelerations deforming a constellation of two or more orbiting reference test masses (TM). The LISA TM system requires TM in free fall with residual stray accelerations approaching the fm/s

^{2}

/Hz [...] Read more.

Like gravitational wave detection, inter-spacecraft geodesy is a measurement of gravitational tidal accelerations deforming a constellation of two or more orbiting reference test masses (TM). The LISA TM system requires TM in free fall with residual stray accelerations approaching the fm/s

^{2}

/Hz

^{1 / 2}

level in the mHz band, as demonstrated in the LISA Pathfinder “Einstein’s geodesic explorer” mission. Current geodesy missions are limited by accelerometers with 100 pm/s

^{2}

/Hz

^{1 / 2}

level, due to intrinsic design limitations, as well as the challenging low Earth orbit environment and operating conditions. A reduction in the TM acceleration noise could lead to an important improvement in the scientific return of future geodesy missions focusing on mass change, especially in a scenario with multiple pairs of geodesy satellites. We present here a preliminary assessment of how the LISA TM system, known as the “gravitational reference sensor” (GRS), could be adapted for use in future geodesy missions aiming at residual TM accelerations noise at the pm/s

^{2}

/Hz

^{1 / 2}

level, addressing the major design issues and performance limitations. We find that such a performance is possible in a geodesy GRS that is simpler and smaller than that used for LISA, with a lighter, sub-kg TM and gaps reduced from 4 mm to less than 1 mm. Acceleration noise performance limitations will likely be closely tied to the required levels of applied actuation forces on the TM. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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26 pages, 13496 KiB

Open AccessArticle

Drag and Attitude Control for the Next Generation Gravity Mission

by Stefano Cesare, Sabrina Dionisio, Massimiliano Saponara, David Bravo-Berguño, Luca Massotti, João Teixeira da Encarnação and Bruno Christophe

Remote Sens. 2022, 14(12), 2916; https://doi.org/10.3390/rs14122916 - 18 Jun 2022

Cited by 5 | Viewed by 1836

Abstract

The Next Generation Gravity Mission (NGGM), currently in a feasibility study phase as a candidate Mission of Opportunity for ESA-NASA cooperation in the frame of the Mass Change and Geo-Sciences International Constellation (MAGIC), is designed to monitor mass transport in the Earth system [...] Read more.

The Next Generation Gravity Mission (NGGM), currently in a feasibility study phase as a candidate Mission of Opportunity for ESA-NASA cooperation in the frame of the Mass Change and Geo-Sciences International Constellation (MAGIC), is designed to monitor mass transport in the Earth system by its variable gravity signature with increased spatial and temporal resolution. The NGGM will be composed by a constellation of two pairs of satellites, each providing the measurement of two quantities from which the map of Earth’s gravity field will be obtained: the variation of the distance between two satellites of each pair, measured by a laser interferometer with nanometer precision; and the relative non-gravitational acceleration between the centers of mass of each satellite pair, measured by ultra-sensitive accelerometers. This article highlights the importance of the second “observable” in the reconstruction of the lower harmonics of Earth’s gravity field, by highlighting the tight control requirements in linear and angular accelerations and angular rates, and the expectable performances from the drag-free, attitude, and orbit control system (DFAOCS) obtained through an end-to-end (E2E) simulator. The errors resulting from different mission scenarios with varying levels of drag-free control and pointing accuracy are then presented, demonstrating that a high-performance accelerometer alone is not sufficient to achieve the measurement quality necessary to achieve the mission objectives, if the spacecraft does not provide to this sensor a suitable drag-free environment and a precise and stable pointing. The consequences of these different mission scenarios on the gravity field retrieval accuracy, especially for the lower spherical harmonic degrees, are computed in order to quantitatively justify the rationale for these capabilities on the NGGM spacecraft. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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17 pages, 597 KiB

Open AccessArticle

Earth Gravity In-Orbit Sensing: MPC Formation Control Based on a Novel Constellation Model

by Mattia Boggio, Luigi Colangelo, Mario Virdis, Michele Pagone and Carlo Novara

Remote Sens. 2022, 14(12), 2815; https://doi.org/10.3390/rs14122815 - 11 Jun 2022

Cited by 9 | Viewed by 1628

Abstract

Missions finalized at measuring the space-time variations of the Earth gravity field have become of high relevance in recent years. These missions are indeed of interest for scientific purposes and applications in several fields. Precise observations of the Earth gravity field can be [...] Read more.

Missions finalized at measuring the space-time variations of the Earth gravity field have become of high relevance in recent years. These missions are indeed of interest for scientific purposes and applications in several fields. Precise observations of the Earth gravity field can be accomplished by measuring the distance between two satellites flying in suitable orbits. Several mission concepts foresee an active formation control to maintain the distance variations between the two satellites within given bounds. In this paper, we first present an original constellation model, called the Triangle Dynamics (TD) model, which is particularly suitable to describe the orbital dynamics of satellite pairs. Open-loop simulations are performed, where the TD model is compared with a standard model, derived from the well-known Hill–Clohessy–Wiltshire (HCW) equations. The simulation results show that the TD model provides more accurate predictions than the HCW model. Then, we propose a formation control approach based on a new Model Predictive Control (MPC) algorithm. The core of this algorithm is the TD model, which is used in real-time to predict the behavior of the satellite pair, allowing the computation of an optimal formation control command. A case study concerned with the Next Generation Gravity Mission (NGGM) is presented to demonstrate the effectiveness of the proposed MPC-TD algorithm. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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4 pages, 184 KiB

Open AccessCommunication

An Improved Next Generation Gravity Mission

by Peter L. Bender

Remote Sens. 2022, 14(4), 948; https://doi.org/10.3390/rs14040948 - 16 Feb 2022

Cited by 3 | Viewed by 1497

Abstract

There is an opportunity to make a major reduction in the acceleration noise level for the first Next Generation Gravity Mission by replacing the accelerometers used on the GRACE Follow-On Mission by a highly simplified version of the Gravitational Reference Sensors flown very [...] Read more.

There is an opportunity to make a major reduction in the acceleration noise level for the first Next Generation Gravity Mission by replacing the accelerometers used on the GRACE Follow-On Mission by a highly simplified version of the Gravitational Reference Sensors flown very successfully on the LISA Pathfinder mission of ESA. The reduced measurement noise level can make possible much-improved measurements of the short-period and short-wavelength variations in the geopotential. This would be particularly from the along-track analysis of the results, which can permit repeat measurements about half a day apart along ground tracks within 200 km of each other over a substantial part of the globe. Such a mission would permit considerably improved testing of geophysical models for the geopotential variations due to changes in the Earth’s mass distribution. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

Other

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14 pages, 1939 KiB

Open AccessTechnical Note

Absolute Frequency Readout of Cavity against Atomic Reference

by Emily Rose Rees, Andrew R. Wade, Andrew J. Sutton and Kirk McKenzie

Remote Sens. 2022, 14(11), 2689; https://doi.org/10.3390/rs14112689 - 3 Jun 2022

Cited by 3 | Viewed by 2534

Abstract

Future space-based geodesy missions such as the Mass Change Mission and the Next Generation Gravity Mission are expected to rely on laser ranging as their primary instrument. Short-term laser frequency stability has previously been achieved on the GRACE Follow On mission by stabilizing [...] Read more.

Future space-based geodesy missions such as the Mass Change Mission and the Next Generation Gravity Mission are expected to rely on laser ranging as their primary instrument. Short-term laser frequency stability has previously been achieved on the GRACE Follow On mission by stabilizing the lasers to an optical cavity. The development of a technique to provide long-term laser frequency stability is expected to be required. We have previously demonstrated a technique to track long-term frequency changes by using measurements of the optical cavity’s free spectral range. In this paper, we calibrate this technique to absolute frequency by using an atomic reference. We have also validated an approach for on-ground calibration to allow the absolute frequency to be determined whilst in orbit. Full article

(This article belongs to the Special Issue Space-Borne Gravimetric Measurements for Quantifying Earth System Mass Change)

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