pimiПриборы и методы измеренийDevices and Methods of Measurements2220-95062414-0473BNTU10.21122/2220-9506-2016-7-3-54-65pimi-266Research ArticleСредства измеренийMeasuring instrumentsЭТАПЫ РАЗВИТИЯ И СОСТОЯНИЕ РАЗРАБОТОК ГРАВИТАЦИОННЫХ ГРАДИЕНТОМЕТРОВ ДЛЯ ПОДВИЖНЫХ ОБЪЕКТОВ. (Обзор)STAGES OF DEVELOPMENT AND STATE OF ENGINEERING OF GRAVITY GRADIOMETERS FOR MOVING OBJECTS. (Review)ДжилавдариИ. З.GilavdaryI. Z.

Адрес для переписки: Джилавдари И.З. – Белорусский национальный технический университет, пр. Независимости, 65, 220013, г. Минск, Беларусь  e-mail: gilavdary@mail.ru

Address for correspondence: Gilavdary I. – Belarusian National Technical University, Nezavisimosty Ave., 65, 220013, Minsk, Belarus  e-mail: gilavdary@mail.ru

gilavdary@mail.ruРизноокаяН. Н.RiznookayaN. N.Белорусский национальный технический университетБеларусьBelarusian National Technical UniversityBelarus20160712201673235246Copyright © Джилавдари И.З., Ризноокая Н.Н., 20162016Джилавдари И.З., Ризноокая Н.Н.Gilavdary I.Z., Riznookaya N.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://pimi.bntu.by/jour/article/view/266

На основании анализа открытых литературных источников рассматриваются основные этапы создания гравитационных градиентометров для измерений неоднородности гравитационных полей с различных подвижных носителей, в том числе в условиях невесомости. Анализируется роль этих приборов в современной науке и технике. Описываются основные физические принципы, позволившие создать приборы, которые реально используются в настоящее время. Также описываются основные параметры этих приборов, характеризующие их качество. Цель данного исследования состояла в том, чтобы установить основные проблемы, которые приходиться решать при создании этих приборов и которые препятствуют их широкому внедрению в различные области науки и техники, сформулировать основные тенденции и состояние их разработки в настоящее время. Показывается, что существующие приборы являются слишком дорогими, тяжелыми и массивными, чтобы иметь возможность их широко применять как в условиях действия силы тяжести, так и в условиях невесомости. Описывается стремление разработчиков создавать более простые, надежные и малобюджетные приборы, в первую очередь предназначенные для использования на микроспутниках, созданию которых уделяется все большее внимание. Делается вывод, что разработки гравитационных градиентометров на основе технологий микромеханических электронных систем в настоящее время не могут преодолеть проблемы, связанные с уровнем шума, свойственные подобным приборам. Данное исследование в некоторой степени является обоснованием для следующей работы авторов, в которой будут изложены новые принципы построения гравитационных градиентометров, которые, возможно, позволят решить некоторые из проблем, описанных ниже. 

The main steps of creating the gravity gradiometers for the measurement of inhomogineasly of gravitational fields on different mobile carriers, including in conditions of space, are considered on the basis of the analysis of the open literature. The role of these devices in modern science and technology is described. There are the basic physical principles which allowed to create devices that are actually used at the moment. The basic parameters of these devices characterizing their quality are also described. The aim of this study is to establish the basic problems that have to be solved to create these instruments, as well as obstacles to their widespread adoption in the various areas of science and technology and to formulate the basic tendencies and state of development at the moment. It is shown that the existing devices are too expensive, heavy and massive to be used widely on the Earth and in space. Here is described the desire of developers to create more simple, reliable and low-budget devices, which primarily intended for using in micro satellites is described here. It is concluded that the development of gravity gradiometer based on micromechanical and electromechanical technologies currently can not overcome the problems associated with noises inherent such instruments. This study in some ways is the rationale for the following work of authors, which sets out the principles of the new gravity gradiometer, which may help to solve some of the problems are described here.

гравитационный градиентометрфизические принципыгибридный градиентометрвнутренние шумымикроспутникиgravity gradiometersphysical principleshybrid gradiometersinternal noisesmicrosatellitesReferencesForward, R.L. Review of artificial satellite gravity gradiometer techniques for geodesy. The Use of Artificial Satellites for Geodesy and Geodynamics, 1974, vol. 1, pp. 157–192.Forward, R.L. Review of artificial satellite gravity gradiometer techniques for geodesy. The Use of Artificial Satellites for Geodesy and Geodynamics, 1974, vol. 1, pp. 157–192.Forward R.L., Lemmen R.M., Lowe R.W., Peterson R.W., Tonai I., Williams W.E. Rotating gravity gradiometer study. Hughes research laboratories. Malibu, 1976, p. 174.Forward R.L., Lemmen R.M., Lowe R.W., Peterson R.W., Tonai I., Williams W.E. Rotating gravity gradiometer study. Hughes research laboratories. Malibu, 1976, p. 174.Paik H.J., Leung J.S., Morgan S.H., Parker J. Global gravity survey by an orbiting gravity gradiometer. Eos, Transactions American Geophysical Union. 1988, vol. 69, no. 48, pp. 1601–1611.Paik H.J., Leung J.S., Morgan S.H., Parker J. Global gravity survey by an orbiting gravity gradiometer. Eos, Transactions American Geophysical Union. 1988, vol. 69, no. 48, pp. 1601–1611.Forward R.L., Bell C.C., Lahue P.M., Mallove E.F., Rouse D.W. Development of a rotating gravity gradiometer for earth orbit applications (AAFE). Available at: http://ntrs.nasa.gov/archive/nasa/casi.ntrs. nasa.gov/19730023608.pdf (accessed 19.12.2015).Forward R.L., Bell C.C., Lahue P.M., Mallove E.F., Rouse D.W. Development of a rotating gravity gradiometer for earth orbit applications (AAFE). Available at: http://ntrs.nasa.gov/archive/nasa/casi.ntrs. nasa.gov/19730023608.pdf (accessed 19.12.2015).Forward R., Bell C., Morris J. Rotating gravitational sensors. Available at: http://www. gravityresearchfoundation.org/pdf/awarded/1965/forward_bell_morris.pdf (accessed: 19.12.2015).Forward R., Bell C., Morris J. Rotating gravitational sensors. Available at: http://www. gravityresearchfoundation.org/pdf/awarded/1965/forward_bell_morris.pdf (accessed: 19.12.2015).Bell R.E. Gravity Gradiometry. Scientific American, 1998, pp. 74–79.Bell R.E. Gravity Gradiometry. Scientific American, 1998, pp. 74–79.Beachy D. Bell Geospace Inc. takes a high-tech look at mining, oil and gas sites. Houston Business Journal. News. Measuring up, Jan 2, 2005.Beachy D. Bell Geospace Inc. takes a high-tech look at mining, oil and gas sites. Houston Business Journal. News. Measuring up, Jan 2, 2005.Metzger E.H. Development Experience of a Moving Base Gravity Gradiometer and Discussion of Future Applications. Proceedings of 14th Annual Gravity Gradiometry Conference, Colorado Springs, 1986, 392 p.Metzger E.H. Development Experience of a Moving Base Gravity Gradiometer and Discussion of Future Applications. Proceedings of 14th Annual Gravity Gradiometry Conference, Colorado Springs, 1986, 392 p.Carroll K.A. Detectability of Natural Resource Structures by a Low-Noise Airborne Gravity Gradiometer System. AGU Fall Meeting Abstracts, 2009, vol. 1, pp. 8.Carroll K.A. Detectability of Natural Resource Structures by a Low-Noise Airborne Gravity Gradiometer System. AGU Fall Meeting Abstracts, 2009, vol. 1, pp. 8.Dransfield M. Airborne gravity gradiometry in the search for mineral deposits. Proceedings of exploration, 2007, vol. 7, pp. 341–354.Dransfield M. Airborne gravity gradiometry in the search for mineral deposits. Proceedings of exploration, 2007, vol. 7, pp. 341–354.Araya A., Kanazawa T., Shinohara M., Yamada T., Fujimoto H., Iizasa K., Ishihara T. A gravity gradiometer to search for submarine ore deposits. Underwater Technology (UT), 2011 IEEE Symposium on and 2011 Workshop on Scientific Use of Submarine Cables and Related Technologies (SSC), 2011, pp. 1–3.Araya A., Kanazawa T., Shinohara M., Yamada T., Fujimoto H., Iizasa K., Ishihara T. A gravity gradiometer to search for submarine ore deposits. Underwater Technology (UT), 2011 IEEE Symposium on and 2011 Workshop on Scientific Use of Submarine Cables and Related Technologies (SSC), 2011, pp. 1–3.Gravity Gradiometry. Available at: http://www.lockheedmartin.com/us/products/gravity-gradiometry.html (accessed: 19.12.2015).Gravity Gradiometry. Available at: http://www.lockheedmartin.com/us/products/gravity-gradiometry.html (accessed: 19.12.2015).Welker T.C., Pachter M., Huffman R.E. Gravity gradiometer integrated inertial navigation. Control Conference, 2013, pp. 846–851.Welker T.C., Pachter M., Huffman R.E. Gravity gradiometer integrated inertial navigation. Control Conference, 2013, pp. 846–851.Using Gravity to Detect Underground Threats. Available at: http://www.lockheedmartin.com/us/mst/features/2010/100714-using-gravity-to-detectunderground-threats-.html (accessed: 19.12.2015).Using Gravity to Detect Underground Threats. Available at: http://www.lockheedmartin.com/us/mst/features/2010/100714-using-gravity-to-detectunderground-threats-.html (accessed: 19.12.2015).Lockheed martin gravity systems. Cutting-Edge Resource and Exploration Technologies. Available at: http://www.lockheedmartin.com/content/dam/lockheed/data/ms2/documents/LM-Gravity-Systems-brochure.pdf (accessed: 19.12.2015).Lockheed martin gravity systems. Cutting-Edge Resource and Exploration Technologies. Available at: http://www.lockheedmartin.com/content/dam/lockheed/data/ms2/documents/LM-Gravity-Systems-brochure.pdf (accessed: 19.12.2015).Annecchione M., Moody M., Carroll K., Dickson D., Main B. Benefits of a high performance airborne gravity gradiometer for resource exploration. Proceedings of Exploration 07: Fifth Decennial International Conference on Mineral Exploration, 2007, pp. 889–893.Annecchione M., Moody M., Carroll K., Dickson D., Main B. Benefits of a high performance airborne gravity gradiometer for resource exploration. Proceedings of Exploration 07: Fifth Decennial International Conference on Mineral Exploration, 2007, pp. 889–893.Christensen A.N., Dransfield M.H., Van Galder C. Noise and repeatability of airborne gravity gradiometry. First break, 2015, vol. 33, no. 4, pp. 55–63.Christensen A.N., Dransfield M.H., Van Galder C. Noise and repeatability of airborne gravity gradiometry. First break, 2015, vol. 33, no. 4, pp. 55–63.Murphy C.A. Exploring prospects with FTG Gravity. 9-th Biennial International Conference & Exposition on Petroleum Geophysics. Hyderabad, 2012, p. 141.Murphy C.A. Exploring prospects with FTG Gravity. 9-th Biennial International Conference & Exposition on Petroleum Geophysics. Hyderabad, 2012, p. 141.Mataragio J. Exploring for Gold and Geothermal Systems in the Great Basin Using Full Tensor Gravity Gradiometry. GRC Transactions, 2012, vol. 36, pp. 1009–1012.Mataragio J. Exploring for Gold and Geothermal Systems in the Great Basin Using Full Tensor Gravity Gradiometry. GRC Transactions, 2012, vol. 36, pp. 1009–1012.Süss F. The small original Eötvös – torsion balance. Budapest, 1928, 13 p.Süss F. The small original Eötvös – torsion balance. Budapest, 1928, 13 p.Miller A.H. The Theory and Operation of the Eötvös Torsion Balance with Plates I, II, III. Journal of the Royal Astronomical Society of Canada, 1934, vol. 28, pp. 1–31.Miller A.H. The Theory and Operation of the Eötvös Torsion Balance with Plates I, II, III. Journal of the Royal Astronomical Society of Canada, 1934, vol. 28, pp. 1–31.Bell R.E., Hansen R.O. The rise and fall of early oil field technology: The torsion balance gradiometer. The Leading Edge, 1998, vol. 17, no. 1, pp. 81–83.Bell R.E., Hansen R.O. The rise and fall of early oil field technology: The torsion balance gradiometer. The Leading Edge, 1998, vol. 17, no. 1, pp. 81–83.Fischbach E. Geophysical Tests for IntermediateRange Forces. Purdue univ lafayette in, 1993.Fischbach E. Geophysical Tests for IntermediateRange Forces. Purdue univ lafayette in, 1993.Adelberger E.G., Gundlach J.H., Heckel B.R., Hoedl S., Schlamminger S. Torsion balance experiments: A low-energy frontier of particle physics. Progress in Particle and Nuclear Physics, 2009, vol. 62, no. 1, pp. 102–134.Adelberger E.G., Gundlach J.H., Heckel B.R., Hoedl S., Schlamminger S. Torsion balance experiments: A low-energy frontier of particle physics. Progress in Particle and Nuclear Physics, 2009, vol. 62, no. 1, pp. 102–134.Tomarken S. Gravitational Torsion Balance. Available at: http://www.hep.vanderbilt.edu/~johnswe/classes/225a/cavmain.pdf (accessed 19.10.2016). doi: org/10.1063/1.4944709Tomarken S. Gravitational Torsion Balance. Available at: http://www.hep.vanderbilt.edu/~johnswe/classes/225a/cavmain.pdf (accessed 19.10.2016). doi: org/10.1063/1.4944709Steiner G. Gravitational torsion balance. Houston, 1925, 17 p.Steiner G. Gravitational torsion balance. Houston, 1925, 17 p.Liu H., Pike W.T., Dou G. A seesaw-lever forcebalancing suspension design for space and terrestrial gravity-gradient sensing. Journal of Applied Physics, vol. 119, no 12, p. 124508. doi: org/10.1063/1.4944709Liu H., Pike W.T., Dou G. A seesaw-lever forcebalancing suspension design for space and terrestrial gravity-gradient sensing. Journal of Applied Physics, vol. 119, no 12, p. 124508. doi: org/10.1063/1.4944709Van Essen M.C. Capacitive MEMS-based sensors: Thermo-mechanical stability and charge trapping. Enschede, University of Twente, 2009, 229 p.Van Essen M.C. Capacitive MEMS-based sensors: Thermo-mechanical stability and charge trapping. Enschede, University of Twente, 2009, 229 p.Rogers M. An Investigation into the Feasibility of using a Modern Gravity Gradient Instrument for Passive Aircraft Navigation and Terrain Avoidance. Air Force Institute of Technology, Ohio, 2009, 165 p.Rogers M. An Investigation into the Feasibility of using a Modern Gravity Gradient Instrument for Passive Aircraft Navigation and Terrain Avoidance. Air Force Institute of Technology, Ohio, 2009, 165 p.Streland A. Going deep: a system concept for detecting deeply burie d facilities from space. Air War College, 2003, 64 p.Streland A. Going deep: a system concept for detecting deeply burie d facilities from space. Air War College, 2003, 64 p.Grujic M. Data processing requirements for an 1 Eo/√Hz AGG system. 22nd International Geophysical Conference and Exhibition. Brisbane, 2012, pp. 1–4.Grujic M. Data processing requirements for an 1 Eo/√Hz AGG system. 22nd International Geophysical Conference and Exhibition. Brisbane, 2012, pp. 1–4.Murphy C.A., Brewster J., Robinson J. Evaluating Air-FTG survey data: bringing value to the full picture. Preview, 2007, vol. 126, pp. 24–28.Murphy C.A., Brewster J., Robinson J. Evaluating Air-FTG survey data: bringing value to the full picture. Preview, 2007, vol. 126, pp. 24–28.Dransfield M. Advances in airborne gravity gradiometry at Fugro Airborne Surveys. EGM 2010 International Workshop Adding new value to Electromagnetic. Gravity and Magnetic Methods for Exploration. Capri, 2010, 5 p.Dransfield M. Advances in airborne gravity gradiometry at Fugro Airborne Surveys. EGM 2010 International Workshop Adding new value to Electromagnetic. Gravity and Magnetic Methods for Exploration. Capri, 2010, 5 p.Murphy C.A. Exploring prospects with FTG. 9 Biennial International Conference and Exposition on Petroleum Geophysics, Hederabat, 2012, p. 141.Murphy C.A. Exploring prospects with FTG. 9 Biennial International Conference and Exposition on Petroleum Geophysics, Hederabat, 2012, p. 141.Dransfield M.H., Christensen A.N. Performance of airborne gravity gradiometers. The Leading Edge, 2013, vol. 32, no. 8, pp. 908–922. doi: org/10.1190/tle32080908.1Dransfield M.H., Christensen A.N. Performance of airborne gravity gradiometers. The Leading Edge, 2013, vol. 32, no. 8, pp. 908–922. doi: org/10.1190/tle32080908.1NEOS and Lockheed Martin to Develop ‘New Generation’ Sensor. NEOS press release, July 6, 2016. Available at: //www.neosgeo.com/wpcontent/uploads/2016/08/NEOS_Release_FTG-PlusSensor_160706.pdf (accessed 19.10.2016).NEOS and Lockheed Martin to Develop ‘New Generation’ Sensor. NEOS press release, July 6, 2016. Available at: //www.neosgeo.com/wpcontent/uploads/2016/08/NEOS_Release_FTG-PlusSensor_160706.pdf (accessed 19.10.2016).Christophe B., Marque J-P., Foulon B. Accelerometers for the ESA GOCE mission: one year of in-orbit results. GPHYS SYMPOSIUM. Paris, 2010, 26 p.Christophe B., Marque J-P., Foulon B. Accelerometers for the ESA GOCE mission: one year of in-orbit results. GPHYS SYMPOSIUM. Paris, 2010, 26 p.Drinkwater M.R., Haagmans R., Muzi D., Popescu A., Floberghagen R., Kern M., Fehringer M. The GOCE gravity mission: ESA’s first core Earth explorer. Proceedings of the 3rd international GOCE user workshop. Noordwijk, 2006, pp. 6–8.Drinkwater M.R., Haagmans R., Muzi D., Popescu A., Floberghagen R., Kern M., Fehringer M. The GOCE gravity mission: ESA’s first core Earth explorer. Proceedings of the 3rd international GOCE user workshop. Noordwijk, 2006, pp. 6–8.GOCE. Fact and figures. European space agency. Available at: http://www.esa.int/Our_Activities/Observing_the_Earth/GOCE/Facts_and_figures (accessed 19.10.2016).GOCE. Fact and figures. European space agency. Available at: http://www.esa.int/Our_Activities/Observing_the_Earth/GOCE/Facts_and_figures (accessed 19.10.2016).Gravity Field and Steady-State Ocean Circulation Explorer. Wikipedia. Available at: https://en.wikipedia.org/wiki/Gravity_Field_and_Steady-State_Ocean_Circulation_Explorer (accessed 19.10.2016).Gravity Field and Steady-State Ocean Circulation Explorer. Wikipedia. Available at: https://en.wikipedia.org/wiki/Gravity_Field_and_Steady-State_Ocean_Circulation_Explorer (accessed 19.10.2016).Douch K., Foulon B., Christophe B., Panet I. A new planar electrostatic gravity gradiometer for airborne surveys. Journal of Geodesy, 2013, vol. 89, no 12, pp. 1216–1219.Douch K., Foulon B., Christophe B., Panet I. A new planar electrostatic gravity gradiometer for airborne surveys. Journal of Geodesy, 2013, vol. 89, no 12, pp. 1216–1219.Marque J.P., Christophe B., Liorzou F., Bodovillé G., Foulon B., Guérard J., Lebat V. The ultra sensitive accelerometers of the ESA GOCE mission. The 59th International Astronautical Congress, Glasgow, 2008. Available at: http://onera-windtunnel.com/dmph/goce/IAC-08-B1.3.7.pdf (accessed 19.07.2016).Marque J.P., Christophe B., Liorzou F., Bodovillé G., Foulon B., Guérard J., Lebat V. The ultra sensitive accelerometers of the ESA GOCE mission. The 59th International Astronautical Congress, Glasgow, 2008. Available at: http://onera-windtunnel.com/dmph/goce/IAC-08-B1.3.7.pdf (accessed 19.07.2016).Silvestrin P. Control and navigation aspects of the new Earth observation missions of the European Space. Annual Reviews in Control, 2005, vol. 29, no. 2, pp. 247– 260. doi: org/10.1016/j.arcontrol.2005.05.004Silvestrin P. Control and navigation aspects of the new Earth observation missions of the European Space. Annual Reviews in Control, 2005, vol. 29, no. 2, pp. 247– 260. doi: org/10.1016/j.arcontrol.2005.05.004Christophe B., Marque J-P., Foulon B. Accelerometers for the ESA GOCE mission: one year o in-orbit results. Available at: https://earth.esa.int/c/document_library/get_file?folderId=14168&name=DL FE-678.pdf (accessed 19.07.2016).Christophe B., Marque J-P., Foulon B. Accelerometers for the ESA GOCE mission: one year o in-orbit results. Available at: https://earth.esa.int/c/document_library/get_file?folderId=14168&name=DL FE-678.pdf (accessed 19.07.2016).Schiermeier Q. Gravity mission to launch. Nature, 2009, vol. 458. Available at: http://www.nature. com/news/2009/090311/full/458133a.html (accessed 19.10.2016). doi: org/10.1038/458133aSchiermeier Q. Gravity mission to launch. Nature, 2009, vol. 458. Available at: http://www.nature. com/news/2009/090311/full/458133a.html (accessed 19.10.2016). doi: org/10.1038/458133aBuckler G. Eye in the sky spots diamonds in the rough. The Globe and Mail, Mar. 13, 2009. Available at: http://www.theglobeandmail.com/report-on-business/eyein-the-sky-spots-diamonds-in-the-rough/article17993239 (accessed 19.10.2016).Buckler G. Eye in the sky spots diamonds in the rough. The Globe and Mail, Mar. 13, 2009. Available at: http://www.theglobeandmail.com/report-on-business/eyein-the-sky-spots-diamonds-in-the-rough/article17993239 (accessed 19.10.2016).Wermuth M.K. Gravity Field Analysis from the Satellite Missions CHAMP and GOCE. Technische Universität München, 2008, 100 p.Wermuth M.K. Gravity Field Analysis from the Satellite Missions CHAMP and GOCE. Technische Universität München, 2008, 100 p.Drennan R. Ready to market. Mississauga News, Jan 30, 2015. Available at: http://www.mississauga.com/news-story/5295543-ready-to-market (accessed 19.10.2016).Drennan R. Ready to market. Mississauga News, Jan 30, 2015. Available at: http://www.mississauga.com/news-story/5295543-ready-to-market (accessed 19.10.2016).Anstie J. Preparation for flight testing the VK1 gravity gradiometer. Airborne Gravity 2010, 2010, pp. 5–12.Anstie J. Preparation for flight testing the VK1 gravity gradiometer. Airborne Gravity 2010, 2010, pp. 5–12.Flokstra J. Gravity Gradient Sensor Technology for future planetary missions. Enschede, University of Twente, 2005, 12 p.Flokstra J. Gravity Gradient Sensor Technology for future planetary missions. Enschede, University of Twente, 2005, 12 p.Carroll K. Gravity gradiometry for lunar surface exploration. 42nd Lunar and Planetary Science Conference, 2011. Available at: http://www.lpi.usra.edu/meetings/lpsc2011/pdf/1108.pdf (accessed 19.10.2016).Carroll K. Gravity gradiometry for lunar surface exploration. 42nd Lunar and Planetary Science Conference, 2011. Available at: http://www.lpi.usra.edu/meetings/lpsc2011/pdf/1108.pdf (accessed 19.10.2016).Spencer H. Lunette: Lunar Farside Gravity Mapping by Nanosat. 19th Annual AIAA/USU Conference on Small Satellites, 2005. Available at: http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1635&context=smallsat (accessed 19.10.2016).Spencer H. Lunette: Lunar Farside Gravity Mapping by Nanosat. 19th Annual AIAA/USU Conference on Small Satellites, 2005. Available at: http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1635&context=smallsat (accessed 19.10.2016).Allen J. Micro-System Inertial Sensing Technology Overview. Albuquerque, New Mexico, 2009, 32 p.Allen J. Micro-System Inertial Sensing Technology Overview. Albuquerque, New Mexico, 2009, 32 p.Tutorial: Noise in micromechanical systems. MEMS material. Available at: http://www.kaajakari.net/~ville/research/tutorials/tutorials.shtml (accessed 19.10.2016).Tutorial: Noise in micromechanical systems. MEMS material. Available at: http://www.kaajakari.net/~ville/research/tutorials/tutorials.shtml (accessed 19.10.2016).Li J., Fang J., Du M., Dong H. Analysis and fabrication of a novel MEMS pendulum angular accelerometer with electrostatic actuator feedback. Microsystem technologies, 2013, vol. 19, no. 1, pp. 9–16. doi: org/10.1007/s00542-012-1630-xLi J., Fang J., Du M., Dong H. Analysis and fabrication of a novel MEMS pendulum angular accelerometer with electrostatic actuator feedback. Microsystem technologies, 2013, vol. 19, no. 1, pp. 9–16. doi: org/10.1007/s00542-012-1630-xYazdi N., Ayazi F., Najafi K. Micromachined inertial sensors. Proceedings of the IEEE, 1998, vol. 86, no. 8, pp. 1640–1659.Yazdi N., Ayazi F., Najafi K. Micromachined inertial sensors. Proceedings of the IEEE, 1998, vol. 86, no. 8, pp. 1640–1659.Cuperus R. MEMS based gravity gradiometer for Space Application. Available at: https://escies. org/download/webDocumentFile?id=7188 (accessed 19.10.2016).Cuperus R. MEMS based gravity gradiometer for Space Application. Available at: https://escies. org/download/webDocumentFile?id=7188 (accessed 19.10.2016).De Simone A. Design and realization of a setup for mechanical tests on a MEMS based micro gravity-gradiometer. Delft, Delft University of Technology, 2008, 89 p.De Simone A. Design and realization of a setup for mechanical tests on a MEMS based micro gravity-gradiometer. Delft, Delft University of Technology, 2008, 89 p.Selig A. Development of a Micro-gradiometer for Planetary Gravity Field Mapping. Available at: http://jupiter-europa.cesr.fr/static_pages/presentations/Berlin/SRON_gravity.pdf (accessed 19.10.2016).Selig A. Development of a Micro-gradiometer for Planetary Gravity Field Mapping. Available at: http://jupiter-europa.cesr.fr/static_pages/presentations/Berlin/SRON_gravity.pdf (accessed 19.10.2016).Ghose K. MEMS Inertial Sensor to Measure the Gravity Gradient Torque in Orbit. Pour l’obtention du grade de docteur ès sciences école polytechnique fédérale de Lausanne, 2012, no. 5231. Available at: http:// infoscience.epfl.ch/record/169608/files/EPFL_TH5231. pdf (accessed 19.10.2016).Ghose K. MEMS Inertial Sensor to Measure the Gravity Gradient Torque in Orbit. Pour l’obtention du grade de docteur ès sciences école polytechnique fédérale de Lausanne, 2012, no. 5231. Available at: http:// infoscience.epfl.ch/record/169608/files/EPFL_TH5231. pdf (accessed 19.10.2016).Murphy C.A. The Air-FTG airborne gravity gradiometer system. ASEG-PESA Airborne Gravity 2004 Workshop, 2004, pp. 7–14.Murphy C.A. The Air-FTG airborne gravity gradiometer system. ASEG-PESA Airborne Gravity 2004 Workshop, 2004, pp. 7–14.Metzger E.H., Jirdtano A., Affleck C. Satellite borne gravity gradiometer study. Buffalo, NASA Goddard space flight center, 1976, 62 p.Metzger E.H., Jirdtano A., Affleck C. Satellite borne gravity gradiometer study. Buffalo, NASA Goddard space flight center, 1976, 62 p.Gerber M.A. Gravity gradiometry-something new in inertial navigation. Astronautics Aeronautics, 1978, vol. 16, pp. 18–26.Gerber M.A. Gravity gradiometry-something new in inertial navigation. Astronautics Aeronautics, 1978, vol. 16, pp. 18–26.Richeson J.A. Gravity gradiometer aided inertial navigation within non-GNSS environments. ProQuest, 2008, 438 p.Richeson J.A. Gravity gradiometer aided inertial navigation within non-GNSS environments. ProQuest, 2008, 438 p.Jekeli C. Precision free-inertial navigation with gravity compensation by an onboard gradiometer. Journal of guidance, control, and dynamics, 2006, vol. 29, no. 3, pp. 704–713. doi: org/10.2514/1.15368Jekeli C. Precision free-inertial navigation with gravity compensation by an onboard gradiometer. Journal of guidance, control, and dynamics, 2006, vol. 29, no. 3, pp. 704–713. doi: org/10.2514/1.15368Flokstra J., Cuperus R., Wiegerink R.J., van Essen M.C. MEMS based gravity gradiometer for future planetary missions. Cryogenics, 2009, vol. 49, issue 11, pp. 665–668. doi: org/10.1016/j.cryogenics.2008.12.019Flokstra J., Cuperus R., Wiegerink R.J., van Essen M.C. MEMS based gravity gradiometer for future planetary missions. Cryogenics, 2009, vol. 49, issue 11, pp. 665–668. doi: org/10.1016/j.cryogenics.2008.12.019Matthews R. Mobile Gravity Gradiometry. Western, University of Western, 2002, 429 p.Matthews R. Mobile Gravity Gradiometry. Western, University of Western, 2002, 429 p.Touboul P., Willemenot E., Foulon B., Josselin V. Accelerometers for CHAMP, GRACE and GOCE space missions: synergy and evolution. Bollettino di geofisica teorica ed applicata, 1999, vol. 40, no. 3–4, pp. 321–327.Touboul P., Willemenot E., Foulon B., Josselin V. Accelerometers for CHAMP, GRACE and GOCE space missions: synergy and evolution. Bollettino di geofisica teorica ed applicata, 1999, vol. 40, no. 3–4, pp. 321–327.Lenoira B., Lévya A., Foulona B., Lamineb B., Christophea B., Reynaudb S. Electrostatic accelerometer with bias rejection for gravitation and Solar System physics. Advances in Space Research, 2011, vol. 48, pp. 1248–1257. doi: org/10.1016/j.asr.2011.06.005Lenoira B., Lévya A., Foulona B., Lamineb B., Christophea B., Reynaudb S. Electrostatic accelerometer with bias rejection for gravitation and Solar System physics. Advances in Space Research, 2011, vol. 48, pp. 1248–1257. doi: org/10.1016/j.asr.2011.06.005Berman D. Effects of Mechanical Imperfections on Performance of a Rotating Gravity Gradiometer. Journal of Spacecraft and Rockets, 1968, vol. 5, no. 10, pp. 1193–1198.Berman D. Effects of Mechanical Imperfections on Performance of a Rotating Gravity Gradiometer. Journal of Spacecraft and Rockets, 1968, vol. 5, no. 10, pp. 1193–1198.Stibrany P., Carroll K.A. The microsat way in Canada. Proc. 11th CASI Conference on Astronautics, 2001, 10 p.Stibrany P., Carroll K.A. The microsat way in Canada. Proc. 11th CASI Conference on Astronautics, 2001, 10 p.Gravity gradient earth sensor experiment on rexus 11. Available at: https://infoscience.epfl.ch/ record/187717/files/ghose%20ESA%20Thun%202013.pdf (accessed 12.11.2016).Gravity gradient earth sensor experiment on rexus 11. Available at: https://infoscience.epfl.ch/ record/187717/files/ghose%20ESA%20Thun%202013.pdf (accessed 12.11.2016).Allasio A., Muzi D., Vinai B., Cesare S., Catastini G., Bard M., Marque J.P. GOCE: space technology for the reference Earth gravity field determination. Proceedings of the European Conference for AeroSpace Sciences, 2009, 13 p.Allasio A., Muzi D., Vinai B., Cesare S., Catastini G., Bard M., Marque J.P. GOCE: space technology for the reference Earth gravity field determination. Proceedings of the European Conference for AeroSpace Sciences, 2009, 13 p.Vasilescu G. Electronic noise and interfering signals: principles and applications. Springer Science & Business Media, 2006, 709 p.Vasilescu G. Electronic noise and interfering signals: principles and applications. Springer Science & Business Media, 2006, 709 p.Carroll K.A. Near-Term Lunar Surface Gravimetry Science Opportunities. Annual Meeting of the Lunar Exploration Analysis Group, Maryland, 2015, 31 p.Carroll K.A. Near-Term Lunar Surface Gravimetry Science Opportunities. Annual Meeting of the Lunar Exploration Analysis Group, Maryland, 2015, 31 p.Carroll K.A., Spencer H., Zee R.E. An Asteroid Lander/Rover for Asteroid Surface Gravity Surveying. 30-th Annual AIAA/USU Conference on small satellites, 2016. Available at: http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3408&context=smallsat (accessed 12.11.2016).Carroll K.A., Spencer H., Zee R.E. An Asteroid Lander/Rover for Asteroid Surface Gravity Surveying. 30-th Annual AIAA/USU Conference on small satellites, 2016. Available at: http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3408&context=smallsat (accessed 12.11.2016).Steiger C., Romanazzo M., Emanuelli P. P., Floberghagen R., Fehringer M. The Deorbiting of ESA’s Gravity Mission GOCE–Spacecraft Operations in Extreme Drag Conditions. Proceedings SpaceOps, Pasadena, USA, 2014, 12 p.Steiger C., Romanazzo M., Emanuelli P. P., Floberghagen R., Fehringer M. The Deorbiting of ESA’s Gravity Mission GOCE–Spacecraft Operations in Extreme Drag Conditions. Proceedings SpaceOps, Pasadena, USA, 2014, 12 p.McBarnet, A. Gravity gradiometry has graduated! OE Digital. Saturday, 01 June 2013, http://www.oedigital.com/geoscience/item/3201-gravitygradiometry-has-graduated (accessed 12.11.2016).McBarnet, A. Gravity gradiometry has graduated! OE Digital. Saturday, 01 June 2013, http://www.oedigital.com/geoscience/item/3201-gravitygradiometry-has-graduated (accessed 12.11.2016).

The authors declare that there are no conflicts of interest present.