空间激光干涉引力波探测

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doi:10.6052/1000-0992-13-044

1 中国科学院力学研究所,北京100190
2 中国科学院数学与系统科学研究院,北京100190
3 首都师范大学物理系,北京100048
4 北京工业大学应用数理学院,北京100022
5 华中科技大学物理学院,武汉430074

基金项目:中国科学院科研装备研制项目(Y231411YB1)；中国科学院战略性先导科技专项：空间科学预先研究项目(XDA04070400)；理论物理国家重点实验室(中国科学院理论物理研究所) 开放课题基金(Y3KF281CJ1) 资助.

详细信息

作者简介:
罗子人，1980 年出生，2010 年获中国科学院数学与系统科学研究院理学博士，现任中国科学院力学研究所助理研究员，参与了中国短臂长空间引力波探测器的可行性研究和中国先进重力卫星关键技术论证工作，主要从事引力波探测的空间激光干涉测距技术的理论分析和方案设计.

中图分类号:O431.2
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出版历程
- 收稿日期:2013-06-17
- 刊出日期:2013-07-25

Gravitational wave detection by space laser interferometry

1 Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3 Department of Physics, Capital Normal University, Beijing 100048, China
4 College of Applied Sciences, Beijing University of Technology, Beijing 100022, China
5 School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

摘要

摘要:为印证广义相对论和开拓引力波天文学窗口，引力波探测是当前国际研究热点. 本文围绕空间激光干涉引力波探测，对其科学意义、发展状况、关键技术等进行了回顾. 与地面激光干涉引力波探测相比，空间探测的工作频段更低，从10 ^-4»10 Hz，在工作距离为百万公里量级上，预计能探测到双致密星系统、超大质量比双黑洞绕转系统、中等质量比双黑洞绕转系统，以及星系合并引起的超大质量黑洞并合等波源. 为此，测距精度须达到皮米的量级，并且保证测距技术有效工作的无拖曳航天技术亦有很高的要求. 本文以欧洲的空间激光引力波探测计划为例，主要对上述两项技术进行分析和阐述，并展望了空间引力波探测在我国的发展趋势和前景.
- 引力波探测/
- 激光干涉测距系统/
- 无拖曳航天技术/
- 惯性传感器/
- 微推进器/
- 引力波天文学
Abstract:Gravitational wave detection is now more than a mere veri¯cation of Einstein's relativity. It opens a brand-new window to explore gravitational wave astronomy, therefore attracts increasing attention of scientists from all over the world. Focusing on space laser interferometer gravitational wave detection, we give a comprehensive review on its scienti¯c objectives, recent status and key technologies. With arm-length being of million kilometers, a space detector works within a frequency band from 0.1mHz to 10Hz. Its possible sources include compact binary star system, extreme mass ratio inspiral, intermediate mass ratio inspiral, super mass black hole merge, etc. The success of space gravitational wave detection mission requires a pico-meter precision laser interferometer, and a state-of-the-art drag- free control system. Taking European space gravitational wave detector as an example, we analyze space laser interferometer and drag-free control system in detail. The trend and perspective of Chinese space gravitational wave detection mission are also discussed.
- gravitational wave detection/
- laser interferometer ranging system/
- drag-free technology/
- inertial sensor/
- micro-thruster/
- gravitational wave astronomy

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参考文献 (120)

[1]	Abbott B P, Abbott R, Adhikari R, Ajith P, Allen B, Allen G, Bridges D O. 2009. LIGO: The laser interferometer gravitational-wave observatory. Reports on Progress in Physics, 72: 076901
[2]	Abbott B, Abbott R, Adhikari R, Ageev A, Allen B, Amin R, Butler W E. 2005. Limits on gravitational-wave emis- sion from selected pulsars using LIGO data. Physical Review Letters, 94: 181103
[3]	Abbott B, Abbott R, Adhikari R, Ageev A, Allen B, Amin R, Cadonati L. 2004. Analysis of LIGO data for gravita- tional waves from binary neutron stars. Physical Review D, 69: 122001
[4]	Abbott B P, Abbott R, Acernese F, Adhikari R, Ajith P, Allen B, Bizouard M A. 2010. Searches for gravitational waves from known pulsars with science run 5 LIGO data. The Astrophysical Journal, 713: 671
[5]	Abramovici A, Althouse W E, Drever R W, GÄursel Y, Kawamura S, Raab F J, Zucker M E. 1992. LIGO: The laser interferometer gravitational-wave observatory. Sci- ence, 256: 325-333
[6]	Accadia T, Acernese F, Antonucci F, Aoudia S, Arun K G, Astone P, Cuoco E. 2010. Status and perspectives of the Virgo gravitational wave detector. Journal of Physics: Conference Series, 203(012074)
[7]	Audley H, Danzmann K, Mar¶n A G, Heinzel G, Monsky A, Nofrarias M, Guzm¶an F. 2011. The LISA Pathfinder interferometry hardware and system testing. Classical and Quantum Gravity, 28: 094003
[8]	Amaro-Seoane P, Aoudia S, Babak S, Bin¶etruy P, Berti E, Boh¶e A, Ward H. 2012. Low-frequency gravitational- wave science with eLISA/NGO. Classical and Quantum Gravity, 29, 124016.
[9]	Ando M, Arai K, Takahashi R, Heinzel G, Kawamura S, Tatsumi D, Shibata M. 2001. Stable operation of a 300- m laser interferometer with sufficient sensitivity to de- tect gravitational-wave events within our galaxy. Physi- cal Review Letters, 86: 3950-3954
[10]	Antoniadis J, Freire P C, Wex N, Tauris T M, Lynch R S, van Kerkwijk M H, Whelan D G. 2013. A massive pulsar in a compact relativistic binary. Science, 340
[11]	Armstrong J W, Estabrook F B, Tinto M. 1999. Time- delay interferometry for space-based gravitational wave searches. The Astrophysical Journal, 527: 814
[12]	Astone P, Bassan M, Bonifazi P, Carelli P, Coccia E, Cos- melli C, Votano L. 1997. The gravitational wave detector NAUTILUS operating atT=0:1 K. Astroparticle Physics, 7: 231-243
[13]	Babak S, Baker J G, Benacquista M J, Cornish N J, Larson S L, Mandel I, Whelan J T. 2010. The mock LISA data challenges: From challenge 3 to challenge 4. Classical and Quantum Gravity, 27: 084009
[14]	Barack L, Cutler C. 2007. Using LISA extreme-mass-ratio inspiral sources to test off-Kerr deviations in the geome- try of massive black holes. Physical Review D, 75: 042003
[15]	Barriga P, Blair D G, Coward D, Davidson J, Dumas J C, Howell E, Zhang Y. 2010. AIGO: A southern hemisphere detector for the worldwide array of ground-based inter- ferometric gravitational wave detectors. Classical and Quantum Gravity, 27: 084005 1-084005 12
[16]	Bassner H, Killinger R, Leiter H, MÄuller J, Box P. 2001. Development steps of the RF-ion thrusters RIT. In: Pro- ceedings 27th International Electric Propulsion Confer- ence, Pasadena, 15-19
[17]	Bender P L. 2004. Additional astrophysical objectives for LISA follow-on missions. Classical and Quantum Grav- ity, 21: S1203
[18]	Bender P, Brillet A, Ciufolini I, Cruise A M, Cutler C, Danzmann K, Winkler W. 1998. LISA pre-phase a re- port. Max-Planck-Institut fÄur Quantenoptic, Garching Bender P L. 2005. Wavefront distortion and beam pointing for LISA. Classical and Quantum Gravity, 22: S339
[19]	Berti E, Cardoso V, Will C M. 2006. Gravitational-wave spectroscopy of massive black holes with the space inter- ferometer LISA. Physical Review D, 73: 064030
[20]	Bonny L S. 2002. Overview of Disturbance Reduction Re- quirements for LISA . California: Jet Propulsion Labo- ratory, California Institute of Technology
[21]	Bortoluzzi D, Bosetti P, Carbone L, Cavalleri A, Ciccolella A, Da Lio M, Weber W J. 2003. Testing LISA drag-free control with the LISA technology package flight experi- ment. Classical and Quantum Gravity, 20: S89
[22]	Bradaschia C, Del Fabbro R, Di Virgilio A, Giazotto A, Kautzky H, Montelatici V, Natale G. 1990. The VIRGO project: A wide band antenna for gravitational wave de- tection. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detec- tors and Associated Equipment, 289: 518-525
[23]	Bykov I, Delgado J J E, Mar¶³n A F G, Heinzel G, Danz- mann K. 2009. LISA phasemeter development: Ad- vanced prototyping. Journal of Physics: Conference Se- ries, 154: 012017
[24]	Cerdonio M, Bonaldi M, Carlesso D, Cavallini E, Caruso S, Colombo A, Zendri J P. 1997. The ultracryo- genic gravitational-wave detector AURIGA. Classical and Quantum Gravity, 14: 1491
[25]	Coleman Miller M, Colbert E J. 2004. Intermediate-mass black holes. International Journal of Modern Physics D, 13: 1-64
[26]	Crowder J, Cornish N J. 2005. Beyond LISA: Exploring future gravitational wave missions. Physical Review D, 72: 083005
[27]	Cutler C, Thorne K S. 2002. An overview of gravitational wave sources. in: Proceedings of the GR16 Conference on General Relativity and Gravitation, ed. N. Bishop and SD Maharaj (World Scientific), 72-111
[28]	DeBra D B. 2003. Drag-free control for fundamental physics missions. Advances in Space Research, 32: 1221- 1226
[29]	Dhurandhar S V, Tinto M. 2005. Time-delay interferome- try. Living Reviews in Relativity, 8: 4
[30]	Di Cara S S, Perez J R, Stagnaro L, Leiter H, Killinger R. 2011. RIT micropropulsion system on lisa pathfinder. in: Proceeding of International Electric Propulsion Confer- ence.
[31]	Danzmann K. 2005. Phase locking to a LISA arm: First results on a hardware model. Classical and Quantum Gravity, 22: S235
[32]	Dolesi R, Bortoluzzi D, Bosetti P, Carbone L, Cavalleri A, Cristofolini I, Vitale S. 2003. Gravitational sensor for LISA and its technology demonstration mission. Classi- cal and Quantum Gravity, 20: S99
[33]	Drever RWP, Hall J L, Kowalski F V, Hough J, Ford G M, Munley A J, Ward H. 1983. Laser phase and frequency stabilization using an optical resonator. Applied Physics B, 31: 97-105
[34]	Einstein A, Lawson R W, Geroch R, Cassidy D C. 1920. Relativity: The Special and the General Theory, Priot: Pi-Press
[35]	Fabbiano G. 2005. The hunt for intermediate-mass black holes. Science, 307: 533-534
[36]	Farmer A J, Phinney E. 2003. The gravitational wave back- ground from cosmological compact binaries. Monthly Notices of the Royal Astronomical Society, 346: 1197- 1214
[37]	Farrell S A, Webb N A, Barret D, Godet O, Rodrigues J M. 2009. An intermediate-mass black hole of over 500 solar masses in the galaxy ESO 243-49. Nature, 460: 73-75
[38]	Feili D, Loeb W, Schartner K H,Weis S, Kirmse D, Meyer B K, Mueller H. 2005. Testing of new ¹N-RITs at Giessen. AIAA Paper, 4263: 2005
[39]	Fichter W, Schleicher A, Szerdahelyi L, Theil S, Airey P. 2005. Drag-free control system for frame dragging mea- surements based on cold atom interferometry. Acta As- tronautica, 57: 788-799
[40]	Finn L S, Thorne K S. 2000. Gravitational waves from a compact star in a circular, inspiral orbit, in the equato- rial plane of a massive, spinning black hole, as observed by LISA. Physical Review D, 62: 124021
[41]	Folkner W M, Hechler F, Sweetser T H, Vincent M A, Ben- der P L. 1997. LISA orbit selection and stability. Clas- sical and Quantum Gravity, 14: 1405
[42]	Gath P F, Fichter W, Kersten M, Schleicher A. 2004. Drag free and attitude control system design for the LISA Pathfinder mission. Measurement, 1: 2
[43]	Gath P F, Schulte H R,Weise D, Johann U. 2007. Drag free and attitude control system design for the LISA science mode. AIAA Paper, 6731
[44]	Gong X, Xu S, Bai S, Cao Z, Chen G, Chen Y, Zhou Z. 2011. A scientific case study of an advanced LISA mis- sion. Classical and Quantum Gravity, 28: 094012
[45]	Gottardi L, de Waard A, Usenko O, Frossati G, Podt M, Flokstra J, Rocchi A. 2007. Sensitivity of the spherical gravitational wave detector MiniGRAIL operating at 5K. Physical Review D, 76: 102005
[46]	GÄurkan M A, Fregeau J M, Rasio F A. 2006. Massive black hole binaries from collisional runaways. The Astrophysi- cal Journal Letters, 640: L39
[47]	Harry G M. 2010. Advanced LIGO: The next generation of gravitational wave detectors. Classical and Quantum Gravity, 27: 084006
[48]	Hellings R W. 2001. Elimination of clock jitter noise in spaceborne laser interferometers. Physical Review D, 64: 022002
[49]	Heinzel G, Braxmaier C, Danzmann K, Gath P, Hough J, Jennrich O, Schulte H. 2006. LISA interferometry: Re- cent developments. Classical and Quantum Gravity, 23: S119
[50]	Heinzel G, Wand V, Garcia A, Jennrich O, Braxmaier C, Robertson D, Danzmann K. 2004. The LTP interferome- ter and phasemeter. Classical and Quantum Gravity, 21: S581
[51]	Huerta E A, Gair J R. 2009. Influence of conservative cor- rections on parameter estimation for extreme-mass-ratio inspirals. Physical Review D, 79: 084021
[52]	Hulse R A, Taylor J H. 1975. Discovery of a pulsar in a binary system. The Astrophysical Journal, 195: L51-L53
[53]	Jennrich O. 2011. NGO (New Gravitational wave Obser- vatory) assessment study report. ESA/SRE, 19
[54]	Johann U A, Ayre M, Gath P F, Holota W, Marenaci P, Schulte H R, Weise D. 2008. The European Space Agency's LISA mission study: Status and present results. Journal of Physics: Conference Series, 122: 012005
[55]	Klipstein W, Halverson P G, Peters R, Cruz R, Shaddock D. 2006. Clock noise removal in LISA. in: Laser Inter- ferometer Space Antenna: 6th International LISA Sym- posium, 873: 312-318
[56]	Kramer M, Stairs I H, Manchester R N, McLaughlin M A, Lyne A G, Ferdman R D, Camilo F. 2006. Tests of gen- eral relativity from timing the double pulsar. Science, 314: 97-102
[57]	Kuroda K, Ohashi M, Miyoki S, Tatsumi D, Sato S, Ishizuka H, Tobar M E. 1999. Large-scale cryogenic grav- itational wave telescope. International Journal of Mod- ern Physics D, 8: 557-579
[58]	Lange B. 1964. The drag-free satellite. AIAA Journal, 2: 1590-1606
[59]	Larson S L, Hiscock W A, Hellings R W. 2000. Sensitivity curves for spaceborne gravitational wave interferometers. Physical Review D, 62: 062001
[60]	Lewis A, Challinor A. 2006. Weak gravitational lensing of the CMB. Physics Reports, 429: 1-65
[61]	梁灿彬, 周彬. 2009. 微分几何入门与广义相对论. 北京：科学出版社
[62]	李利亮, 董丰, 王海燕. 2011. Drag-Free 技术在卫星工程中的应用. 飞行控制与光电探测, 4: 39-43
[63]	Livas J, Arsenovic P, Castellucci K, Generie J, Howard J, Stebbins R T, Mueller G. 2010. Preliminary LISA tele- scope spacer design. in: 38th COSPAR Scientific Assem- bly, 38: 3783
[64]	Lyne A G, Burgay M, Kramer M, Possenti A, Manchester R N, Camilo F, Freire P C C. 2004. A double-pulsar sys- tem: A rare laboratory for relativistic gravity and plasma physics. Science, 303: 1153-1157
[65]	McNamara P W. 2005. Weak-light phase locking for LISA. Classical and Quantum Gravity, 22: S243
[66]	McNamara P W. 2012. The LISA pathfinder mission. In- ternational Journal of Modern Physics D. Madau P, Rees M J. 2001. Massive black holes as popu- lation III remnants. The Astrophysical Journal Letters, 551: L27
[67]	Maggiore M. 2007. Gravitational Waves: Volume 1: The- ory and Experiments. Oxford: Oxford University Press Mandel I, Gair J R. 2009. Can we detect intermediate mass ratio inspirals. Classical and Quantum Gravity, 26: 094036
[68]	Marin A F G, Heinzel G, Schilling R, RÄudiger A, Wand V, Steier F, Matsushita S, Kawabe R, Matsumoto H, Tsuru T G, Kohno K, et al. 2000. Formation of a massive black hole at the center of the superbubble in M82. The Astrophysical Journal Letters, 545: L107
[69]	Matticari G, Noci G E, Siciliano P, Colangelo G, Schmidt R. 2006. Cold gas micro propulsion prototype for very fine spacecraft attitude/position control. in: Proceed- ings of AIAA/ASME/SAE/ASEE 42nd Joint Propulsion Conference, Sacramento, USA, 5378-5390
[70]	Miller M C, Hamilton D P. 2002. Production of intermediate-mass black holes in globular clusters. Monthly Notices of the Royal Astronomical Society, 330: 232-240
[71]	Miller M C. 2002. Gravitational radiation from intermediate-mass black holes. The Astrophysical Jour- nal, 581: 438
[72]	Misner C W, Thorne K S, Wheeler J A. 1973. Gravitation. New York: WH Freeman.
[73]	Nguyen H, KÄohler J, Stenmark L. 2002. The merits of cold gas micropropulsion in state-of-the-art space mis- sions. in: 34th COSPAR Scientific Assembly, the Second World Space Congress, Houston
[74]	Ni W T. 2012. ASTROD-GW: Overview and progress. In- ternational Journal of Modern Physics D.
[75]	Noyola E, Gebhardt K, Bergmann M. 2008. Gemini and Hubble Space Telescope evidence for an intermediate- mass black hole in Centauri. The Astrophysical Jour- nal, 676: 1008
[76]	Paita L, Cesari U, Nania F, Priami L, Rossodivita A, Giusti N, Estublier D. 2013. Alta FT-150: The Thruster for LISA Pathfinder and LISA/NGO Missions. in: Astro- nomical Society of the Pacific Conference Series, 467: 245
[77]	Phinney S, Bender P, Buchman R, Byer R, Cornish N, Fritschel P, Vitale S. 2004. The big bang observer: Di- rect detection of gravitational waves from the birth of the Universe to the Present. NASA Mission Concept Study.
[78]	Punturo M, Abernathy M, Acernese F, Allen B, Andersson N, Arun K, Glampedakis K. 2010. The einstein telescope: A third-generation gravitational wave observatory. Clas- sical and Quantum Gravity, 27: 194002
[79]	Reyes R, Mandelbaum R, Seljak U, Baldauf T, Gunn J E, Lombriser L, Smith R E. 2010. Confirmation of general relativity on large scales from weak lensing and galaxy velocities. Nature, 464: 256-258
[80]	Rowan S, Hough J. 2000. Gravitational wave detection by interferometry (ground and space). Living Rev. Relativ- ity, 3
[81]	Ryan F D. 1997. Accuracy of estimating the multipole mo- ments of a massive body from the gravitational waves of a binary inspiral. Physical Review D, 56: 1845
[82]	Sallusti M, Gath P, Weise D, Berger M, Schulte H R. 2009. LISA system design highlights. Classical and Quantum Gravity, 26: 094015
[83]	Sanjuan J, Preston A, Korytov D, Spector A, Freise A, Dixon G, Mueller G. 2011. Carbon fiber reinforced poly- mer dimensional stability investigations for use on the laser interferometer space antenna mission telescope. Re- view of Scientific Instruments, 82: 124501-124501
[84]	Sathyaprakash B S, Schutz B F. 2009. Physics, astrophysics and cosmology with gravitational waves. Living Rev. Relativity, 12
[85]	Saulson P R. 1994. Fundamentals of Interferometric Grav- itational Wave Detectors. Singapore: World Science Pub Co Inc.
[86]	Shaul D N A, Ara¶ujo H M, Rochester G K, Schulte M, Sum- ner T J, Trenkel C, Wass P. 2008. Charge management for LISA and LISA Pathfinder. International Journal of Modern Physics D, 17: 993-1003
[87]	Scharlemann C, Buldrini N, Killinger R, Jentsch M, Polli A, Ceruti L, Nicolini D. 2011. Qualifciation test series of the indium needle FEEP micro-propulsion system for LISA Pathfinder. Acta Astronautica, 69: 822-832
[88]	Schutz B F. 1999. Gravitational wave astronomy. Classical and Quantum Gravity, 16: A131
[89]	Schuldt T, Gohlke M, Weise D, Johann U, Peters A, Brax- maier C. 2009. Picometer and nanoradian optical het- erodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor. Classical and Quantum Gravity, 26: 085008
[90]	Schumaker B L. 2003. Disturbance reduction requirements for LISA. Classical and Quantum Gravity, 20: S239
[91]	Sesana A, Gair J, Berti E, Volonteri M. 2011. Reconstruct- ing the massive black hole cosmic history through gravi- tational waves. Physical Review D, 83: 044036
[92]	Sesana A, Haardt F, Madau P, Volonteri M. 2005. The gravitational wave signal from massive black hole bina- ries and its contribution to the LISA data stream. The Astrophysical Journal, 623: 23
[93]	Sesana A, Volonteri M, Haardt F. 2007. The imprint of massive black hole formation models on the LISA data stream. Monthly Notices of the Royal Astronomical So- ciety, 377: 1711-1716
[94]	Seto N, Kawamura S, Nakamura T. 2001. Possibility of di- rect measurement of the acceleration of the universe us- ing 0.1 Hz band laser interferometer gravitational wave antenna in space. Physical Review Letters, 87: 221103
[95]	Sheard B S, Gray M B, McClelland D E, Shaddock D A. 2003. Laser frequency stabilization by locking to a LISA arm. Physics Letters A, 320: 9-21
[96]	Stairs I H. 2004. Pulsars in binary systems: Probing bi- nary stellar evolution and general relativity. Science, 304: 547-552
[97]	Sutton A, Shaddock D A. 2008. Laser frequency stabiliza- tion by dual arm locking for LISA. Physical Review D, 78: 082001
[98]	Tajmar M, Scharlemann C, Genovese A, Buldrini N, Boss M, Killinger R. 2006. Indium FEEP micropropulsion dubsystem for LISA pathfinder. in: Proceedings of 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 9-12
[99]	Tapley B D, Bettadpur S, Watkins M, Reigber C. 2004. The gravity recovery and climate experiment: Mission overview and early results. Geophysical Research Let- ters, 31
[100]	Thorne K S. 1994. Black holes and time warps: Einstein's outrageous legacy. New York: WW Norton & Company. Thorpe J I, Mueller G. 2005. Experimental verification of arm-locking for LISA using electronic phase delay. Physics Letters A, 342: 199-204
[101]	Tinto M, Rakhmanov M. 2004. On the laser frequency stabilization by locking to a LISA arm. arXiv preprint gr-qc/0408076.
[102]	Tinto M, Estabrook F B, Armstrong J W. 2004. Time delay interferometry with moving spacecraft arrays. Physical Review D, 69: 082001
[103]	Tinto M, Shaddock D A, Sylvestre J, Armstrong J W. 2003. Implementation of time-delay interferometry for LISA. Physical Review D, 67: 122003
[104]	Trudel T A, Bil¶en S G, Micci M M. 2009. Design and per- formance testing of a 1-cm miniature radio-frequency ion thruster. in: 31st Internationational Electric Propulsion Conference, IEPC, 167: 20-24
[105]	UmstÄatter R, Christensen N, Hendry M, Meyer R, Simha V, Veitch J,Woan G. 2005. LISA source confusion: Iden- tification and characterization of signals. Classical and Quantum Gravity, 22: S901
[106]	Unnikrishnan C S. 2012. IndIGO and LIGO-India: Scope and plans for gravitational wave research and precision metrology in india. International Journal of Modern Physics D, 22: 1341010
[107]	Van Straten W, Bailes M, Britton M. 2001. A test of gen- eral relativity from the three-dimensional orbital geome- try of a binary pulsar. Nature, 412: 158-160
[108]	Volonteri M, Haardt F, Madau P. 2003. The assembly and merging history of supermassive black holes in hierar- chical models of galaxy formation. The Astrophysical Journal, 582: 559
[109]	Weber J. 1969. Evidence for discovery of gravitational ra- diation. Physical Review Letters, 22: 1320-1324
[110]	Weber J. 1970. Anisotropy and polarization in the gravitational-radiation experiments. Physical Review Letters, 25: 180-184
[111]	Weinberg S. 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley
[112]	Winkler W. 1997. A truncated Gaussian beam in the far field. Classical and Quantum Gravity, 14: 1579
[113]	Will C M. 1993. Theory and Experiment in Gravitational Physics. Cambridge: Cambridge University Press
[114]	Willke B, Aufmuth P, Aulbert C, Babak S, Balasubrama- nian R, Barr B W, Rowan S. 2002. The GEO 600 gravi- tational wave detector. Classical and Quantum Gravity, 19: 1377
[115]	Yoshizawa T. 2009. Handbook of Optical Metrology: Prin- ciples and Applications. 10. CRC PressI Llc
[116]	Ziegler T, Fichter W. 2007. Test mass stiffness estimation for the lisa pathfinder drag-free system. AIAA Paper, 6669
[117]	Ziemer J K, Randolph T, Hruby V, Spence D, Demmons N, Roy T. 2008. STT-DRS colloid thruster system de- velopment and performance sumarry. AIAA Paper, 4824
[118]	Martin R. 2006. Colloid microthrust propulsion for the space technology 7 (ST7) and LISA missions. in: AIP Conference Proceedings, 873: 548
[119]	Ziemer J, Hruby V, Randolph T, Spence D, Demmons N, Roy T, Franklin G. 2010. Precision electric propulsion for the ST7 and LISA missions. Bulletin of the Ameri- can Astronomical Society, 42: 575
[120]	Zwart S F P, McMillan S L. 2002. The runaway growth of intermediate-mass black holes in dense star clusters. The Astrophysical Journal, 576: 899