ASTROD2006+Abstracts

on Laser Astrodynamics, Space Test of Relativity and Gravitational-Wave Astronomy and on Laser Astrodynamics, Space test of Relativity and Gravitational-Wave Astronomy **国际暨中德双边激光天文动力学研讨会 ** Beijing, China, July 14 - 16, 2006 Registration: July 13; Lab Visit: July 17 First day of Meeting: First Floor Meeting Room, Institute of Theoretical Physics; Second and Third day of Meeting: First Floor Meeting Room, Morningside Center of Mathematics (No. 55, Zhong Guan Cun Dong Road, Beijing 100080) Sino-German Center for Science Promotion, Beijing, China Morningside Center of Mathematics, CAS, Beijing, China China Center of Advanced Science and Technology, CAS, Beijing, China Purple Mountain Observatory, CAS, Nanjing, China National Astronomical Observatories, CAS, Beijing, China Shanghai Astronomical Observatory, CAS, Shanghai, China Institute of Theoretical Physics, CAS, Beijing, China Institute of Physics, CAS, Beijing, China Chinese Astronomical Society, Nanjing, China China Society on Gravitation and Relativistic Astrophysics Foundation of Minor Planets of Purple Mountain Observatory ZARM, University of Bremen, Bremen, Germany ** ** Schedule ** First day of Meeting: First Floor Meeting Room, Institute of Theoretical Physics; Second and Third days of Meeting: First Floor Meeting Room, Morningside Center of Mathematics CAS (No. 55, Zhong Guan Cun Dong Road, Beijing 100080) Session 1 Friday, July 14th, 9:30-10:30 09:30-10:00 The fundamental astronomical reference system for space missions and the expansion of the universe Michael Soffel, Lohrmann Observatory, Dresden Technical University 10:00-10:30 ASTROD and ASTROD I: overview and progress Wei-Tou Ni, Purple Mountain Observatory, CAS 10:30 Coffee/Tea Break Session 2 Friday, July 14th, 10:50-12:10
 * Third International ASTROD Symposium **
 * First Sino-German Bilateral Symposium**
 * // Sponsors: //****
 * // Thursday, July 13th, 2006 //**
 * // Registration and Reception 15:00-20:00 //**First Floor, Morningside Center of Mathematics CAS (No. 55, Zhong Guan Cun Dong Road, Beijing 100080)
 * // Friday, July 14, 2006 //** First Floor Meeting Room, Institute of Theoretical Physics (No. 55, Zhong Guan Cun Dong Road, Beijing 100080)
 * // Welcome and introduction 9:00-9:30 //**
 * // Director Reinhard Rutz, Sino-German Center for Science Promotion //**
 * // Academician Lo Yang, Morningside Center of Mathematics, CAS //**
 * // Academician Minghan Ye, China Center of Advanced Science and Technology, CAS //**
 * // Academician Shu Hua Ye, Shanghai Astronomical Observatory, CAS //**
 * // Deputy Director Hansjoerg Dittus, ZARM, University of Bremen //**
 * Astrodynamics and Solar-System Measurement I **
 * Chairman: Hansjoerg Dittus, ZARM, Bremen University **
 * Mission **** Studies I **
 * Chairman: Lo Yang, ****Morningside Center of Mathematics, CAS**

10:50-11:20 ESA technology development activities for fundamental physics space missions B. Leone, E. Murphy, and E. Armandillo European Space Research and Technology Centre, ESA 11:20-11:50 Satellite System OPTIS - Platform for Precision Experiments Hansjörg Dittus, ZARM, Bremen University 11:50-12:20 The T2L2 (Time Telemetry by Laser Light) Experiment : Status Report Jonathan Weick and Étienne Samain, Observatoire de la Cote D’Azur 12:20 Lunch Session 3 Friday, July 14th, 14:00-15:50 14:00-14:30 LISA Pathfinder Gerhard Heinzel and Albrecht Rüdiger, Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Hannover 14:30-14:55 Optimization of LISA orbit configuration Guangyu Li, Purple Mountain Observatory, CAS 14:55-15:25 Charge management for LISA Diana Shaul, Imperial College London 15:25-15:50 Low frequency sensitivity to gravitational waves for ASTROD A. Pulido Patón, Purple Mountain Observatory, CAS 15:50 Coffee/Tea Break Session 4 Friday, July 14th, 16:10-18:20 16:10-16:35 Inertial sensor and its application in space fundamental experiments Ze-Bing Zhou, Huazhong University of Science and Technology 16:35-17:00 Fiber optic accelerometer using the wavefront-splitting interferometry Hsien-Chi Yeh, Zhongshan University, and Shulian Zhang, Tsinghua University. 17:00-17:25 Tracing the measurement of photon pressure to SI unit using strip torsion balance Sheau-shi Pan, Center for Measurement Standards, ITRI, Hsinchu 17:25-17:50 The development of optical frequency standards and its application to space missions Naicheng Shen and Yuxin Nie, Institute of Physics, CAS 17:50-18:20 Quantum sensors for space and time on ground and in space Ernst M. Rasel, Institute for Quantum Optics, University of Hannover Session 5 Saturday, July 15th, 8:30-10:45 08:30-09:00 ESA Technology Development for LISA Oliver Jennrich, European Space Research and Technology Centre, ESA 09:00-09:30 Precise modeling of satellite and test mass dynamics for drag-free satellites Stephan Theil, ZARM, Bremen University 9:30-09:50 In-orbit calibration of drag-free satellites Michel Silas Guilherme, ZARM, Bremen University 09:50-10:15 Space environmental study for ASTROD I Qingxiang Zhang, Deep Space Exploration & Space Science Technology Research Division, Research & Development Center, China Academy of Space Technology 10:15-10:45 Science, technology, and mission design for LATOR mission Slava Turyshev, Jet Propulsion Laboratory, Caltech
 * Gravitational Waves I **
 * Chairman: Shu Hua Ye, Shanghai Astronomical Observatory, CAS **
 * Advanced Technology I **
 * Chairman: **** Andreas Wicht, ****Heinrich-Heine-Universität Düsseldorf**
 * // Saturday, July 15, 2006 //**First Floor Meeting Room, Morningside Center of Mathematics, CAS (No. 55, Zhong Guan Cun Dong Road, Beijing 100080)
 * Mission **** Studies II **
 * Chairman: Yuan-Zhong Zhang, Institute of Theoretical Physics, CAS **

10:45-11:05 Coffee/Tea Break

Session 6 Saturday, July 15th, 10:05-12:20 11:05-11:35 Some research objects in general relativity --- multiple moments, quasi-rigid body, elastic body, fluid, quasi-incompressible fluid and others Chongming Xu, Purple Mountain Observatory and Nanjing Normal University 11:35-11:55 Second post-Newtonian approximation of scalar-tensor theory of gravity Yi Xie, Nanjing University 11:55-12:20 Supermassive central black hole masses in blazars Junhui Fan, Guangzhou University
 * General relativity and relativistic gravity I **
 * Chairman: Achim Peters, Humboldt-University Berlin **

12:20 Lunch Session 7 Saturday, July 15th, 14:00-16:00 14:00-14:30 Detecting gravitational waves using detector arrays Linqing Wen, Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Golm 14:30-15:00 Selection and Detection of High-Frequency Relic Gravitational Waves Fangyu Li, Chongqing University 15:00-15:30 Relic gravitational waves in accelerating universe and CMB polarization Yang Zhang, University of Science and Technology of China 15:30-16:00 Angular Momentum Carried by Gravitational Radiation Shan Bai, Zhoujian Cao, Xuefei Gong, //Yun-Kau Lau//, Yuguang Shi, and Xiaoning Wu, Morningside Mathematics Center, CAS, and Peking University 16:00 Coffee/Tea Break Session 8 Saturday, July 15th, 16:20-18:20 16:20-16:50 Laser ranging technique for the ASTROD I mission Yaoheng Xiong, Yunnan Observatory, NAOC, CAS 16:50-17:15 FADOF and study in its application to ASTROD and ASTROD I missions Albrecht Rüdiger, Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Hannover 17:15-17:35 Test mass charging and disturbances for ASTROD I Gang Bao, Purple Mountain Observatory, and Diana Shaul, Imperial Colleage London (UK) 17:35-17:55 Dynamics modeling and first design of drag-free controller for ASTROD I Hongyin Li, Purple Mountain Observatory, and Stephan Theil, ZARM, Bremen University Session 9 Sunday, July 16th, 8:30-10:30 08:30-09:00 Precision control of optical pulse trains Long-Sheng Ma, East China Normal University 09:00-09:30 A modern Michelson-Morley experiment using ultra-stable optical resonators Achim Peters, Humboldt-University Berlin 09:30-09:55 Optical Frequency Combs for Precision Tests of Fundamental Physics – Activities at the University of D üsseldorf Andreas Wicht, Heinrich-Heine-Universität Düsseldorf 09:55-10:15 Optical clocks in space Stephan Schiller, A. G ö rlitz, J. Koelemeij, A. Nevsky, and Andreas Wicht, Heinrich-Heine-Universität Düsseldorf 10:15-10:40 S table 200MHz frequency comb by difference frequency the ultrabroaden 7 fs Ti:sapphire laser Zhiyi Wei, Institute of Physics, CAS 10:40 Coffee/Tea Break Session 10 Sunday, July 16th, 11:00-12:30 11:00-11:30 Uniformly accelerated frames and equivalence principle Chao-Guang Huang, Institute of High Energy Physics, CAS 11:30-12:00 Relativity and astrometry in the micro-arcsecond level Sergei Klioner, Lohrmann Observatory, Dresden Technical University 12:00-12:20 Light deflection and perihelion shift in the second post-Newtonian approximation of scalar-tensor theory of gravity Peng Dong, Purple Mountain Observatory, CAS 12:20 Lunch Session 11 Sunday, July 16th, 13:30-15:40 14:00-14:30 Testing gravity with lunar laser ranging Slava Turyshev, Jet Propulsion Laboratory, Caltech 14:30-15:00 Astrometry and astrophysics with the space telescope RADIOASTRON Alexander F. Zakharov, Institute of Theoretical and Experimental Physics, Moscow 15:00-15:30 An astrodynamical model for co-orbit restricted problem, and its application to astronomy and astronautics Zhao-hua Yi, Nanjing University and Purple Mountain Observatory 15:30-16:00 Do we really understand the physics within the Solar System? Claus Lämmerzahl, ZARM, Bremen University 16:00 Coffee/Tea Break Session 12 Sunday, July 16th, 16:20-18:00 Outlook for future fundamental physics missions Sino-German collaboration International collaboration 18:30 Banquet
 * Gravitational Waves II **
 * Chairman: Sergei Klioner, Lorrmann Observatory, Dresden Technical University **
 * Mission **** Studies III **
 * Chairman: **** Claus Lämmerzahl, ZARM, Bremen University **
 * // Sunday, July 16, 2006 //**First Floor Meeting Room, Morningside Center of Mathematics, CAS (No. 55, Zhong Guan Cun Dong Road, Beijing 100080)
 * Advanced Technology II **
 * Chairman: Renxin Xu, Peking University **
 * General Relativity and Relativistic Gravity II **
 * Chairman: Diana Shaul, Imperial College **
 * Astrodynamics and Solar-System Measurement II **
 * Chairman: Suijian Xue, National Astronomical Observatories ****, CAS**
 * Round Table Discussion **
 * // Monday, July 17, 2006 //**
 * Lab Visit of Institute of Physics and National Astronomical Observatories **

09:30-12:00 Institute of Physics, CAS

12:00 Lunch

13:30 -16:00 National Astronomical Observatories, CAS Solar, Cosmic Ray and Environmental physics (SCoRE) for/with ASTROD and ASTROD I Wei-Tou Ni, Purple Mountain Observatory, CAS Orbit design and orbit simulation for ASTROD and ASTROD I Yan Xia, Purple Mountain Observatory, CAS
 * Posters (will be posted on the first floor of Morningside Center of Mathematics, CAS in the afternoon of July 14 through July 16): **

Calibration and performance tests on T2L2 (Time Telemetry by Laser Light) Cheng Zhao and Étienne Samain, Observatoire de la Cote D’Azur

An all-optical readout for the inertial sensor on the space based gravity-wave detector LISA Achim Peters, Humboldt-University Berlin

Atomic quantum gases in microgravity - a demonstration experiment at the Bremen droptower Achim Peters, Humboldt-University Berlin The generalized Chaplygin gas model with interaction Ya-Bo Wu, Song Li, Jianbo Lu and Xiuyi Yang, Liaoning Normal University Laser interference method to measure one-way velocity of light and to test new version of Einstein’s equation Shao-Guang Chen, Jiangxi Provincial Academy of Sciences ASTROD2006 ABSTRACTS

** FRIDAY 9:30-10:30 ** ** The fundamental astronomical reference system for space missions and the expansion of the universe ** ** Michael Soffel, ** S.Klioner**, Lohrmann Observatory, Dresden Technical University ** The basic astronomical reference system for space missions like GAIA is the Barycentric Celestial Reference System (BCRS). From this a corresponding Geocentric- or Topocentric- Celestial Reference System can be deduced. The BCRS assumes the solar system to be isolated and it is asymptotically flat. Hence every mass-energy outside the solar system is neglected. We found ways to include the expansion of the universe in the BCRS. To this end the Robertson-Walker metric is rewritten in terms of local coordinates. The problem if the global Hubble expansion has local influences is also discussed. Orders of magnitude for such local cosmological effects are given. Over the next decade the gravitational physics community will benefit from dramatic improvements in many technologies critical to the tests of gravity and gravitationalwave detection. The highly accurate deep space navigation, interplanetary laser ranging and communication, interferometry and metrology, high precision frequency standards, precise pointing and attitude control, together with the drag-free technologies will revolutionize the field of the experimental gravitational physics. Deep-space laser ranging will be ideal for gravitational-wave detection, and testing relativity and measuring solar-system parameter to an unprecedented accuracy. ASTROD I is such a mission with single spacecraft; it is the first step of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) with 3 spacecraft. In this paper, we will present the progress of ASTROD and ASTROD I with emphases on the acceleration noises, mission requirement, charging simulation, drag-free control and low frequency gravitational-wave sensitivity. ** FRIDAY 10:50-12:10 ** This paper gives an overview of the European Space Agency (ESA) technology development activities for applications in fundamental physics space missions. Tests to General Relativity and other fundamental physics theories rely on high precision metrology in one form or another. The focus at ESA is to answer this need through the development of stabilized lasers, atom interferometry and atomic clocks and their subsequent miniaturization and space qualification. Scheithauer, A. Wicht, **, ZARM, Bremen University ** OPTIS is a mission which gives a complete test of Lorentz invariance and of the universality of the gravitational redshift, both being important principles of the foundation of Einsteins General Relativity. Furthermore, also consequences of General Relativity can be tested, namely the Lense-Thirring effect as well as the perihelion advance. All these test can be performed with a precision being up to three orders of magnitude better than previous tests or observations. In this talk we present recent progress made in the experimental techniques as well as in the treatment (numerical and analytical) of the deformation of bodies - in our case the optical resonators - in the gravity gradient field. The latter might also be of importance for other space missions using test masses. T2L2 is an experience based on laser ranging technique coupled with time-frequency metrology. The goal consists in synchronizing ground and space clocks using short light pulses travelling between the ground and a satellite. The instrument is in phase C/D until end of 2006 and will be integrated to the Jason-2 altimetric satellite which launch is scheduled in June 2008 for a five-year nominal duration. The experiment should enhance the performances of time transfer by one or two magnitudes compared to existing microwave techniques like GPS and Two-Way. ** FRIDAY 14:00-15:50 ** LISA (Laser Interferometer Space Antenna) is the joint NASA/ESA project for the detection of gravitational waves (GWs). It consists of three spacecraft in an equilateral triangle of 5 million km sides, orbiting on an Earth-like orbit around the sun. Each spacecraft houses two free-falling test masses that determine the distances to the other spacecraft. Distance changes due to GWs are monitored by laser interferometry, down to minute relative changes in the order of 10−23. The extremely small GW signals make a technology demonstrator, the “LISA Pathfinder” LPF, very desirable, to verify that the employed technologies of (1) laser stability, (2) picometer interferometry, (3) drag-free control, and (4) micronewton thrusters can meet the challenge. The LPF will be carried on the ESA Smart-2 mission to be placed near the Lagrange point L1, with launch expected for 2009. LPF will consist of one spacecraft with two independent test masses; the distances between these two test masses, and the position changes with respect to the optical bench (spacecraft) will be monitored with a resolution only one power of ten away from the requirements of LISA proper. A flight module of the optical bench has been built and has passed the necessary tests for space qualification. Gerhard Heinzel 3, Oliver Jennrich 4 LISA is an ESA-NASA mission. It’s primary scientific goal is to detect gravitational waves with wavelength from 0.1 mHz to 1 Hz. Three spacecraft will be launched around 2015, and reach it’s heliocentric orbits. In order to carry out precise laser interferometer measure between the three spacecraft, high requirement for the stability of the LISA constellation was put forward. In this paper we discuss some problems in the optimization of the LISA orbits using both analytical and numerical methods. On the base of plane co-orbit restricted problem we deduced the analytical formula for the variation of the heliocentric distance and trailing angle of the constellation center. And we found that the precision of our first-order approximate analytical solution satisfies the requirements of the spacecraft orbit design. In this paper we also presented two sets of preliminary optimized LISA orbits, whose stabilitities are close to the requirement of LISA mission. Solar and cosmic ray particles will charge up the isolated LISA test masses. The interaction of the charged test mass with the conducting surfaces that surround it is one of the main sources of spurious accelerations for LISA. This presentation will describe the problems caused by test mass charging and the hardware that has been developed for the LISA technology demonstrator, LISA Pathfinder that will be used to manage this problem. ASTROD is a relativity mission concept encompassing multi-purposes. Within its main objectives are mapping the solar-system gravity, measuring the related solarsystem parameters, testing relativistic gravity and detecting gravitational waves. Since ASTROD will be after LISA, in the Cosmic Vision time-frame 2015-2025, a ten-fold improvement over LISA’s accelerometer noise goal can be expected, allowing ASTROD to test relativistic gravity to 1 ppb, and improve gravitational wave sensitivity. We discuss ways of suppressing noise due to thermal, electromagnetic and local gravitational effects to improve drag-free performance, with emphasis in the low-frequency regime (below 0.1 mHz). To measure relative displacements between the proof mass and the spacecraft capacitive and/or optical sensing are considered.We discuss various possibilities of lower-frequency gravitational-wave responses and their significance to potential astrophysical sources. ** FRIDAY 16:10-18:20 ** ASTROD I is the first step of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices), which measures the relativistic parameters and detects gravitational waves at the lower frequencies compared with LISA. The inertial sensor design is similar to one developed for LISA. The requirements of the inertial sensor for ASTROD I are listed as (1) limit of spurious accelerations applied on the inertial sensor is 10-13 m s-2 Hz-1/2 at 0.1 mHz, and (2) limit of the relative displacement between each sensor proof-mass and the spacecraft to 3 ´ 10-7 m Hz-1/2 at 0.1 mHz [1-2].
 * Astrodynamics and Solar-System Measurement I **
 * 09:30-10:00 **
 * 10:00-11:30 **
 * ASTROD and ASTROD I: overview and progress **
 * Wei-Tou Ni, Purple Mountain Observatory, CAS **
 * Mission **** Studies I **
 * 10:50-11:20 **
 * ESA technology development activities for fundamental physics space mission **
 * B. Leone, E. Murphy, and E. Armandillo, ESA **
 * 11:20-11:50 **
 * Satellite System OPTIS - Platform for Precision Experiments **
 * H. Dittus **, E. Hackmann, C. Lämmerzahl, A. Peters, S. Schiller, S.
 * 11:50-12:20 **
 * The T2L2 (Time Telemetry by Laser Light) Experiment : Status Report **
 * Jonathan Weick and Étienne Samain, **** Observatoire de la Cote D’Azur **
 * Gravitational Waves I **
 * 14:00-14:30 **
 * LISA Pathfinder **
 * Gerhard Heinzel and Albrecht Rüdiger, **** Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Hannover **
 * 14:30-14:55 **
 * Some problems in the optimization of the LISA orbits **
 * Guangyu Li 1, ** Zhaohua Yi 1,2, Yan Xia 1,
 * 1. Purple Mountain Observatory, CAS **
 * 2. Nanjing University **
 * 3. Max Planck Institute for Gravitational Physics **
 * 4. European Space Research and Technology Cente r  **
 * 14:55-15:25 **
 * Charge management for LISA **
 * Diana Shaul, Imperial College London **
 * 15:25-15:50 **
 * Low frequency sensitivity to gravitational waves for ASTROD **
 * A. Pulido Paton ****, W.T. Ni, Purple Mountain Observatory, CAS**
 * Advanced Technology I **
 * 16:10-16:35 **
 * Torsion Pendulum to test performance of Inertial Sensor for ASTROD-1 **
 * Z B Zhou, ** S B Qu, H B Tu, Y Z Bai, S C Wu, Q Y Wan, J Luo
 * Huazhong **** University of Science and Technology, Wuhan **

The inertial sensor consists of a test mass and a set of electrodes that are used to read out the position and orientation with respective to the spacecraft. The inertial sensor is free along its sensitive axis as an end reference mass of optical measurement, while other axes should be controlled by electrostatic actuators [3-4].

The torsion pendulum, as a high sensitive probe in laboratory, is used to investigate the effects to the inertial sensor of the environmental parameters on ground, such as temperature, pressure, parasitical stiffness of capacitance transducer and so on [3]. In addition, the coupling between the sensitive and electrostatically servo axes should be controlled within the requirement.

To test performance of an inertial sensor for ASTROD I, a torsion pendulum facility is constructed, and the twist motion of the torsion pendulum is used to simulate the state of inertial sensor in space due to its very soft linkage. A torsion pendulum facility has been constructed in our laboratory [5]. Here the test mass is a cubic aluminum block with 50 mm on each side and a mass of 330 g. A tungsten fiber with a diameter of 50 micrometer and a length of about 1.1 m is used to suspend the test mass to act a torsion pendulum. The twist motion of the pendulum has been electrostatic-servo locked-in, and preliminary experiment shows that its torque noise level comes to 9 ´ 10-12 N m Hz-1/2 from 1 mHz to 0.1 Hz. The residual disturbances acting on the test mass are being analyzed and measured by the modulating experiments. References [1] Ni W. T., //Int. J. Mod. Phys. D//, **11**, 947, 2002. [2] Ni W. T. et al, //Class. Quantum Grav.//, **21**, S641, 2004. [3] Carbone L. et al, //Phys. Rev. Lett.// **91**, 151101, 2003. [4] Touboul P. et al., Aerospace Sci. Technol., **8**, 431, 2004. [5] Zhou Z. B. et al, //Class. Quantum Grav.//, **22**, S537, 2005. A fiber-optic accelerometer based on the wavefront-splitting interferometry is described in this paper. Within a compact sensing space surrounded by two single-mode fibers and a flat specimen surface, two-beam interferences occur by superimposing radiations with split wavefronts caused by reflections on specimen surface. Due to a small divergence angle of Gaussian laser beam emitting from the single-mode light-emitting fiber, radiations traversing toward the specimen have an incident angle of nearly 90o, and consequently the reflection coefficient becomes relatively high for most of the materials with a flat surface. Using this sensing scheme, we designed a displacement-type accelerometer, shown in Figure 1. The stainless-steel proof-mass having a weight of 23.2 g is connected to a base by using an OHP transparency strip, in order to obtain a larger damping coefficient and hence a wider sensing spectrum range. The resonance frequency of proof mass was measured to be 12.5 Hz. In the preliminary experiments, the whole system was put on an optical table, and an ambient noise level of 5 nm was obtained, which is corresponding to an acceleration of30 m g.  Figure 1 showing the structure of fiber-optic accelerometer. Keywords: Accelerometer; Fiber optic sensors; Wavefront-splitting interferometer //** Jeah-Sheng Wu1, ** ** Hsien **** - **** Chi ** ** Yeh **** 2 **** and Sheau-shi Pan3 ** // //** 3 **** Center for Measurement Standards ****, **** Hsinchu ** // The development of optical frequency standards during 1980’s quickly led to cold atom cloud temperatures of below 1mK within optical molasses and magneto-optical traps. With such cooling capability, it became possible to virtually remove Doppler broadening and shift to an unprecedented level. 1S-2S two-photon transition in atomic hydrogen plays an important role in the determination of Rydberg constant. The 532nm iodine stabilized Nd:YAG lasers are becoming the important standard of optical frequency and wavelength, owing to their high frequency stability, reproducibility and reliability. We are improving its frequency reproducibility by using new iodine cells made in our laboratory. The important problem about frequency standards and their application to space missions is the synchronization of clocks using signals from orbiting satellites, such as in the Global Positioning System (GPS) and GLONASS. Various manufacturers use GPS receivers in which precise time is derived from one of the atomic clocks in the satellites (GPS Time Receiver). In certain applications, there is a need to synchronize these Time Receivers with each other. The method is to synchronize the satellite clock to the reference by making measurement of times of transmissions and arrivals of a sequence of two-way transmissions and using those measurements deriving a correction term to be applied to the satellite clock. A promising technique for fundamental tests in the quantum domain are matter-wave sensors based on cold atoms or atom lasers, which use atoms as unperturbed microscopic test bodies for measuring inertial forces or as frequency references. The talk will give an overview on matter-wave sensors and our development of inertial sensors. Microgravity is expected to be a decisive ingredient for the next leap in tests in fundamental physics of gravity, relativity and theories beyond the standard model. Microgravity is also of high relevance for matter-wave interferometers and experiments with quantum matter (Bose-Einstein Condensates or degenerate Fermi gases) as it permits the extension the unperturbed free fall of these test particles in a low-noise environment. Experiments in such an environment will also help to establish a new scientific avenue in the research on degenerate quantum gases as it will substantially extend the science of quantum gases towards nowadays inaccessible regimes at lowest temperatures, to macroscopic dimensions, and to unequalled durations of unperturbed evolution of these distinguished quantum objects. With the launch of the development of a mobile BEC platform QUANTUS for microgravity experiments in the drop tower and during parabolic flights within a pilot project, running since January 2004, the DLR took a major first step to establish this field of research in Germany.
 * 16:35-17:00 **
 * Fiber-optic accelerometer using the wavefront-splitting interferometry **
 * Hsien-Chi Yeh, School of Engineering, Zhongshan University, Guangzhou**
 * 17:00-17:25 **
 * Tracing the measurement of photon pressure to SI unit using strip torsion balance **
 * 1 **** Center for Measurement Standards ****, **** Hsinchu **** , **
 * 2 **
 * Zhongshan **** University ****, **** Guangzhou **** , **
 * CMS has established a system to probe the micro force down to 10-9 Newton based on a very stable strip torsion balance with restoring torque constant 5.25×10-6 N m/rad. The system has included an angular interferometer that could measure the deflection of strip torsion balance with resolution of 1.95×10-7 rad. In this report, we present the measurement of optical power by the torsion balance. The methods of signal modulation generated by varying power of laser and the polarized modulation of laser beam were individually used to shift the deflection of strip torsion balance from its standing position. Angular deflection torque measurement agrees with photon generating torque to within 30% using power modulation method. The agreement using polarized modulation is better than 5%. Finally, the method of tracing of optical power to SI unit with strip torsion balance will be discussed. **
 * Keywords: ** photon pressure, SI unit
 * 17:25-17:50 **
 * The Development of Optical Frequency Standards and Its Application to Space Missions **
 * Naicheng Shen, Institute of Physics, CAS **
 * 17:50-18:20 **
 * Quantum sensors for space and time on ground and in space **
 * Ernst Maria Rasel, Institute for Quantum Optics, University of Hannover **

LISA is a joint ESA/NASA mission to detect and observe gravitational waves in space in a frequency range inaccesible to ground based detectors. It will allow to study numerous sources for low-frequency graviational waves, such as coalescing supermassive black holes, galactic binary systems and signals from capture events of compact objects by massive black holes. An overview of the science of LISA, the astrophysical and cosmological aspects of the sources and the gravitational wave signals will be given. Drag-Free Satellite (DFS) is a class of scientifc satellite missions basically for research on fundamental physics as well as geodesy. The Drag-Free Attitude Control System (DFACS) is the more complex technology on-board these satellites, with state of the art sensors and actuators specially developed for this purpose, and not yet tested in space. In the case of the accelerometer, to measure accelerations of the order of < 10−15 m /s2, or below, the inertial sensor is not yet tested in space. This key technology allows to reduce the residual accelerations on experiments on board the satellites significantly. In order to achieve this very low disturbance environment the Drag-Free Control system has to be optimized.
 * SATURDAY 8:30-10:45 **
 * Mission **** Studies II **
 * 08:30-09:00 **
 * ESA Technology Development for LISA **
 * Oliver Jennrich, European Space Research and Technology Centre, ESA**
 * 09:00-09:30 **
 * Precise modeling of satellite and test mass dynamics for drag-free satellites **
 * Stephan Theil, **** ZARM, Bremen University **
 * 09:30-09:50 **
 * In-orbit calibration of drag-free satellites **
 * M. S. Guilherme, S. Theil, W. C. Leite Filho, H. Selig, H. Dittus, ZARM - University of Bremen **

The optimization process is required because of uncertainties in system parameters which demand a robustness of the control system. The paper will present an approach for the in-orbit estimation/identification of a drag-free control system.

The discussion includes the modeling, with scale factors and cross-talk couplings, possible excitation signals as well as simulation results. Keywords: Drag-free satellite; Calibration; Accelerometer; Parameter Estimation For ASTROD I program, the distance from the Sun is from 0.5 AU to 1.04 AU. Without shielding of Earth’s magnetosphere, the satellite will be exposed directly to cosmic rays, solar event particle and solar wind particle and the longevity and reliability of some enable techniques for ASTROD I, such as capacitive sensors, thrusters, lasers and optics will be influenced. In this paper, the spaceenvironments and their effect for ASTROD I is analyzed. It also proposed the study of interplanetary environment as a science object for ASTROD I and a light radiation monitor will be onboard. The Laser Astrometric Test of Relativity (LATOR) is a Michelson-Morley-type experiment designed to improve current tests of Einstein’s general theory of relativity by more than four orders of magnitude. The space experiment uses laser interferometry between two laser sources placed on two small spacecraft separated by 1 degree (as seen from the Earth), whose lines of sight several times pass close by the Sun, to measure accurately the deflection of light by the solar gravitational field. The key element of the experimental design is a redundant geometry optical truss provided by a long-baseline (~100m) Michelson stellar optical interferometer that is used to measure the angle between the two spacecraft (with accuracy of 0.1 picoradian). The three arms of the light triangle formed by three space nodes are monitored with laser metrology (accurate to about 1 cm). By using a combination of independent time-series of highly accurate measurements of gravitational deflection of light in the immediate proximity to the Sun, along with measurements of the Shapiro time delay on the interplanetary scales, LATOR will significantly improve our knowledge of relativistic gravity in the solar system. The experiment will measure the key post-Newtonian Eddington parameter γ with accuracy of 1 part in a billion and will also conduct a number of other unique measurements of the gravity effects on light propagation. This primary measurement pushes to unprecedented accuracy the search for cosmologically relevant scalar-tensor theories of gravity by looking for a remnant scalar field in today's solar system. LATOR will lead to robust advances in the tests of fundamental physics: this mission could discover a violation or extension of general relativity and/or reveal the presence of an additional long range interaction in the physical law.
 * 09: 50-10:15 **
 * Space environmental study for ASTROD I **
 * Qingxiang Zhang, ** Li Wang, Xinbin Hou, Wanglin Shi, Hui Wang, Zhengji Song, Jijun Chang **, Deep Space Exploration & Space Science Technology Research Division, Research & Development Center, China Academy of Space Technology **
 * 10:15-10:45 **
 * Science, Technology and Mission Design for the Laser Astrometric Test of Relativity **
 * Slava G. Turyshev, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA **

In this talk we will discus the science, technology and mission design for the LATOR experiment. The work described here was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. In this paper, we shall systematically study on the practical and useful research objects in 1PN level and in multiple reference systems by means of comparing with Newtonian counterpart. We divide the research objects into two kinds: with limited degrees of freedom and unlimited degrees of freedom. For the system with limited degrees of freedom we introduce DSX (Damour-Soffel-Xu) formalism to describe the system in terms of the mass- and spin- multiple moments (compact support BD moments) defined in the local coordinates system and the tidal moments. The traslational equations and the rotational equations of motion expressed by multiple moments and tidal moments are shown with bilinear form. The application of DSX in the satellite motion and binary systems are mentioned. We also discuss the special case in limited degrees of freedom, i.e. quasi-rigid body which is the Newtonian counterpart (rigid body ( 6 degrees of freedom)). For the systems with unlimited degrees of freedom, we consider the relativistic theory of elastic body (solid state) and the relativistic hydrodynamic equations and thermodynamic equations for nonperfect fluid in multiple coordinate systems. We also discuss the special case in nonperfect fluid: quasi-incompressible fluid (PN liquid). In the whole paper we introduce our work in brief to show what we have done and have to be done to cause our colleague to pay the attention.
 * SATURDAY 11:05-12:20 **
 * General relativity and relativistic gravity I **
 * 11:05-11:35 **
 * Some **** Research Objects in General Relativity - multiple moments, quasi-rigid body, elastic body, fluid, quasi-incompressible fluid and others **
 * Chongming Xu, Purple Mountain Observatory; Nanjing Normal University **

Deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, together with astrometry missions like GAIA and LATOR will be able to test relativistic gravity to an unprecedented level of accuracy. More precisely, these missions will enable us to test relativistic gravity to 10-7-10-9, and will require 2nd post-Newtonian approximation of relevant theories of gravity. The first post-Newtonian approximation if valid to 10-6 and the second post-Newtonian is valid to 10-12. The scalar-tensor theory is widely discussed and used in tests of relativistic gravity, especially after the interests in inflation and dark energy in cosmology. Here we present the full second post-Newtonian approximation of the scalar-tensor theory. We derive the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the 2nd post-Newtonian approximation in scalar-tensor theory; all terms inclusive of O(c^{-4}) are retained consistently in the equation of motion. The various conserved quantities to O(c^{-4}) are isolated with the aid of the energy-momentum complex in scalar-tensor theory. ** Supermassive central black hole masses in blazars ** We determined the central black hole masses (//M//) for 25 //γ//-ray-loud blazers using their available variability timescales. We found that the black hole masses range between 107 //M////⊙ // and 109 //M////⊙ //. For the black hole mass there is no clear difference between BLs and FSRQs, which suggests that the central black hole masses do not play an important role in the evolutionary sequence of blazars or there is no evolution between BLs and FSRQs. We present a coherent data analysis strategy using a network of gravitational wave (GW) detectors. Our approach is applicable for an arbitary number of detectors and can be used to construct optimal detection statistics, null steam, and stable solutions to GW waveforms. I also discuss the angular resolution of the network. Both the quintessential inflationary models (QIM) and some string cosmology scenarios predict high energy density regions of relic gravitons in the microwave band (108-1010Hz). There exist corresponding root mean square values of metric perturbations of the relic gravitational waves (GWs) in the region of approximately //h//~10-30-10-32. A electromagnetic detecting system for these GWs is described in which we measure the perturbative photon flux (PPF) or signal generated by such high-frequency relic GWs (HFRGWs) via a coupling system of fractal membranes and a Gaussian beam (GB) passing through a static magnetic field. It is found that under the synchro-resonance condition, the HFRGWs may produce the PPFs of ~102s-1 to 103s-1 in a surface of 10-2m2 area at the waist of the GB. The PPF reflected or transmitted by the fractal membranes exhibits a very small decay rate compared with the much stronger background photon flux. We also discuss the system’s noise issues, selection capability and directional sensitivity for the resonant components from the stochastic relic GW background. This scheme might provide a new means of detecting HFRGWs. The accelerating expansion of the universe at the present stage is a pro-cess that has great implications on the relic gravitational waves (RGW) and CMB. We present calculations, both analytically exact and numer-ical, for the spectrum of RGW in the scenario of accelerating Universe = 1. The results from both calculations are consistent with each other. The analytic spectrum formula contains explicitly the parameters of acceleration, inflation, reheating, and the (tensor/scalar) ratio, so that it can be employed for a variety of cosmological models. The spectrum is found to depend on the behavior of the present accelerating expansion, and there are new features associated with the acceleration in the result-ing spectrum. In the low frequency range the peak of spectrum is now located at a frequency //, //where is the Hubble frequency, and there appears a new segment of spectrum between  and. In all other intervals of frequencies, the spectral amplitude acquires an extra factor  , due to the current acceleration, otherwise the shape of spectrum is similar to that in the decelerating models. The recent WMAP result of CMB anisotropies is used to normalize the amplitude for RGW. The amplitude of RGW for the model = 0//.//65 is about 50% greater than that of the model  = 0//.//7, an effect accessible to the designed sensitivities of LIGO and LISA. The spectrum sensitively depends on the in°ationary models with, and a larger  yields a flatter spectrum, producing more power. The current LIGO re-sults rule out the in°ationary models of. The LIGO with its design sensitivity and the LISA will also be able to test the model of = -1.9. We also examine the constraints on the spectral energy den-sity of RGW. Both the LIGO bound and the nucleosynthesis bound point out that the model = //-//1//.//8 is ruled out, but the model  = //-//2//.//0 is still alive. The exact analytic results also confirm the numerical spectrum. We then develop Polnarev's analytic method to calculate of the polar-ization power spectrum of CMB generated by cosmic RGW. The ana-lytic polarization spectra have been obtained with following several im-provements over the previous results. 1. The approximate analytic re-sult of CMB polarization is quite close to the numerical one evaluated from the cmbfast code, especially, for the first three peaks of the spec-trum that are observable. By using the analytic exact solution of RGW from the sudden-change approximation, we have demonstrated the de-pendence of polarization on the dark energy and the baryon. 2. Our analytic half-gaussian approximation of the visibility function fits ana-lytically better than the usual Gaussian model, and its time integration yields a arameter-dependent damping factor. This improves the spec-trum //~// 30% around the second and third peaks. 3. The second order of tight coupling limit educes the amplitude of spectra by 58%, comparing with the first order. 4. The influence of the power spectrum index of RGW is such that a larger value of the power index //nT// produces higher polarization spectra. Shan Bai, Zhoujian Cao, Xuefei Gong, **Yun-Kau Lau,** Yuguang Shi, and Xiaoning Wu, **Morningside Mathematics Center, CAS, and Peking University ** Motivated by the prospect of describing angular momentum carried away by gravitational waves in the characteristic formulation of numerical relativity, by means of asymptotic expansion of the eikonal equation. a Bondi-Sachs (BS) coordinates spanned by null hypersurfaces near null infinity are constructed for the Kerr metric. The asymptotic structure near null infinity of the Kerr metric is studied and the Newman-Penrose constants of the Kerr metric is also calculated to be zero. ** Laser Ranging Technique for ASTROD I Mission ** ** Xiong Yaoheng, ** Zheng Xiangming, Song Fenggan**, Yunnan** **Observatory** ** CAS ** One of suggested ground stations for ASTROD1 mission is Yunnan Observatory 1.2mTelescope laser ranging system. In this paper we present a talk about some necessary technique for the ASTROD I mission laser ranging, include pulse and CW laser ranging. The main parts of this talk are: Introduction Key Requirements of Ground LR Station for ASTROD I Telescope Pointing and Pointing Ahead Day-Time Laser Ranging Technique Optical Layout of LR for the ASTROD I Mission Unlike the LISA case, the entry of direct sunlight into the optical telescope cannot be prevented for the space probes ASTROD and ASTROD I. Great care must be taken to filter the incoming light in such a way that the desired very faint laser light (100 fW) from the other spacecraft enters unobstructed, that on the other hand the sunlight (close to 100 W) is kept away from the sensitive optics of the optical bench. A number of measures are required for such a filtering by 15 powers of ten. First, there is the possibility to shut off light coming from directions sufficiently far from the direct line of sight between the spacecraft. This is an appropriate adaptation of the coronagraph scheme. Then, there is the possibility of using filters of dielectric layers for a narrow optical bandpass, and such narrowband filters, of bandwidths down to 10 (or even 1) nm have been produced. Their filtering effect is, however, at best only of the order 10^(-3). A much narrower bandwidth can be gained with Faraday Anomalous Dispersion Filters (FADOFs), utilizing the anomalous dispersion of atomic lines. At proper temperature, proper magnetic field, and proper size, a cell filled with the active gas can rotate the polarisation at the proper wavelength by 90°, but not at other wavelengths. The bandwidth can be as low as 3 GHz. However, the FADOF effect cannot be had at just any wavelength: so far no medium for the workhorse line of 1.064 µm is known. For the frequency-doubled line of 532 nm, a certain excited state in Rb vapour exists, and FADOFs for that wavelength have been produced. One great difficulty is the large relative velocity of the ASTROD (I) spacecraft, of up to 20 km/s, leading to a Doppler shift of up to 20 GHz, more than the FADOF bandwidth. With proper tuning (temperature, magnetic field), the transmission wavelength can be shifted slightly, but to what extent is not yet determined. Much further study must go into the scheme of FADOF application to make it a viable filter scheme for the ASTROD missions. ** Further computation of the test mass charging and disturbances in ASTROD I ** ** G. Bao **** a, b ****, L. Liu **** a ****// , //**** b **** , D. Shaul **** c **** , H. Araújo **** c **** , W.-T. Ni **** a ** ** and T. Sumner **** c ** ** a **** Purple **** Mountain **** Observatory, CAS ** ** b **** Graduate **** University of the Chinese Academy of Science, Beijing ** ** c **** Department of Physics, Imperial College London, London, SW7 2BZ, UK ** The test mass of ASTROD I (the Astrodynamical Space Test of Relativity using Optical Devices I) will become charged due to exposure of the spacecraft to energetic particles in the space environment. Test mass charging will result in Coulomb and Lorentz forces and hence spurious test mass motions. To estimate the size of these effects, it is important to accurately model the test mass charging process. Earlier work, using GEANT 4 and a simplified ASTROD I geometry, predicted that the acceleration noise associated with test mass charging would be well below the ASTROD I residual acceleration noise target. Here we present results of a more accurate simulation, implementing a more realistic geometry model. We have simulated the charging processes due to cosmic-ray protons and alpha particles using this geometry model, at solar minimum and maximum. The magnitude of acceleration noise and stiffness associated with charging are estimated. The Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) mainly aims at testing relativistic gravity and measuring the solar-system parameters with high precision, by carrying out laser ranging between a spacecraft in a solar orbit and ground stations. It is the first step of ASTROD with 3 spacecraft. In order to design the Drag-Free and Attitude Control system (DFACS) for the spacecraft a numerical simulator of spacecraft and test mass dynamics as well as models of main forces and torques are established using Matlab/Simulink. The aims of the DFACS are to reduce the acceleration disturbance on the test mass to a level of 10−13m · s−2 · Hz−1/2 at a frequency of 0.1 mHz in one axis and keep the telescope pointing to the ground stations on the earth. The dynamics of spacecraft and test mass is a coupled multiple degree of freedom non-linear system. So the first step of the DFACS design is to reduce the order of the system with assumptions without loss of generality. Then the system is linearized at nominal state. With the linear state space model of the system a Linear Quadratic Gaussian Regulator (LQG) is derived. LQR and the feed-forward of a constant disturbance constitute the controller. This paper will present the numerical simulator and the first drag-free controller design for ASTROD I. It will show the development of the simulator, the derivation of the controller as well as first simulation results. //** 1 **** Bureau International des Poids et Mesures, Pavillon de Breteuil, 92312 Sevres, FRANCE **// //** 2 **** Key Laboratory of Optical and Magnetic Resonance Spectroscopy, East China Normal University, Shanghai 200062, CHINA **// //** 3 **** National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA. **// //** 4 **** OFS Laboratories, 700 Mountain Avenue, Murray Hill, New Jersey 07974, USA ** // Optically referenced femtosecond laser frequency comb can generate optical field precisely in both time and frequency domain. We will present results illustrating the achievable levels of control of the optical pulse train emitted by a mode-locked laser. By rigorously comparing four Kerr-lens mode-locked Ti:sapphire lasers from three laboratories, we find that the relative frequency reproducibility of the optical comb mode frequency and the associated ~1 GHz optical pulse train can be 1 × 10-19 and 2 × 10-18, respectively, with confidence levels of 95%. This talk will present a modern version of the classic Michelson-Morley experiment testing the isotropy of light propagation and thus the foundations of Special elativity. From a modern perspective, this measurement is one out of a more general class of experiments investigating the validity of Lorentz-Invariance in the light of new theoretical approaches – such as string theory or loop quantum gravity – suggesting small violations. The experiment itself is performed by monitoring the resonance frequency of an optical resonator continuously rotating on a precision turntable, making it possible to achieve a sensitivity at theΔcθ/c ≈ 10-16 level for a direction dependent variation of the speed of light. We also present initial results of our latest experimental setup employing new resonators in conjunction with active vibration isolation, and discuss the potential for improvements in sensitivity by up to three orders of magnitude. ** 09:30-09:55 ** We are currently setting up an optical frequency comb to be used for a multitude of experiments aiming at fundamental physics test. These include a comparison of the frequency of cryogenic and room temperature ultra-stable optical resonators, the realization of an optical gear for an ytterbium atomic clock, and a precision measurement of the HD+ molecular spectra. The experimental techniques developed for the latter will provide the means to test precision three-body QED-calculations of the HD+ molecular structure, to realize molecular optical clocks of different type (vibronic and rotational clocks), and to implement molecular quantum interferometers. The results will be important, for example, for space based tests of the equivalence principle. We give a short overview of our activities and then focus at the application of the frequency comb to molecular spectroscopy. Optical clocks are currently gaining a lot of attention for future space missions aiming at a test of fundamental physics, or simply as a precision tool for more applied tasks as (space craft) navigation or geodesics. An overview about the history of atomic clocks (in space) is given, advanced optical clock concepts are described, and their expected performance is estimated. We report on our current activities to implement an Ytterbium atomic clock, which might be used as ground based time reference for future ESA missions. Finally, international activities towards the demonstration of optical clocks in space and related technologies are described. A stable optical frequency comb was developed based an ultrabroaden femtosecond Ti:sapphire laser at a repetition rate of 173MHz. With the optimized dispersion control, we directly generated the laser pulse of shorter than 7fs, the laser resonator consists in only three chirped mirrors and one 10% output coupler, as our best knowledge, this is the simplest laser configuration for sub-10fs laser pulse. By difference frequency the ultrabroaden spectrum with a PPLN crystal, we obtained a beat frequency with signal noise ratio of about 30dB. Locking the frequency and repetition rate to a Cs clock, we realized a stable optical comb without the photonic crystal fiber. In addition to the well-known M//ø//ller frame (or Rindler frame), we may construct another frame to describe the uniformly accelerated system. In the new frame, all `static' (//i.e.// spatial coordinates keep unchanged) observers have the same proper acceleration but each has his own horizon. In contrast, the proper acceleration of a static observer in M//ø//lller frame (or Rindler frame) depends on his position, but the horizon is (static-)observer-independent. We argue that the new uniformly accelerated frame is more suitable than M//ø//lller frame to describe the system in an accelerated rocket. It is possible to distinguish the M//ø//lller frame and the new uniformly accelerated frame by high-precision experiments (such as arrival-time- and/or redshift-measurements) in an accelerated rocket. When the non-relativistic limit is taken, the second law of mechanics and Schödinger equation in the new uniformly accelerated frame are all different from those in M//ø//lller frame. The thermal properties of the new frame and of M//ø//lller frame are also different. The effects on the equivalence principle is discussed. We argue that even the spacetime curvature is ignored, it is still possible in some sense to distinguish gravity from acceleration. The boost of the accuracy of astrometric observations makes it indispensable to use general theory of relativity to model and process the observational data. At the level of accuracy of 1 microarcsecond it is impossible to interpret the data in a purely Newtonian way. Moreover, such an accuracy requires a high level of consistency between various parts of data processing chain. In this talk the relativistic modelling for microarcsecond astrometry will be reviewed. All the effects which enter the relativistic model can be in turn used to test relativity. An overview of various possible relativistic tests to be realized with future microarcsecond astrometric data will be also given.
 * 11:35-11:55 **
 * Second post-Newtonian approximation of scalar-tensor theory of gravity **
 * Y. Xie ** (1), P. Dong (2), and W.-T. Ni (2,)
 * ( **** 1 **** ) Nanjing University, ( **** 2 **** ) Purple Mountain Observatory, CAS **
 * 11:55-12:20 **
 * J. H. Fan J.Li, Y. X. Wang, J. H. Yang, J.S. Zhang **
 * SATURDAY 14:00-16:00 **
 * Gravitational Waves II **
 * 14:00-14:30 **
 * Detecting gravitational waves using detector arrays **
 * Linqing Wen, **** Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Golm **
 * 14:30-15:00 **
 * Selection and Detection of High-Frequency Relic Gravitational Waves **
 * Fangyu Li1, Robert M. L. Baker, Jr.2 and Zhenya Chen1 **
 * 1. **** Department of Physics, Chongqing University, Chongqing 400044, P. R. China **
 * 2 **** . **** GRAWAVE® LLC, 8123 Tuscany Avenue, Playa del Rey, California 90293, USA **
 * 15:00-15:30 **
 * Relic Gravitational Waves and CMB Polarization in Accelerating Universe **
 * Y. Zhang, ** W. Zhao, X.Z. Er, and T.Y. Xia
 * Astrophysics **** Center University of Science and Technology of China **
 * Hefei ****, Anhui, China **
 * 15:30-16:00 **
 * Angular Momentum Carried by Gravitational Radiation **
 * SATURDAY 16:20-18:20 **
 * Mission **** Studies III **
 * 16:20-16:50 **
 * 16:50-17:15 **
 * FADOF and study in its application to ASTROD and ASTROD I missions **
 * Albrecht Rüdiger, **** Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut), Hannover **
 * 17:15-17:35 **
 * 17:35-17:55 **
 * Dynamics Modeling and First Design of Drag-Free Controller for ASTROD **** Hongyin Li ** (1, 2)**, S. Theil,** (1) **L. Pettazzi** (1) **M. S. Guilherme** (1) **and W.-T. Ni** (2) **(1) ZARM, University of Bremen (2) Purple Mountain Observatory, CAS**
 * SUNDAY ** **8:30-10:30**
 * Advanced Technology II **
 * 08:30-09:00 **
 * Precision Control of Optical Pulse Trains **
 * Long-Sheng Ma2,1, Zhiyi Bi2, Albrecht Bartels3, Kyoungsik Kim3 **
 * Lennart Robertsson1, Massimo Zucco1, Robert S. Windeler4 **
 * Guido Wilpers3, Chris Oates3, Leo Hollberg3, Scott A. Diddams3 **
 * 09:00-09:30 **
 * A modern Michelson-Morley experiment using ultra-stable optical resonators **
 * Achim Peters, Sven Herrmann, Alexander Senger, Katharina Moehle; **
 * Humboldt-University Berlin **
 * Optical Frequency Combs for Precision Tests of Fundamental Physics – Activities at the University of Düsseldorf **
 * A. Wicht, I. Ernsting, N. Strauss, B. Roth, J. Koelemeij, S. Schiller **
 * Institute for Experimental Physics **
 * Heinrich-Heine University of Düsseldorf **
 * Universitätsstr. 1, D-40225 Düsseldorf **
 * 09:55-10:15 **
 * Optical Clocks in Space **
 * Stephan Schiller and Andreas Wicht, **** Heinrich-Heine-Universität Düsseldorf **
 * S. Schiller, A. Görlitz, J. Koelemeij, A. Nevsky, A. Wicht **
 * Institute for Experimental Physics **
 * Heinrich-Heine University of Düsseldorf **
 * Universitätsstr. 1, D-40225 Düsseldorf **
 * 10:15-10:40 **
 * Stable 200MHz frequency comb by difference frequency the ultrabroaden 7fs Ti:sapphire laser **
 * Zhiyi Wei, ** Yanying Zhao, Hainian Han, Wei Zhang, Jiangfeng Zhu, Peng Wang
 * Joint Laboratory of Advanced Technology in Measurements, **** Beijing National Laboratory for Condensed Matter Physics /Institute of Physics, CAS **
 * SUNDAY ** **11:00-12:30**
 * General Relativity and Relativistic Gravity II **
 * 11:00-11:30 **
 * Uniformly Accelerated Reference Frames ** ** and Equivalence Principle **
 * Chao-Guang Huang ,** ** Institute **** of High **** Energy Physics, CAS **
 * 11:30-12:00 **
 * Relativity and astrometry in the microarcsecond level **
 * S. A. Klioner, Lohrmann Observatory, Dresden Technical University **

In the previous paper, we have derived the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the 2nd post-Newtonian approximation in scalar-tensor theory. In this paper, we use these results (i) to derive the deflection of light and radio propagation and compare it with previous work, and (ii) to derive the perihelion shift for objects (planets, asteroids, and spacecraft) in a bound solar orbit. These results will be useful for deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, and astrometry missions like GAIA and LATOR, which aim at testing relativistic gravity to 10−7-10−9, and require 2nd post-Newtonian approximation for this accuracy. The applications to these missions are considered. Analysis of Lunar Laser Ranging (LLR) data provides science results: gravitational physics and ephemeris information from the orbit, lunar science from rotation and solid-body tides, and Earth science. __Science from the orbit__: Sensitive tests of gravitational physics include the equivalence principle, limits on the time variation of the gravitational constant G, and geodetic precession. The equivalence principle test is used for an accurate determination of the parameterized post-Newtonian parameter beta. Lunar ephemerides are a product of the LLR analysis used by current and future spacecraft missions. The analysis is sensitive to astronomical parameters such as orbit, masses, and obliquity. The dissipation-caused acceleration in orbital longitude is -25.7 "/cent2, dominated by tides on Earth with a 1% lunar contribution. The soon to be operational Apache Point LLR observatory would provide for almost 50 times increase in range accuracy, reaching a mm level. With these advances LLR provides for a very sensitive test of general relativity. __Lunar science__: lunar rotational variation has sensitivity to interior structure, physical properties, and energy dissipation. The second-degree lunar Love numbers are detected; k2 has an accuracy of 11%. Lunar tidal dissipation is strong and its Q has a weak dependence on tidal frequency. A fluid core of about 20% the moon's radius is indicated by the dissipation data. Evidence for the oblateness of the lunar fluid-core/solid-mantle boundary is getting stronger. This would be independent evidence for a fluid lunar core. __Earth science__: Station positions and motion, Earth rotation variations, and precession are determined from analyses. APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation) is a new effort in lunar laser ranging that uses the Apollo-landed retroreflector arrays to perform tests of gravitational physics. APOLLO achieved its first range return in October, 2005, and began its science campaign the following spring. The strong signal (>2500 photons in a ten minute period) translates to one-millimeter random range uncertainty, constituting at least an order-of-magnitude gain over previous stations. One-millimeter range precision will translate into order-of-magnitude gains in our ability to test the weak and strong equivalence principles, the time rate of change of Newton's gravitational constant, the phenomenon of gravitomagnetism, the inverse-square law, and the possible presence of extra dimensions.
 * 12:00-12:20 **
 * Light deflection and perihelion shift in the second post-Newtonian approximation of scalar-tensor theory of gravity **
 * P. Dong** (1), W.-T. Ni (1), and Y. Xie (2)
 * (1) Purple Mountain Observatory, CAS (2) Nanjing University, Nanjing**
 * SUNDAY ** **13:30-15:40**
 * Astrodynamics and Solar-System Measurement II **
 * 14:00-14:30 **
 * Lunar Laser Ranging and Tests of General Relativity **
 * Slava G. Turyshev **
 * Jet Propulsion Laboratory, California Institute of Technology, **** Pasadena ****, CA 91109 **

This talk will emphasize the open frontier that exists in solar system tests of general relativity, briefly discussing technologies that can extend our knowledge of gravity by orders-of-magnitude. The work described here was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. It is well-known that gravitational lensing is a powerful tool to investigate matter distributions including DM. Typical angular distances between images and typical time scales depend on gravitational lens masses. For microlensing case angular distances between images or typical astrometric shifts due to microlensing are about 10-5-10-6. Such an angular resolution will be reached with the space space—ground interferometer Radioastron. The basic targets for microlensing searches should be bright point-like radio sources at cosmological distances. In this case, an analysis of their variability and a solid determination of microlensing could lead to an estimation of their cosmological mass density, moreover, in this case one could not exclude a possibility that non-baryonic dark matter also form microlenses if the corresponding optical depth will be high enough. To search for microlensing the most perspective objects are gravitational lensed systems as usually, like CLASS gravitational lens B1600+434, for instance. However, for direct resolving these images and direct detection of apparent motion of the knots, a Radioastron sensitivity have to be improved, since an estimated flux density is too low and to observe the phenomena one should improve sensitivity in 10 times at 6~cm wavelength, for instance, otherwise, it is necessary to increase an integration time (assuming that a radio source has a typical core – jet structure and microlensing phenomenon is caused superluminal apparent motion of knots). In the case of a confirmation (or a disproval) of claims about microlensing in gravitational lens systems one can speculate about a microlens contribution into the gravitational lens mass. Astrometric microlensing due Galactic MACHOs actions is not very important because of low optical depths and long typical time scales. Therefore, a launch of space interferometer Radioastron will give new excellent facilities to investigate microlensing in radio band, since in this case there is a possibility not only to resolve microimages but also observe astrometric microlensing. We discuss also a possibility to evaluate paramameters of supermassive black holes to analyzing shapes and sizes of shadows around them. Based on many co-orbital phenomena in astronomy and astronautics, a dynamical model — co-orbit restricted problem is pointed out. To study the orbit of LISA looks as an example. It is a 2+3 co-orbit restricted problem which can be divided into two parts. First, to discuss the motion of C, the center of mass of 3 spacecraft under the gravitation of the sun and the earth (plus moon) looks as a co-orbit restricted 3-body problem (planar and circular). The analytical result of position variation of C is given. Second, the configuration of 3 spacecraft that constitute an equilateral triangle at origin of time is discussed; it is found that the armlengths of triangle vary sensitively with the inclination angle between the plane defined by 3 spacecraft to the ecliptic plane. The optimal inclination angle is given. Present day gravitational physics experiences a huge success in obtaining better and better experimental results. These results cover the range from cosmology to the search for non-Newtonian forces in the sub-mm range. In some cases the observations do not fit with the present knowledge. Very popular are the issues of dark matter and dark energy which are needed for the explanation of the galactic rotation curves and gravitational lensing, and of the accelerated expansion of our universe. Though these are phenomena on the cosmological scale they may influence the physics within the Solar system. Further observations are the Pioneer anomaly, an anomalous constant acceleration of the Pioneer spacecrafts toward the Sun which until now found no explanation. Another unexplained observation is the flyby anomaly, a velocity increase of satellites during an Earth flyby, which has been observed at many instances. Yet another phenomenon is the secular increase of the astronomical unit by approximately 7 meters per century which has been established last year by taking into account more than 100 years of Solar system data. Finally there is a quadrupole and octopole anomaly of the cosmic microwave background: the quadrupole and octopole part of the cosmic microwave background seems to be correlated with the orientation of the Solar system. We report on these phenomena, try to establish links and to propose missions to explore these unexplained phenomena. ** POSTERS ** ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) is a proposed three spacecraft, drag-free, deep-space, laser ranging mission. Two spacecraft would be placed in distinct solar orbits, between 0.77 AU and 1.32 AU from the Sun, and the third spacecraft would be placed at either L1 or L2. From the precise determination of the spacecraft orbits, the solar quadrupole moment parameter could be determined to 0.3-1 × 10 − 10 ; from the difference in clockwise and counterclockwise interferometry measurements, the solar Lense-Thirring effect and hence, solar angular momentum could be measured to 1 × 10 − 5. These measurements would also place strict constraints on models of solar rotation and the interior structure of the Sun. Further, the high precision of ASTROD interferometry, combined with the eccentric spacecraft orbits would result in higher sensitivity to solar g-modes than any other mission, current or proposed. ASTROD I is a first step towards the development of ASTROD. In ASTROD I, laser light would be shone between a single drag-free spacecraft, placed in a solar orbit, between 0.5-1.04 AU from the Sun, and Earth laser stations. ASTROD I will allow an improvement in the accuracy of the determination of the solar quadrupole moment parameter to 3 × 10 − 9. In this paper we discuss the possibilities for solar, cosmic ray and space weather studies using ASTROD and ASTROD I, using both the science instruments and monitors included in the payload. Although these studies are similar to those that could be performed using LISA, the diverse orbits of these missions could provide a unique opportunity for such observations. In addition, as for LISA, the drag-free error signals from both ASTROD and ASTROD I can potentially provide information on the momentum flux on the spacecraft due to environmental disturbances. For example, the spectral density of the momentum flux of solar electromagnetic radiation (sunlight) and the solar-wind could be measured. The potential for measuring the momentum flux from other sources, such as SEP’s and micro-meteorites, is also discussed.
 * 14:30-15:00 **
 * Astrometry and astrophysics with the space telescope RADIOASTRON **
 * Alexander F. Zakharov, Institute of Theoretical and Experimental Physics,Moscow, Russia**
 * 15:00-15:30 **
 * A Dynamical Model—Co-orbit Restricted Problem and its Application to Astronomy and Astronautics **
 * Zhaohua Yi 1,2, Guangyu Li 1, **
 * Gerhard Heinzel 3, Oliver Jennrich 4 **
 * 1. Purple Mountain Observatory, CAS **
 * 2. Nanjing University **
 * 3. Max Planck Institute for Gravitational Physics **
 * 4. European Space Research and Technology Center **
 * 15:30-16:00 **
 * Is the physics within the Solar system really understood? **
 * C. Laemmerzahl, H. Dittus,** ** ZARM, Bremen University **
 * Solar, Cosmic Ray and Environmental physics (SCoRE) for/with ASTROD and ASTROD I **
 * Wei-Tou Ni1 and Diana Shaul2, 1. Purple Mountain Observatory, CAS, 2. Imperial College **

ASTROD (ASTRODynamical Space Test of Relativity using Optical Devices) mission concept is to have two spacecrafts in separate solar orbit carrying a payload of a proof mass, two telescopes, two 1-2 W lasers, a clock and a drag-free system, together with a similar L1/L2 spacecraft. The three spacecraft range coherently with one another using lasers to map the solar-system gravity, to test relativistic gravity and to detect gravitational waves. The distances among spacecraft depend critically on solar-system gravity, underlying gravitational theory and incoming gravitational waves, hence a precision determination of the distances as functions of time will determine all these causes. With a simple noise model, we then present our orbit simulation for 2015 orbits using 31 parameters of relativistic parameters, celestial-body masses, solar quadrupole parameters and spacecrafts initial state. From the simulation, we estimate the uncertainties of the determination of the relativistic parameters γ and β to be about 10-9, and J2 of sun to be 4×10-11. ASTROD I is a first step of ASTROD, to have one spacecraft on solar orbit ranging between Earth station. We have designed the orbits for 2010, 2012, 2013 and 2015 launches, and done the simulation for each orbit, then got the uncertainties of γ and β to be about 10-7, and the uncertainties of other parameters can also be improved considerably.
 * Orbit simulation for ASTROD and ASTROD I **
 * Y. Xia **, W.-T. Ni and G. Li , **Purple** **Mountain** **Observatory, CAS**

T2L2 Test Bed is aimed to measure the performances and calibration of T2L2 space instruments. It includes 3 types of measures: Performance, Calibration and AIV(T2L2 integrated on Jason 2). The Whole test bed consists of four main elements: the optical bench that produces laser pulses and bring them onto the detectors, the energy bench that monitors the output of the latter, the chronometry bench that times departure pulse from the laser, the EGSE that supports the T2L2 MV. The control and data retrieval of all these components is assured by a control Rack. The space-based gravitational wave detector LISA (Laser Interferometer Space Antenna) utilizes a high performance position sensor in order to measure the translation and tilt of the free flying test mass with respect to the optical bench. Depending on the LISA optical bench design, this position sensor must have up to pm/sqrt(Hz) sensitivity for the translation measurement and up to nrad/sqrt(Hz) sensitivity for the tilt measurement – requirements which can only be met by an optical readout.
 * Calibration and performance tests on T2L2 (Time Telemetry by Laser Light) **
 * Étienne Samain and Cheng Zhao, Observatoire de la Cote D’Azur **
 * An all-optical readout for the inertial sensor on the space based gravity-wave detector LISA **
 * Achim Peters** **, Humboldt-University Berlin **

EADS Astrium GmbH (Friedrichshafen/Germany) – in collaboration with the Humboldt-University Berlin/Germany and the University of Applied Sciences Konstanz/Germany – develops a heterodyne interferometer based on a design by Wu et al. (National Tsing Hua University, Taiwan), combined with differential wavefront sensing for the tilt measurement. The interferometer design exhibits maximum symmetry where measurement and reference arm have the same frequency and polarization. It is therefore, in principle, free of frequency and polarization mixing. The interferometer can be set up free of polarizing optical components preventing possible problems with thermal dependencies not suitable for space environment.

As a first demonstrator, we developed a mechanically highly stable and compact setup which is located in a temperature stabilized vacuum chamber in order to minimize environmental path length disturbances. We present first results of the translation and tilt measurements of our interferometer and discuss their limitations. A planned future setup will utilize hydroxide-catalysis bonding technology to realize a quasi-monolithic glass material setup leading to a very compact, modular and high sensitivity interferometer suitable for LISA, but also with potential applications beyond.

Weightlessness promisses to substantially extend the science of quantum gases towards nowadays inaccessible regimes of low temperatures, macroscopic dimensions of coherent matter-waves and enhanced duration of unperturbed evolution. Targeting the long-term goal of studying cold quantum gases on a space platform, we currently focus on the implementation of an 87Rb Bose-Einstein-condensate (BEC) experiment under microgravity condition at the ZARM drop tower in Bremen (Germany). Special challenges in the construction of the experimental setup are posed by a low volume of the drop capsule (<1m3) as well as critical vibrations during capsule release and peak decelerations of up to 50g during recapture at the bottom of the tower. All mechanical and electronic components have thus been designed with stringent demands on miniaturisation, mechanical stability and reliability. Additionally the system provides extensive remote control capabilities as it is not manually accessible in the tower 2 hours before and during the drop.
 * Atomic quantum gases in microgravity - a demonstration experiment at the Bremen droptower **
 * Achim Peters ****, Humboldt-University Berlin **

On his poster we present the robust system in detail and show results from first tests at the drop tower in Bremen. The project is funded by the German Space Agency (DLR) within grant DLR 50 WM 0346. A two-fluid generalized Chaplygin gas(GCG) model including two different cases is considered in this paper. Concretely, the evolution of GCG model with interaction is discussed and the statefinder diagnostic for the GCG models is performed, respectively. By analysis, we show that the effective state parameter of dark energy can cross the so-called phantom divide // ω //= -1, the behavior of GCG will be like ΛCDM in the future and therefore our Universe will not end up with Big Rip in the future. In addition, we find that the statefinder diagnostic can differentiate the GCG model with or without interaction. Also, trajectories of both the GCG model mixed with cold dark matter(CDM) and the pure GCG model in the parameter plane are illustrated to be significantly diffferent. We use the laser heterodyne beat-frequency  technique to test the basal principle of special relativity, the isotropy of two-way speed of light had been verified to the precision of 1×10 -18 【 1 】. But we can not measure the one-way velocity of light, because of before to  measure one-way velocity of light  we must calibrate the clocks in different locus , but the  calibration of clocks  must transfer signal with light known speed, thereby, it make up of the logic circle. Based on the international definition about the length and time units, I propose a measuring method for one-way velocity of light in vacuum:  by means of heterodyne interference and beat-frequency  a  wavelengthλi and  a  periodτi of  iodine-stabilized laser  compare respectively with a wavelengthλkr of krypton radiation  and  a periodτcs of cesium radiation to avoid the calibration of clocks in different locus, the  one-way velocity of light  λi /τi obtained from metricalλi /λkr andτi /τcs may reach the precision of 10    - 8. Further, withλi  and  τi as new length and time units,  the invariability principle of one-way velocity of light may be tested in the  precision of 10    -1 3  ～  10 -1 5. The gravitational red-shift and the relationship between velocity of light and gravitational potential may also be tested. According to the inductive gravitation formula deduced by H.Bondi from Einstein’s equation 【 2 】, the mass of un-isolated body is variable. Again from the mathematical relationshipδ( // m //// **v** // )/δ//t// ＝ // m // (δ **// v //** /δ//t// ) ＋ **// v //** (δ//m///δ//t// ), a new gravitational formula was obtained: // **f** // ＝ δ( // m //// **v** // )/δ//t// ＝ **// f //** P ＋ **//f//** C ＝ － G( // m M // / // r // 2 ) ( **// r //** / // r // ) <span style="font-family: 宋体; font-size: 12pt;">－ G( // m M // / // r // 2 ) (**//v//**/c) (1) because of Newtonian gravitation law is included in the general relativity, when not partial-difference for //m// the mass //m// is invariable, i.e., the mass may produce the gravitational field but the gravitational field should not lead to the variance in mass, the gravitational equation should change into linear from nonlinear, and Einstein’s equation should degenerate into Newtonian law **//f//** P <span style="font-family: 宋体; font-size: 12pt;">＝ // m // δ**//v//**/δ//t// <span style="font-family: 宋体; font-size: 12pt;">＝ <span style="font-family: 宋体; font-size: 12pt;">－ G // m M // **// r //** / // r // 3. According to the mass-energy relationship in special relativity we get δ//m// /δ//t// <span style="font-family: 宋体; font-size: 12pt;">＝ δ//E// / c2δ//t//, again from the conservation of four dimension momentum–energy vector **//P//**–//E// in special relativity we get δ//E// /δ//t// <span style="font-family: 宋体; font-size: 12pt;">＝ c δ∣**//P//** ∣/δ//t ,// so , **// f //** C embodies the tangled interaction between field and source , Eq.(1) is equivalent to Einstein’s equation and as a new version of Einstein’s equation, then, the multi-bodiesgravitational problems now can be strictly solved. With laser interference technique the velocity dependency of gravitation **//f//** C in Eq. (1) can directly be tested by the absolutely measure the gravitational acceleration in laboratory using long vacuum falling pipe method or using projection method in vacuum. In a 20 meter long falling pipe, owing to the difference of velocity of falling object the gravitational acceleration //g// within 0 <span style="font-family: 宋体; font-size: 12pt;">～ 0.5 second is different from that with 1.5 <span style="font-family: 宋体; font-size: 12pt;">～ 2.0 second in a magnitude of 5×10 <span style="font-family: 宋体; font-size: 12pt;">－ 8. The variation of //g// with height can be calibrated by relative gravimeter. In projection method in vacuum, the time of the object pass through two fixed points is Δ //t// up and Δ //t// down for the rising course and the falling course respectively. According to Newtonian gravitation law, there is Δ //t// up =Δ //t// down. According to Eq. (1), **//f//** C will increase the gravitational acceleration //g// up in the rising course and decrease the gravitational acceleration //g// down in the falling course, then, //g// up <span style="font-family: 宋体; font-size: 12pt;">＞ // g // down and Δ//t// down <span style="font-family: 宋体; font-size: 12pt;">＞ Δ//t// up. When the length of the vacuum pipe //L// is about 12m, the projecting velocity //v// P≈15ms <span style="font-family: 宋体; font-size: 12pt;">－ 1, Δ //t// down≈1.5s, Δ //t// down <span style="font-family: 宋体; font-size: 12pt;">－ Δ //t// up≈2.5×10 <span style="font-family: 宋体; font-size: 12pt;">－ 8 Δ //t// up. To test the Eq. (1) the measurement precision of the time need reach 1×10 <span style="font-family: 宋体; font-size: 12pt;">－ 8 s, that is easy to reach on the present technical conditions. 【 1 】 Chen Shaoguang et al, Acta Scientiarum Naturalium Universitatis Pekinensis **33** <span style="font-family: 宋体; font-size: 12pt;">（ 5 <span style="font-family: 宋体; font-size: 12pt;">） ,595-599 <span style="font-family: 宋体; font-size: 12pt;">（ 1997 <span style="font-family: 宋体; font-size: 12pt;">） 【 2 】 H. Bondi, Proc. R. Soc. London A 427,249 (1990)
 * The generalized Chaplygin gas model with interaction **
 * Ya-Bo Wu, ** Song Li, Jianbo Lu and Xiuyi Yang**, Liaoning Normal University**
 * Laser interference method to measure one-way velocity of light and to test new version of Einstein’s equation **
 * Shao-Guang Chen, Jiangxi Provincial Academy of Sciences **
 * // f //** C <span style="font-family: 宋体; font-size: 12pt;">＝ **// v //** δ//m// /δ//t// <span style="font-family: 宋体; font-size: 12pt;">＝ **// v //** δ//E// / c2δ//t// <span style="font-family: 宋体; font-size: 12pt;">＝ **// v //** δ∣**//P//** ∣/ cδ//t// <span style="font-family: 宋体; font-size: 12pt;">＝ **// v //** // f // P / c <span style="font-family: 宋体; font-size: 12pt;">＝－ G //m M **v**// /c//r// 2