Gravitational Perturbations on Local Experiments in a Satellite: The Dragging of Inertial Frame in the HYPER Project

We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate the rotation of the telescope due to the aberrations and the deflection of the light in the gravitational field of the Earth. We show that the deflection due to the quadrupolar momentum of the gravity is not negligible if one wants to observe the Lense-Thirring effect of the Earth. We consider some perturbation to the ideal device and we discuss the orders of magnitude of the phase shifts due to the residual tidal gravitational field in the satellite and we exhibit the terms which must be taken into account to calculate and interpret the full signal. Within the framework of a geometric model, we calculate the various periodic components of the signal which must be analyzed to detect the Lense-Thirring effect. We discuss the results which support a reasonable optimism. As a conclusion we put forward the necessity of a more complete, realistic and powerful model in order to obtain a final conclusion on the theoretical feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.     

空间引力波探测望远镜初步设计与分析

引力波的直接观测已开启引力波天文学的新篇章,爱因斯坦的百年预言终获证实。空间引力波探测器使得探测0.1 m Hz~1 Hz频段丰富的引力波源成为可能,与地面引力波探测器互为补充,才可实现更加宽广波段的引力波探测,揭开宇宙早期的更多秘密。空间激光干涉引力波探测采用外差干涉测量技术,测量间距百万公里的两自由悬浮测试质量间10 pm量级的变化量。望远镜是激光干涉测量系统的重要组成部分,1 pm的光程稳定性及苛刻的杂散光要求,不同于传统的几何成像望远镜。本文根据空间太极计划任务需求,对望远镜的功能及技术要求进行了分析,并完成了原理样机的初步方案设计,针对百万公里远场波前分布,分析了望远镜系统的敏感性,同时完成了在轨光机热集成仿真,为后面原理样机的研制奠定了技术基础。     

基于ZEMAX和Python软件的空间引力波望远镜光程差算法研究与实现

利用光学设计软件ZEMAX和Python软件联合实现空间引力波望远镜光程差(optical path difference, OPD)精密求解;通过动态数据交换(dynamic data exchange, DDE)实现ZEMAX软件和Python软件数据交换:首先,Python软件对有限元分析后望远镜镜面数据进行处理,并将分析结果通过DDE传输给ZEMAX进行光线追迹;其次,ZEMAX软件对追迹后的光线坐标再通过DDE传回Python软件;最后,Python软件通过全局坐标系,计算刚体平移带来的光程差和波前的变化。模拟1 mK温度变化下引力波望远镜的受力变形,通过ZEMAX软件和Python软件求解空间引力波望远镜光程差和波前变化,结果表明光程差精度为1e-13米量级,完全可以满足望远镜皮米级稳定性精度要求。本研究可为后续引力波望远镜光机结构方案设计中光程差分析提供技术参考。     

A new type of quantum interferometer for gravitational wave detection

We present an orientational quantum interferometer sensitive to gravitational waves that is based on orienting quantum objects like molecules, atoms, or nuclei in space. The detection principle is based on inducing non-sphericity to the corresponding wave functions by light-pulses. In the field of a gravitational wave these objects then possess spectra that depend on their orientation in space. In our measurement scheme we investigate the adiabatic influence of a monochromatic gravitational wave over a quarter gravitational wave period and compare the corresponding frequencies at instances with maximal and vanishing gravitational wave elongation. We therefore explore the effect over a quarter gravitational wave period (or wavelength) and the resulting frequency shift scales with the binding energy of the system times the amplitude of the gravitational wave. In particular, a gravitational wave with amplitude h = 10⁻²³ will induce a frequency shift of the order of 110 μHz for an atom interferometer based on a 91-fold charged uranium ion.     

Gravitational lensing and rotation curve

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein’s equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation. The gravitational potential U(r) which determines the lensing is directly give by the rotation curve U(r) = −v ²(r). This allows to test general relativity on the scale of galaxies where dark matter is relevant.     

Physical Explanation of Influence of Twin and Three Satellite Formation Mode on the Accuracy of Earth's Gravitational Field

The simulated results of the influence of twin and three satellite formation mode on the accuracy of GRACE Earth＇s gravitational field are interpreted from the viewpoint of physics. Because the effective satellite observation information of Earth＇s gravitational field recovery from three-satellite formation mode is only one time more than that of twin satellites, the improvement of the accuracy of Earth＇s gravitational field is far lower than one order of magnitude based on the simple two-times differences between three satellites. Three efficient ways of improving largely the accuracy of measurement of the Earth＇s gravitational field in the future international satellite gravity measurement programme, including proper decrease of satellite orbital altitude, the increase of accuracy from key payloads and an innovation of satellite observation mode are proposed.     

Shape and gravitational field of the ellipsoidal satellites

The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite’s geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.     

Sources and technology for an atomic gravitational wave interferometric sensor

We study the use of atom interferometers as detectors for gravitational waves in the mHz–Hz frequency band, which is complementary to planned optical interferometers, such as laser interferometer gravitational wave observatories (LIGOs) and the Laser Interferometer Space Antenna (LISA). We describe an optimized atomic gravitational wave interferometric sensor (AGIS), whose sensitivity is proportional to the baseline length to power of 5/2, as opposed to the linear scaling of a more conservative design. Technical challenges are briefly discussed, as is a table-top demonstrator AGIS that is presently under construction at Berkeley. We study a range of potential sources of gravitational waves visible to AGIS, including galactic and extra-galactic binaries. Based on the predicted shot noise limited performance, AGIS should be capable of detecting type Ia supernovae precursors within 500 pc, up to 200 years beforehand. An optimized detector may be capable of detecting waves from RX J0806.3+1527.     

MWIR imaging experiments with large F-number optics on LEO spacecraft

To determine the feasibility of spacecraft imaging in the mid-infrared region (3.0–5.0 μm) utilizing large F-number optics, we create a radiometric simulation of a low-Earth orbit (LEO) extended object, imaging background and noise, in order to predict the signal-to-noise ratio of such objects as viewed from a telescope during the daytime and terminator, etc. We find that the observation of Space Station and other extended targets utilizing large F-number optics for MWIR imaging is possible, given the right conditions. We have developed a large F-number infrared camera with cold stop matched, which is successfully applied to acquire LEO extended object images taken by a 1.23 m telescope. We get clear images of International Space Station, Tian-gong, etc. and our proposed the infrared imaging technology can be demonstrated to greatly improve the imaging ability of current ground-based Optoelectric (OE) telescope for the detection of space activities.     

Probing the gravitational redshift with an Earth-orbiting satellite

We present an approach to testing the gravitational redshift effect using the RadioAstron satellite. The experiment is based on a modification of the Gravity Probe A scheme of nonrelativistic Doppler compensation and benefits from the highly eccentric orbit and ultra-stable atomic hydrogen maser frequency standard of the RadioAstron satellite. Using the presented techniques we expect to reach an accuracy of the gravitational redshift test of order ${10}^{?5}$, a magnitude better than that of Gravity Probe A. Data processing is ongoing, our preliminary results agree with the validity of the Einstein Equivalence Principle.     

On Quantum Spacetime and the horizon problem

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with Doplicher et al. (1995)  [2], imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of  [2] since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations.We shall then describe the influence of this minimal length scale in a cosmological model, namely a simple universe filled with radiation, which is effectively described by a conformally coupled scalar field in a conformal KMS state. Solving the backreaction, a power law inflation scenario appears close to the initial singularity. Furthermore, the initial singularity becomes light like and thus the standard horizon problem is avoided in this simple model. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events, which point to a background dependence of the effective Planck length, through which a-causal effects may be transmitted.     

Brane effects on extra-dimensional scenarios: a tale of two gravitons

We analyze the propagation of a scalar field in multidimensional theories which include kinetic corrections in the brane, as a prototype for gravitational interactions in a four-dimensional brane located in a (nearly) flat extra-dimensional bulk. We regularize the theory by introducing an infrared cutoff given by the size of the extra dimensions, R, and a physical ultraviolet cutoff of the order of the fundamental Planck scale in the higher-dimensional theory, M. We show that, having implemented cutoffs, the radius of the extra dimensions cannot be arbitrarily large for M≳1 TeV. Moreover, for finite radii, the gravitational effects localized on the brane can substantially alter the phenomenology of collider and/or table-top gravitational experiments. This phenomenology is dictated by the presence of a massless graviton, with standard couplings to the matter fields, and a massive graviton which couples to matter in a much stronger way. While graviton KK modes lighter than the massive graviton couple to matter in a standard way, the couplings to matter of the heavier KK modes are strongly suppressed.     

A simulation of the thermal behaviour of the UK-NL millimeter wave telescope

To keep the thermally induced average telescope deformations within 15 m, a thermal design goal has been set which limits the temperature difference between all locations in the panels, backing structure and subframe to 1°C. Temperature gradients are caused by non-homogeneous exposure and by difference in response to a changing exposure for elements with different time constants.Thermal model simulations are used to identify the critical elements in the thermal design of telescope and enclosure. It is shown that an enclosure with a highly reflective paint with high infrared emissivity on the outside surface and an inside zinc coating with low infrared emissivity works as a highly effective radiation shield. A sprayed aluminium coating on the telescope makes free convection the dominant heat transfer mechanism. An enclosure with louvres works as a chimney forcing the inside air temperature to follow the ambient temperature to within a few degrees. The resulting temperature stratification in the area where the telescope reflector is located does not exceed 1.5°C. Structural analysis shows that temperature gradients in the subframe cause reflector surface deformations with a regular pattern, like gravitational deformations, which means that an error budget summation based on independent rms values is not necessarily valid. Knowing the structural analysis coefficients for differential thermal expansion one can decide which time constants in backing structure and subframe have to be matched to achieve optimal performance.     

A solution for galactic disks with Yukawian gravitational potential

We present a new solution for the rotation curves of galactic disks with gravitational potential of the Yukawa type. We follow the technique employed by Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new solution allows an easy comparison between the Newtonian solution and the Yukawian one. Therefore, constraints on the parameters of theories of gravitation can be imposed, which in the weak field limit reduce to Yukawian potentials. We then apply our formulae to the study of rotation curves for a zero-thickness exponential disk and compare it with the Newtonian case studied by Freeman in 1970. As an application of the mathematical tool developed here, we show that in any theory of gravity with a massive graviton (this means a gravitational potential of the Yukawa type), a strong limit can be imposed on the mass (m _g) of this particle. For example, in order to obtain a galactic disk with a scale length of b∼ 10 kpc, we should have a massive graviton of m _g ≪ 10⁻⁵⁹g. This result is much more restrictive than those inferred from solar system observations.     

Peculiar acceleration

It has been proposed recently to observe the change in cosmological redshift of distant galaxies or quasars with the next generation of large telescope and ultra-stable spectrographs (the so-called Sandage–Loeb test). Here we investigate the possibility of observing the change in peculiar velocity in nearby clusters and galaxies. This “peculiar acceleration” could help reconstructing the gravitational potential without assuming virialization. We show that the expected effect is of the same order of magnitude of the cosmological velocity shift. Finally, we discuss how to convert the theoretical predictions into quantities directly related to observations.     

地平式望远镜跟踪机架结构设计与分析

针对某700 mm口径地平式望远镜系统,提出了一种U型跟踪架的结构设计方案。跟踪架结构中方位轴系采用双排密珠球轴承,轴承设计为双排轴向止推钢珠及双排径向钢珠结构,滚珠的密集及均化作用可保证轴系具有高回转精度。俯仰轴系设计采用一端固定、一端游动的结构方式,以补偿机械误差及热变形对回转精度的影响。对望远镜跟踪架进行有限元建模,分析得出其一阶谐振频率可达到47.6 Hz,说明它具有良好的模态特性。使用电子水平仪及自准直仪分别对方位轴及俯仰轴进行定量检测,方位轴轴系晃动优于1.3″,俯仰轴轴系晃动优于1.8″。通过仿真分析及实验测试,证明设计的望远镜跟踪架结构具有高刚度及高回转精度,为同类跟踪架的结构设计提供了一定的参考价值。     

The gravitational faraday rotation for cylindrical gravitational solitons

By using cylindrical soliton solutions, the nonlinear behavior of gravitational waves in vacuum is studied in terms of a rotation of the polarization vector between two independent modes. This effect was emphasized by Piran, Safier, and Stark as a gravitational analogue of the Faraday rotation. The polarization of the soliton wave is calculated, and it is found that the+mode which was dominant near the axis of symmetry is fully converted to the×mode at some interaction region and then the disturbance propagating along a light cone like a gravitational wave pulse contains both polarizations.     

国外地基光电系统空间目标探测的进展

简要介绍了国外先进地基空间监视系统的发展现状,从地基光电系统观测空间目标的角度描述了星火光学靶场35 m口径望远镜系统及367 m口径高级光电(AEOS)望远镜系统,给出了这两种望远镜系统的工作性能和所开展的工作。通过对这两套系统的设计理念和先进单元技术的研究,对构造“用于卫星成像的地基光电系统”的相关技术进行了初步探讨;针对目前提出的“对卫星成像的大口径地基光电观测设备”的总体研制方案,提出了建造应用自适应光学技术的18 m地平式望远镜的观点,提出该系统应设计为一个功能可扩展的光学平台。