Space gravitational wave(GW)detection is to detect and measure the distance change between spacecraft/celestial bodies or status change intra spacecraft/celestial body according to the astrodynamical equations of general relativity or a specific gravitational theory.The basic method is using electromagnetic waves(including radio,microwave,light,X-ray,y-ray,etc.)to Doppler track the spacecraft/celestial body and compare them with the two stable frequency standards(sources)at the emission end and the receiving end,e.g.microwave Doppler tracking,optical clock Doppler tracking,atom-interferometry GW detection,laser-interferomatic GW detection.If the emission phases of the electromagnetic waves are unknown,the statistic Doppler tracking method can be used as in the Pulsar Timing Arrays.If the frequency standards at the emission and the receiving ends are not stable enough in the desired detection frequency band,then it is necessary to exploit the generalized Michelson interferometry based on two paths each consisting of multi-segments of Doppler tracking.In this case,the phase(length metrology)noise at the combination end is proportional to the product of laser source frequency noise times the pathlength difference of the two paths,and the two paths need to be carefully designed and evaluated.Each set of two paths is called a TDI(Time-Dealy Interferometry)configuration.The study of TDI configurations together with the orbit design and the noise requirement at each optical link and the final spacecraft is called TDI interferometry.The final mission products for scientists to use are TDI phase(range)sequences/spectra.These products are also useful for other gravity measurements or testing specific gravitational theories,e.g.measuring gravitomagnetic effects.The current projects under construction and/or study are mainly using this method of generalized Michelson laser-interferometry which includes AMIGO(Astrodynamical Middle-frequency Gravitational Observatory),BBO(Big Bang Observer),B-DECIGO,DECIGO(Deci-Hertz Gravitational Observatory)and DO(Deci-Hertz Observatory)in middle frequency band(0.1-10 Hz),LISA(Laser-Interferometric Space Antenna)and TAIJI/TianQ in the mHz low frequency band(0.1-100 mHz),and ASTROD-GW(Astrodynamical Space Test of Relativity using Optical Devices dedicated for Gravitational wave detection),Folkner's mission,LISAmax,μAries and Super-ASTROD(0.1-100 μHz).In this article,we review the current status quo of these space detection methods and present an outlook.
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