The determination for ideal release point of test masses in drag-free satellites for the detection of gravitational waves

Gravitational waves are ripples in space–time predicted by Albert Einstein's general relativity and provide a new way to understand the universe. Space-borne detectors of gravitational waves, extending to very large scales, can effectively detect the middle and low-frequency gravitational wave source with the frequency band of 0.1 mHz–1 Hz. The test masses are used to make an inertial reference point in the detection of gravitational waves. Currently, there are few studies concerning the ideal release position for the test masses in the detection of gravitational waves. In this study, we give a general solution for test mass release points to minimize the relative motion between the test mass and the satellite mass center. Moreover, we discuss the situation when the release point equation is not satisfied, and the ideal release point of the along-track. Finally, we report on simulations that verify the accuracy of the theoretical derivation.