Spacecraft Doppler tracking with possible violations of LLI andLPI： a theoretical modeling

Currently two-way and three-way spacecraft Doppler tracking techniquesare widely used and play important roles in control and navigation of deep space mis-sions. Starting from a one-way Doppler model, we extend the theory to two-way andthree-way Doppler models by making them include possible violations of the localLorentz invariance （LLI） and the local position invariance （LPI） in order to test theEinstein equivalence principle, which is the cornerstone of general relativity and allother metric theories of gravity. After taking the finite speed of light into account,which is the so-called light time solution （LTS）, we make these models depend on thetime of reception of the signal only for practical convenience. We find that possibleviolations of LLI and LPI cannot affect two-way Doppler tracking under a linear ap-proximation of LTS, although this approximation is sufficiently good for most cases inthe solar system. We also show that, in three-way Doppler tracking, possible violationsof LLI and LPI are only associated with two stations, which suggests that it is betterto set the stations at places with significant differences in velocities and gravitationalpotentials to obtain a high level of sensitivity for the tests.