Relativistic transformation between τ and TCB for Mars missions: Fourier analysis on its accessibility with clock offset

Abstract

In the context of the fact that Einstein's general relativity has become an inevitable part of deep space missions, we will extend previous works on relativistic transformation between the proper time τ of a clock onboard a spacecraft orbiting Mars and the Barycentric Coordinate Time (TCB) by taking the clock offset into account and investigate its accessibility by Fourier analysis on the residuals after fitting the τ-TCB curve in terms of n-th order polynomials. We find that if the accuracy of a clock can achieve better than ∼ 10−5 s or ∼ 10−6 s (depending on the type of clock offset) in one year after calibration, the relativistic effects on the difference between τ and TCB will need to be carefully considered.