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The NASA Discovery-class mission VERITAS, selected in June 2021, will be launched towards Venus after 2027. In addition to the science instrumentation that will build global foundational geophysical datasets, VERITAS proposed to conduct a technology demonstration for the Deep Space Atomic Clock (DSAC-2). A first DSAC successfully operated in low-Earth orbit for more than two years, demonstrated the trapped ion atomic clock technology, and established a new level of performance for clocks in space. DSAC-2 would have further improvements in size, power, and performance. It would host a $1\times{10}^{-13}$ grade USO to produce a frequency output with short-term stability of less than $2\times{10}^{-13}/\sqrtτ$ (where $τ$ is the averaging time). However, due to funding shortfalls, DSAC-2, had to be canceled. The initially foreseen presence of an atomic clock on board the probe, however, raised the question whether this kind of instrumentation could be useful not only for navigation and time transfer but also for fundamental physics tests. In this work, we consider the DSAC-2 atomic clock and VERITAS mission as a specific example to measure possible discrepancies in the redshift predicted by General Relativity by using an atomic clock onboard an interplanetary spacecraft. In particular we investigate the possibility of measuring possible violations of the Local Lorentz Invariance and Local Position Invariance principles. We perform accurate simulations of the experiment during the VERITAS cruise phase. We consider different parametrizations of the possible violations of the General Relativity, different operational conditions, and several different assumptions on the expected measurement performance. Our analysis shows the scientific value of atomic clocks like DSAC-2 hosted onboard interplanetary spacecraft.