Light Deflection under the Gravitational Field of Jupiter -- Testing General Relativity

We measured the relative positions between two pairs of compact extragalactic sources (CESs), J1925-2219 \& J1923-2104 (C1--C2) and J1925-2219 \& J1928-2035 (C1--C3) on 2020 October 23--25 and 2021 February 5 (totaling four epochs), respectively, using the Very Long Baseline Array (VLBA) at 15 GHz. Accounting for the deflection angle dominated by Jupiter, as well as the contributions from the Sun, planets other than Earth, the Moon and Ganymede (the most massive of the solar system's moons), our theoretical calculations predict that the dynamical ranges of the relative positions across four epochs in R.A. of the C1--C2 pair and C1--C3 pair are 841.2 and 1127.9 $\mu$as, respectively. The formal accuracy in R.A. is about 20 $\mu$as, but the error in Decl. is poor. The measured standard deviations of the relative positions across the four epochs are 51.0 and 29.7 $\mu$as in R.A. for C1--C2 and C1--C3, respectively. These values indicate that the accuracy of the post-Newtonian relativistic parameter, $\gamma$, is $\sim 0.061$ for C1--C2 and $\sim 0.026$ for C1--C3. Combining the two CES pairs, the measured value of $\gamma$ is $0.984 \pm 0.037$, which is comparable to the latest published results for Jupiter as a gravitational lens reported by Fomalont \& Kopeikin, i.e., $1.01 \pm 0.03$.