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The periapsis shift of charged test particles in arbitrary static and spherically symmetric charged spacetimes are studied. Two perturbative methods, the near-circular approximation and post-Newtonian methods, are developed, and shown to be very accurate when the results are found to high orders. The former method is more precise when the eccentricity $e$ of the orbit is small while the latter works better when the orbit semilatus rectum $p$ is large. Results from these two methods are shown to agree with each other when both $e$ is small and $p$ is large. These results are then applied to the Reissner-Nordstr\"om spacetime, the Einstein-Maxwell-dilation gravity and a charged wormhole spacetime. The effects of various parameters on the periapsis shift, especially that of the electrostatic interaction, are carefully studied. The periapsis shift data of the solar-Mercury is then used to constrain the charges of the Sun and Mercury, and the data of the Sgr A$^*$-S2 periapsis shift is used to find, for the first time using this method, constraints about the charges of Sgr A$^*$ and S2., Comment: 17 pages, 9 figures

Using a perturbative technique, in this work we study the deflection of null and timelike signals in the extended Einstein-Maxwell spacetime, the Born-Infeld gravity and the charged Ellis-Bronnikov (CEB) spacetime in the weak field limit. The deflection angles are found to take a (quasi-)series form of the impact parameter, and automatically takes into account the finite distance effect of the source and observer. The method is also applied to find the deflections in CEB spacetime with arbitrary dimension. It's shown that to the leading non-trivial order, the deflection in some $n$-dimensional spacetimes is of the order $\mathcal{O}(M/b)^{n-3}$. We then extended the method to spacetimes that are asymptotically non-flat and studied the deflection in a nonlinear electrodynamical scalar theory. The deflection angle in such asymptotically non-flat spacetimes at the trivial order is found to be not $\pi$ anymore. In all these cases, the perturbative deflection angles are shown to agree with numerical results extremely well. The effects of some nontrivial spacetime parameters as well as the signal velocity on the deflection angles are analyzed., Comment: 30 pages, 7 figures; title modified; to match published version in Class.Quant.Grav