@Bertolami2016]. In the work of Bertolami et al. [@Bertolami2016] several ungravity inspired modifications of the Newtonian potential through couplings of the stress-energy tensor or the baryonic current with a rank-$2$ tensor are considered. However, the authors conclude that no modifications of the classical Newtonian potential of this kind can account for the anomalous energy changes detected during the flybys. Consequently, dissipative or velocity-dependent effects accounting for an energy transfer from the spacecraft to the planet should be considered in future studies if the anomalies persist after rigorous analysis. One of the objectives of the present paper is to develop a method from which, in principle, we can infer the form of the perturbation from the trajectory. This way we can test if the perturbation is compatible with a conservative force of takes another form as proposed by Bertolami et al. [@Bertolami2016] and other authors [@Acedo2015].

Another non-standard model has been developed by McCulloch who considers a modified inertia as a consequence of a Hubble Casimir effect (MiHsC model). This model predicts a qualitative agreement with the anomalous velocity change found in some missions [@McCulloch] and it has also been applied to the problem of the rotation of galaxies to predict 