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Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modelling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform rendezvous maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers., Comment: Submitted to Scientific Reports

The recent paper by AlShebli et al. (2020) investigates the impact of mentorship in young scientists. Among their conclusions, they state that female prot\'eg\'es benefit more from male than female mentorship. We herein expose a critical flaw in their methodological design that is a common issue in Astronomy, namely "selection biases". An effect that if not treated properly may lead to unwarranted causality claims. In their analysis, selection biases seem to be present in the response rate of their survey (8.35%), the choice of database, success criterion, and the overlook of the numerous drawbacks female researchers face in academia. We discuss these issues and their implications -- one of them being the potential increase in obstacles for women in academia. Finally, we reinforce the dangers of not considering selection bias effects in studies aimed at retrieving causal relations., Comment: Submitted to Nature Communications on Nov. 27 -- comments are welcome