The Sun–Earth saddle point: characterization and opportunities to test general relativity

Abstract

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits.In this paper, the geometrical and dynamical properties of the Sun-Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on L 1,2 Lagrange point orbits. Sun-Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.

LISA Pathfinder mission extension: A feasibility analysis

“…Due to the nonlinearity of the vector field and the severe requirements on the SP passage (Hees et al, 2016;Galianni et al, 2012;Bekenstein and Magueijo, 2006;Topputo et al, 2018b), even small errors can jeopardize the designed transfer and eventually undermine the probability of an encounter with the SP. Therefore, an analysis of the solution sensitivity to maneuvering errors is of paramount importance for the identification and pruning of those transfers characterized by high sensitivity, for which large control efforts would likely be required.…”

“…1. An exploration of the solution space is performed starting from the real LPF ephemeris (for more details on the exploration see Topputo et al (2018b)). The sole initial epoch, t 0 , is sufficient to fully characterize the initial conditions for the exploration, and a fine search is applied to the variable t 0 .…”

“…Recently, a number of studies assessed the feasibility of leveraging the highly nonlinear Sun-Earth-Moon environment to fly by the Sun-Earth gravitational saddle point (SP) region at affordable cost and duration (Trenkel and Kemble, 2009;Trenkel et al, 2012;Fabacher et al, 2013;Cox and Howell, 2016;Topputo et al, 2018b). Saddle points are defined as those locations in space where the net gravitational acceleration balances.…”

High-Fidelity Trajectory Optimization with Application to Saddle-Point Transfers

“…The impulsive trajectory optimization is to solve the NLP problem min y J(y) s.t. g(y) = 0 and h(y) ≤ 0, (22) where g and h are vector-valued functions stating equality and inequality constraints, respectively. The former read…”

“…Because LISA Pathfinder was proposed to conduct this experiment, the focus has been on finding low-∆v solutions, in the range of 1-2 m/s, which is relative to LISA Pathfinder end-of-life conditions. This stringent requirement justifies the high-fidelity model developed, although the ∆v budget may be larger for dedicated SP missions, thus widening the design space [22]. Moreover, the specific option for LISA Pathfinder restricts the study to the actual spacecraft orbit, and can be retrieved as a special case of the results presented.…”