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

  • Francesco Topputo
  • Diogene A. Dei Tos
  • Mirco Rasotto
  • Masaki Nakamiya
Original Article
Part of the following topical collections:
  1. Recent advances in the study of the dynamics of N-body problem


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.


Saddle point Lagrange point Ballistic orbits General relativity 



Part of the work described in this paper has been conducted under ESA Contract No. 4000118201/16/F/MOS. The authors would like to acknowledge Florian Renk, Gonçalo Aguiar, Erind Veruari, Srikara Cherukuri, and Carmine Giordano for their valuable contributions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Aerospace Science and TechnologyPolitecnico di MilanoMilanItaly
  2. 2.Dinamica SrlMilanItaly
  3. 3.Unit of Synergetic Studies for SpaceKyoto UniversityKyotoJapan

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