Logarithmic spiral trajectories generated by Solar sails

  • Marco Bassetto
  • Lorenzo Niccolai
  • Alessandro A. Quarta
  • Giovanni Mengali
Original Article
Part of the following topical collections:
  1. Innovative methods for space threats: from their dynamics to interplanetary missions


Analytic solutions to continuous thrust-propelled trajectories are available in a few cases only. An interesting case is offered by the logarithmic spiral, that is, a trajectory characterized by a constant flight path angle and a fixed thrust vector direction in an orbital reference frame. The logarithmic spiral is important from a practical point of view, because it may be passively maintained by a Solar sail-based spacecraft. The aim of this paper is to provide a systematic study concerning the possibility of inserting a Solar sail-based spacecraft into a heliocentric logarithmic spiral trajectory without using any impulsive maneuver. The required conditions to be met by the sail in terms of attitude angle, propulsive performance, parking orbit characteristics, and initial position are thoroughly investigated. The closed-form variations of the osculating orbital parameters are analyzed, and the obtained analytical results are used for investigating the phasing maneuver of a Solar sail along an elliptic heliocentric orbit. In this mission scenario, the phasing orbit is composed of two symmetric logarithmic spiral trajectories connected with a coasting arc.


Solar sail Logarithmic spiral trajectories Orbit phasing 


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Copyright information

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

Authors and Affiliations

  • Marco Bassetto
    • 1
  • Lorenzo Niccolai
    • 1
  • Alessandro A. Quarta
    • 1
  • Giovanni Mengali
    • 1
  1. 1.Dipartimento di Ingegneria Civile e IndustrialeUniversity of PisaPisaItaly

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