Bounded relative orbits about asteroids for formation flying and applications

Abstract The relative motion about 4179 Toutatis is studied in order to investigate the feasibility of formation flying as an alternative concept for future asteroid exploration missions. In particular, the existence of quasi-frozen orbits about slowly rotating bodies allows us to compute families of periodic orbits in the body-fixed frame of the asteroid. Since these periodic orbits are of the center×center type, quasi-periodic invariant tori are calculated via fully numerical procedures and used to initialize spacecraft formations about the central body. Numerical simulations show that the resulting in-plane and out-of-plane relative trajectories remain bounded over long time spans; i.e., more than 30 days.

[1]  Massimiliano Vasile,et al.  Uncontrolled spacecraft formations on two-dimensional invariant tori , 2012 .

[2]  Kathleen Ann Connor Howell.  Three-dimensional, periodic halo orbits in the restricted three-body problem , 1983 .

[3]  Kathleen C. Howell,et al.  COMPUTATION OF QUASI-PERIODIC INVARIANT TORI IN THE RESTRICTED THREE-BODY PROBLEM , 2010 .

[4]  Pini Gurfil,et al.  Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem , 2012 .

[5]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[6]  Chunlai Li,et al.  The Ginger-shaped Asteroid 4179 Toutatis: New Observations from a Successful Flyby of Chang'e-2 , 2013, Scientific Reports.

[7]  D. Scheeres,et al.  Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia , 1996 .

[8]  J. Junkins,et al.  Analytical Mechanics of Space Systems , 2003 .

[9]  Stephen B. Broschart,et al.  Quasi-terminator orbits near primitive bodies , 2014 .

[10]  Shengping Gong,et al.  Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids , 2009 .

[11]  Steven J. Ostro,et al.  Shape and Non-Principal Axis Spin State of Asteroid 4179 Toutatis , 1995, Science.

[12]  David Mauro,et al.  Mission Concepts and Operations for Asteroid Mitigation Involving Multiple Gravity Tractors , 2013 .

[13]  D. Scheeres.  Dynamics about Uniformly Rotating Triaxial Ellipsoids: Applications to Asteroids , 1994 .

[14]  André Deprit,et al.  Canonical transformations depending on a small parameter , 1969 .

[15]  D. Scheeres.  Orbital motion in strongly perturbed environments , 2012 .

[16]  D. Vallado.  Fundamentals of Astrodynamics and Applications , 1997 .

[17]  H. Schaub,et al.  J2 Invariant Relative Orbits for Spacecraft Formations , 2001 .

[18]  Christie Alisa Maddock,et al.  Comparison of Single and Multi-Spacecraft Configurations for NEA Deflection by Solar Sublimation , 2007 .

[19]  J. Henrard,et al.  The combined effect of J2 and C22 on the critical inclination of a lunar orbiter , 2006 .

[20]  Massimiliano Vasile,et al.  On the deflection of asteroids with mirrors , 2010 .

[21]  Daniel J. Scheeres,et al.  Spacecraft Motion About Slowly Rotating Asteroids , 2002 .