Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions.

[1]  J. M. Hedo,et al.  A special perturbation method in orbital dynamics , 2007 .

[2]  Stanley G. Love,et al.  Gravitational tractor for towing asteroids , 2005, Nature.

[3]  Claudio Bonanno,et al.  An analytical approximation for the MOID and its consequences , 2000 .

[4]  Giovanni B. Valsecchi,et al.  Orbital and mission planning constraints for the deflection of NEOs impacting on Earth , 2008 .

[5]  Dario Izzo,et al.  Optimization of Interplanetary Trajectories for Impulsive and Continuous Asteroid Deflection , 2007 .

[6]  R. Battin.  An introduction to the mathematics and methods of astrodynamics , 1987 .

[7]  S. Chesley,et al.  Resonant returns to close approaches: Analytical theory ? , 2003 .

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

[9]  Daniel J. Scheeres,et al.  The Mechanics of Moving Asteroids , 2004 .

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

[11]  Asymptotic solution for the two-body problem with constant tangential thrust acceleration , 2011 .

[12]  Andrea Carusi.  Early NEO Deflections: A Viable, Lower-Energy Option , 2005 .

[13]  C. Bombardelli,et al.  Ion Beam Shepherd for Asteroid Deflection , 2011, 1102.1276.

[14]  Andrea Boattini,et al.  Deflecting NEOs in Route of Collision with the Earth , 2002 .

[15]  Massimiliano Vasile,et al.  Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects , 2009 .

[16]  T. Ahrens,et al.  Deflection and fragmentation of near-Earth asteroids , 1992, Nature.

[17]  H. J. Melosh,et al.  Solar asteroid diversion , 1993, Nature.