Searching for Time Optimal Periodic Orbits Near Irregularly Shaped Asteroids by Using an Indirect Method

Periodic orbits over irregularly shaped asteroids and comets are fundamental for understanding vicinal dynamical behaviors and space explorations. In this paper, a new method is proposed to obtain natural periodic orbits, which is based on the optimal control framework with respect to a general form of the irregular gravitational field. Natural elongated asteroids are taken as representatives, whose potentials are approximated by the rotating mass dipole with appropriate parameters. An indirect method is used to transform the optimal control model into a two-point boundary value problem, which can be solved by using a shooting method. Numerical simulations are performed to validate the effectiveness of the proposed method regarding the asteroid 951 Gaspra. Three types of periodic orbits are identified, including the Lyapunov orbit around the collinear equilibrium point, the equatorial retrograde orbit, and the inclined orbit. The connection between the latter two types of orbits is also briefly discussed via numerical continuation.

[1]  Pingyuan Cui,et al.  The present status and prospects in the research of orbital dynamics and control near small celestial bodies , 2014 .

[2]  K. Alfriend,et al.  Solar Sail Body-Fixed Hovering over Elongated Asteroids , 2016 .

[3]  Junfeng Li,et al.  Earth-crossing asteroid intercept mission with a solar sail spacecraft , 2014, IEEE Aerospace and Electronic Systems Magazine.

[4]  Fernando Blesa,et al.  PERIODIC ORBITS AROUND SIMPLE SHAPED BODIES , 2006 .

[5]  Martin Lara,et al.  On the numerical continuation of periodic orbits: An intrinsic, 3-dimensional, differential, predictor-corrector algorithm , 2002 .

[6]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[7]  Hexi Baoyin,et al.  Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach , 2012 .

[8]  D. Scheeres.  Orbital mechanics about small bodies , 2012 .

[9]  Derek F Lawden,et al.  Optimal trajectories for space navigation , 1964 .

[10]  R. S. Hudson,et al.  Orbits Close to Asteroid 4769 Castalia , 1996 .

[11]  Junichiro Kawaguchi,et al.  Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB14 , 2010 .

[12]  D. Scheeres.  Orbital motion in strongly perturbed environments : applications to asteroid, comet and planetary satellite orbiters , 2012 .

[13]  Xiangyuan Zeng,et al.  Study on the connection between the rotating mass dipole and natural elongated bodies , 2015 .

[14]  Hongwei Yang,et al.  Fuel-optimal control for soft landing on an irregular asteroid , 2015, IEEE Transactions on Aerospace and Electronic Systems.

[15]  Hexi Baoyin,et al.  Generating families of 3D periodic orbits about asteroids , 2012 .

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

[17]  Antonio Elipe,et al.  Periodic Orbits Around a Massive Straight Segment , 1999 .

[18]  W. Marsden.  I and J , 2012 .

[19]  V. Szebehely.  Theory of Orbits: The Restricted Problem of Three Bodies , 1968 .

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

[21]  S. R. Vadali,et al.  Using Low-Thrust Exhaust-Modulated Propulsion Fuel-Optimal Planar Earth-Mars Trajectories , 2000 .

[22]  S. Vadali,et al.  Solar Sail Planar Multireversal Periodic Orbits , 2014 .

[23]  Marie Schmidt,et al.  Generating Families In The Restricted Three Body Problem , 2016 .

[24]  Daniel D. Durda,et al.  EROSION AND EJECTA REACCRETION ON 243 IDA AND ITS MOON , 1996 .

[25]  Haibin Shang,et al.  Periodic orbits in the doubly synchronous binary asteroid systems and their applications in space missions , 2015 .

[26]  Daniel J. Scheeres,et al.  Periodic Orbits in Rotating Second Degree and Order Gravity Fields , 2008 .

[27]  Shengping Gong,et al.  Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies , 2014 .

[28]  Daniel J. Scheeres,et al.  Stability bounds for three-dimensional motion close to asteroids , 2002 .

[29]  Clark R. Chapman,et al.  Galileo Photometry of Asteroid 951 Gaspra , 1994 .