Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape

This paper investigates the equilibria and their stabilities in the doubly synchronous binary asteroid systems, which are modelled as the two tri-axial ellipsoids with various shape and system parameters. Particularly, the in uences of shape and system parameters on equilibria are discussed analytically. Firstly, the geometrical models of doubly synchronous binary asteroid systems are established. The dual second degree and order gravity field is employed to approximate the gravitational potential of the system. Six shape and system parameters are defined. Then, based on the linearized perturbation equations, the explicit expressions of the offsets of equilibria in doubly synchronous systems are derived, which clearly illustrate the relationship between the distribution of equilibria and the variations of shape parameters. Further, the approximate expressions are applied to estimate the offsets of equilibria due to parameter errors, respectively. Finally, in order to have a better insight into the equilibriaum structure, the stabilities of equilibria under different system parameters are investigated. In particular, critical regions of triangular equilibria are calculated and the role of the relative distance on the stability is discussed in detail. This study could provide a preliminary analysis of equilibria for the mission design in doubly synchronous binary asteroid systems.

[1]  Daniel J. Scheeres,et al.  Changes in Rotational Angular Momentum due to Gravitational Interactions between Two Finite Bodies* , 2001 .

[2]  Daniel J. Scheeres,et al.  Stability of the planar full 2-body problem , 2009 .

[3]  Hermann Böhnhardt,et al.  MarcoPolo-R near earth asteroid sample return mission , 2011, Proceedings of the International Astronomical Union.

[4]  D. Sinha,et al.  Stability and regions of motion in the restricted three-body problem when both the primaries are finite straight segments , 2014 .

[5]  DJ SCHEERES,et al.  Stability of Relative Equilibria in the Full Two‐Body Problem , 2004, Annals of the New York Academy of Sciences.

[6]  Pamela Woo,et al.  Bounded trajectories of a spacecraft near an equilibrium point of a binary asteroid system , 2015 .

[7]  H. Baoyin,et al.  Orbits and manifolds near the equilibrium points around a rotating asteroid , 2014, 1403.0401.

[8]  Colin R. McInnes,et al.  Trajectories to and from the Lagrange Points and the Primary Body Surfaces , 2006 .

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

[10]  D. Campbell,et al.  Binary Asteroids in the Near-Earth Object Population , 2002, Science.

[11]  Daniel J. Scheeres,et al.  Stability in the Full Two-Body Problem , 2002 .

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

[13]  S. Ostro,et al.  Dynamical Configuration of Binary Near-Earth Asteroid (66391) 1999 KW4 , 2006, Science.

[14]  Jerrold E. Marsden,et al.  Parking a Spacecraft near an Asteroid Pair , 2006 .

[15]  K. Howell,et al.  Stability of orbits near large mass ratio binary systems , 2015 .

[16]  Pamela Woo,et al.  Control of Spacecraft Trajectories near Collinear Equilibrium Points of Binary Asteroid Systems , 2016 .

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

[18]  John A. Arredondo,et al.  On the restricted three body problem with oblate primaries , 2012 .

[19]  Daniel J. Scheeres,et al.  Stability of equilibrium points in the restricted full three-body problem , 2007 .

[20]  M. Birlan,et al.  New determination of the size and bulk density of the binary Asteroid 22 Kalliope from observations of mutual eclipses , 2007, 0710.1471.

[21]  Petr Pravec,et al.  Binary asteroid population 1. Angular momentum content , 2007 .

[22]  W. Wiesel.  Stable orbits about the Martian moons , 1993 .

[23]  P. Michel,et al.  Asteroid Impact and Deflection Assessment mission , 2015 .

[24]  D. Scheeres,et al.  General dynamics in the Restricted Full Three Body Problem , 2006 .

[25]  D. Scheeres,et al.  Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems , 2011, 1404.0801.

[26]  P. Michel,et al.  Rotational breakup as the origin of small binary asteroids , 2008, Nature.

[27]  Pamela Woo,et al.  Equilibrium points in the full three-body problem $ , 2014 .

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

[29]  Hexi Baoyin,et al.  Two-impulse transfer orbits connecting equilibrium points of irregular-shaped asteroids , 2015 .