Dynamics of Orbits Close to Asteroid 4179 Toutatis

Abstract

We use a radar-derived physical model of 4179 Toutatis (975870) to investigate close-orbit dynamics around that irregularly shaped, non-principal-axis rotator. The orbital dynamics about this body are markedly different than the dynamics about uniformly rotating asteroids. The results of this paper are generally applicable to orbit dynamics about bodies in a non-principal-axis rotation state. The radar results support the hypothesis that Toutatis has a homogeneous density distribution, and we assume a density of 2.5 g/cc. The asteroid's gravity field is computed using a truncated harmonic expansion when outside of its circumscribing sphere and a closed-form expression for the potential field of an arbitrary polyhedron when inside that sphere. The complete equations of motion are time-periodic in the Toutatis-fixed frame due to the complex rotation of the asteroid. The system is Hamiltonian and has all the characteristics of such a system, including conservation of phase volume, but there is no Jacobi constant of the motion and zero velocity surfaces cannot be used to analyze the system's behavior. We also examine some of the close-orbit dynamics with the Lagrange planetary form of the equations of motion. Families of quasi-periodic "frozen orbits" that show minimal variations in orbital elements are found to exist very close to the asteroid; some of them are stable and hence can hold natural or artificial satellites. A retrograde family of frozen orbits is especially robust and persists down to semi-major axes of about 2.5 km, comparable to half of Toutatis' longest dimension. We identify families of periodic orbits, which repeat in the Toutatis-fixed frame. Due to the time-periodic nature of the equations of motion, all periodic orbits about Toutatis in its body-fixed frame must be commensurate with the 5.42-day period associated with those equations. Exact calculations of both stable and unstable periodic orbits are made. The sum of surface forces acting on a particle on Toutatis is time-varying, so particles on and in the asteroid are being continually shaken with a period of 5.42 days, perhaps enhancing the uniformity of the regolith distribution. A global map of the gravitational slope reveals that it is surprisingly shallow for such an elongated, irregularly shaped object, averaging 16° globally and less than 35° over 96% of the surface. A global map of tangential accelerations shows no values larger than 0.5 mm/s2, an average value of 0.2 mm/s2, and less than 0.25 mm/s2over 70% of the surface. A global map of the escape speed for launch normal to the surface shows that quantity to be between 1.2 and 1.8 m/s over most of the surface. Each of these mapped quantities has small periodic variations. We have found trajectories that leave the surface, persist in the region of phase space around a frozen orbit, and then impact the surface after a flight time of more than 100 days. Return orbit durations of years seem possible. Whereas a uniformly rotating asteroid preferentially accumulates non-escaping ejecta on its leading sides, Toutatis accumulates ejecta uniformly over its surface. We render a variety of close orbits in inertial and body-fixed frames. © 1998 Academic Press.