Model of the tethered space system in vicinity of ellipsoidal asteroid and its approximations

While planning missions in vicinity of an asteroid/comet body one has to take into account several dynamical problems to overcome and among them are: (a) irregular distribution of the body internal masses; (b) too weak gravity acceleration near the body surface. In case of (a) one offers to apply approximate models of gravity. As an example we consider the case of a triaxial ellipsoid. For the problem (b) we apply docking procedures with help of anchor and a connecting tether. For computing the force field of gravity being generated by the ellipsoid of three axes one has to calculate several values of elliptic integrals at each instant of the simulation process. For this we apply original algorithm interpreting elliptic integrals as a state variables in additional to dynamics system of ODEs. To resolve the problem (b) we use so-called hybrid automata to build up the tethered interconnection between a spacecraft and the asteroid. Ellipsoidal asteroid performs free rotary motions about its mass center thus performing the Euler case of the rigid body rotary motion. The spacecraft moves under the force of gravity from the asteroid and under the tether tension, in case of the constraint being imposed. So we have so-called restricted dynamical model because the asteroid does not “feel” any force from the spacecraft. In addition to the hybrid automata dynamical model including impacts on constraint we also consider approximations of this model being really regularizations of the impact process. All these models are analysed and compared numerically.