Ryotaro Sakamoto, University of Colorado Boulder; Daniel Scheeres, University of Colorado Boulder
Keywords: Energy dissipation, Rotational dynamics, Flexible dynamics, Defunct Satellites
Abstract:
There are several causes which can cause the spin rate change of a space object, both internal and external effects. The Yarkovsky-O’Keefe–Radizievskii-Paddack (YORP) effect led by solar radiation pressure is considered as one cause of changes in the rotational states of defunct geosynchronous earth orbit (GEO) satellites, in some cases taking them from uniform rotation to tumbling. For example, the transition of the rotational rates has been predicted and observed in the GOES 8 satellite. This effect does not only affect defunct satellites, as the rotational rates of small asteroids are also changed by the YORP effect. In terms of the transition of satellite spin states, internal energy dissipation is a key component to track rotational behavior. In ideal situation, the kinetic energy is conserved without any additional torque for rigid body dynamics. But in real life, friction between structural components or sloshing of internal liquid are considered as reasons for dissipation in space. In this study, the deformation is taken into account as the primary cause to energy dissipation and spin rate transition of a satellite model, assuming that a defunct satellite will have spent or vented its propellant.
Finite element analysis calculates the deformational behavior of satellite model based on the damping equation, given a driving acceleration. For a tumbling body, the inertial effects will apply a distributed three-dimensional acceleration to the nodes of the model. Due to the fluctuation of flexible components, the body axis is affected as it is tumbling at the same time. This causes the inertia matrix and its products of inertia to be updated due to the deformation results. Then, flexible body equation, which is based on the Euler equation, provides us an update of the spin state. When combined, these processes can model the interaction of deformation and the spin rate transition of rotational dynamics.
As a tumbling satellite loses energy, the state of the rotational rate approaches rotation along its maximum moment of inertia. In term of the three-dimensional dynamics, rotational rate along its maximum momentum inertia goes to a value based on minimum energy theory with the other rotational rates going to zero. Our goal is to find the relationship between the rate of energy dissipation and material properties for spinning defunct satellites and debris in general.
Our simulation model is comprised of solar array panels and body component using a finite element model. To evaluate the total energy and spin rate transition, the kinetic energy and potential energy are tracked. The entire simulation results are compared with a simple rigid body dynamic. Fluctuation of flexible components varies material properties such as the damping ratio and stiffness. Therefore, variations of these parameters and its effect on the rotational dynamics are explored. Then the relaxation time of spin rates transitions are estimated to enable our approach to be effectively used to analyze a wider range of satellites and debris objects. By comparing our the computed spin rate transitions with observation data for the tumbling satellite GOES-8, we will develop estimates of what appropriate level of dissipation should be used in our simulations for class of satellites.
Date of Conference: September 14-17, 2021
Track: Non-Resolved Object Characterization