Ryotaro Sakamoto, University of Colorado Boulder; Daniel Scheeres, University of Colorado Boulder
Keywords: Finite Element, Energy dissipation,
Abstract:
The transition of defunct satellite rotation states from uniform rotation to tumbling has been predicted and observed recently in the GOES-8 satellite [1]. These transitions are driven by solar radiation pressure torques, similar to the so-called YORP Effect which has been implicated in the evolution of asteroid rotation states [2]. The cycle observed for GOES-8 apparently involves periods of spin-up about the minimum axis of inertia followed by a period of energy dissipation, which brings the satellite back to rotation about its maximum moment of inertia. These dynamics raise a number of interesting question about the evolution of spinning defunct satellites and debris in general. In this research we study one aspect of this cycle, focusing on the dissipation of energy. We develop detailed models for energy dissipation in flexible satellites, using finite element calculations to model the flexible dynamics of a satellite appendage subject to time-varying accelerations arising from a tumbling body. We use these calculations to model the energy dissipation in a satellite appendage over every periodic cycle. The simulations explore the amount of dissipation as a function of model parameters and as a function of the appendage orientation relative to the satellites principal axes. Using the resulting dissipation and model parameters for the satellite, we feed back the energy dissipation into the assumed torque-free rotation of the body to characterize the relaxation time scale. The goal of this research is to develop models that will enable the estimation of energy dissipation on observed satellites.
Our simulations model a simple solar array panel using a finite element method. Our initial model is 2-dimensional, but will be expanded to fully 3-D in the future. To evaluate the response of the model to a tumbling satellite, we model a time-periodic acceleration profile distributed across the component, which has an additional offset from the ideal satellite center of mass. The acceleration acting at a specific point on the appendage is found by combining a torque-free angular rate and acceleration with the relative location of the component, and the finite element method computes the distributed dynamical effect of these accelerations across the appendage. As the accelerations are periodic in the body-fixed frame, the simulations are run over a long enough time for the behavior to settle into a steady oscillation. As the local level of dissipation is increased, the amplitude of the oscillations become smaller. To determine the overall effect on the body spin rate it is necessary to determine the total energy transferred into the appendage oscillation in the absence of dissipation, comparing the peak energy to the dissipation over each cycle. To measure this empirically we track the total amplitude of the steady-state oscillations as the dissipation in the appendage is decreased. This allows the parameter Q to be computed, which can then be directly used to compute the energy dissipation rate. This can be used to modify the spin state in a predictable way, allowing for the relaxation of the excited spin state to be tracked over longer time spans, and evaluated at varying levels of excitation. These calculations will be compared with observations of the tumbling satellite GOES-8 [1] to develop empirical estimates of what appropriate level of dissipation should be used in our simulations for this particular asteroid.
[1] A. Albuja, D.J. Scheeres, R.L. Cognion, W. Ryan and E.V. Ryan. 2018. The YORP Effect on the GOES 8 and GOES 10 Satellites: A Case Study, Advances in Space Research 61: 122-144.
[2] D.P. Rubincam. 2000. Radiative spin-up and spin-down of small asteroids, Icarus 148(1): 2-11.
Date of Conference: September 11-14, 2018
Track: Poster