Dynamics of Flexible MLI-type Debris for Accurate Orbit Prediction

Abstract

Abstract : This study aimed at developing algorithms for accurate, long term propagation of a particular type of space debris, made of multi-layer insulation (MLI) foils, originated from delamination from ageing spacecraft. This type of debris has high area-to-mass ratio, combined with high reflectivity index, and hence it is subject to strong solar radiation pressure (SRP) acceleration. In addition, MLI membranes are highly flexible, therefore their effective, exposed area to the sun is subject to change over time. This effect has been taken into account in the past through averaging techniques. This study attempts, for the first time, to include the dynamics of the deformation in the propagation of the equations of motion (orbit and attitude). The computational cost of modelling a deformable membrane subject to forces can be significant, hence two different models were developed: one uses a linear Bernoulli-Euler beam model, while the second discretizes the membrane properties through lump masses, spring and damper. The latter framework models arbitrarily large deformations, as expected on the lowbending- stiffness membrane. Propagations of typical geostationary orbit (GEO) debris using both models are compared to other models not taking into account the deformation (cannonball model or rigid membrane). The presented results show that considerable difference in the estimation of the orbital parameters (particularly inclination and eccentricity) can be obtained even over tens of days. In addition, in order to reduce the computational burden of the equations of motion, a numerical integrator has been developed, being able to treat coupled dynamics with different typical time-scales, specifically orbit and attitude equations. Assuming the attitude is the fast dynamics, faster integration times can be obtained, with the same level of accuracy of a traditional algorithm, if the computational cost of the fast dynamics is above a certain threshold.