Advanced analytical model for orbital aerodynamic prediction in LEO

The growing interest in low earth orbit (LEO) applications demands for accurate modeling of orbital aerodynamics. But classical analytical models of aerodynamic coefficients in free molecule flow, such as the Sentman’s model, Schamberg’s model and Schaaf-Chambre model, were built upon over simplistic gas-surface interaction models, which degrade the fidelity of aerodynamic prediction. This work presents a new analytical model of orbital aerodynamic coefficients based on the state-of-the-art Cercignani–Lampis–Lord (CLL) gas-surface interaction model, where lobular quasi-specular scattering pattern and separate accommodation degree for different velocity components can be well captured. A key component of the new model is a rigorous function approximation solution of the reflected normal momentum flux based on the CLL model which is derived for the first time and is validated within 1% for any hypothermal flow and surface accommodation conditions. Closed-form analytical solutions of aerodynamic coefficients for simple convex geometries are obtained and exhibit high accuracy (within 0.1%) in typical LEO scenarios. The new analytical model surpasses the classical models in some important aspects, such as overcoming the diffuse scattering hypothesis constraint, considering the variation of normal momentum exchange with the surface incidence angle and being applicable in any hypothermal flow situation. In virtue of the advanced CLL model and feasibility of coupling with the panel method technique, the new analytical model is promising to provide more accurate predictions on the orbital aerodynamic coefficients for LEO applications.     

Orbital error propagation considering atmospheric density uncertainty

Due to the influence of various errors, the orbital uncertainty propagation of artificial celestial objects while orbit prediction is required, especially in some applications such as conjunction analysis. In the orbital error propagation of artificial celestial objects in low Earth orbits (LEOs), atmospheric density uncertainty is one of the important factors that require special attention. In this paper, on the basis of considering the uncertainties of position and velocity, the atmospheric density uncertainty is also taken into account to further investigate the orbital error propagation of artificial celestial objects in LEOs. Artificial intelligence algorithms are introduced, the MC Dropout neural network and the heteroscedastic loss function are used to realize the correction of the empirical atmospheric density model, as well as to provide the quantification of model uncertainty and input uncertainty for the corrected atmospheric densities. It is shown that the neural network we built achieves good results in atmospheric density correction, and the uncertainty quantization obtained from the neural network is also reasonable. Moreover, using the Gaussian mixture model - unscented transform (GMM-UT) method, the atmospheric density uncertainty is taken into account in the orbital uncertainty propagation, by adding a sampled random term to the corrected atmospheric density when calculating atmospheric density. The feasibility of the GMM-UT method considering atmospheric density uncertainty is proved by the further comparison of abundant sampling points and GMM-UT results (with and without considering atmospheric density uncertainty).