Improved alpha shape-based continuum method for long-term density propagation

This paper presents an improved alpha shape-based linear interpolation method, and an improved binning method within the continuum method framework for accurate and efficient planar phase space long-term density propagation. The density evolution equation is formulated for the continuum density propagation under the influence of the solar radiation pressure and Earth’s oblateness using semi-analytical equations. The concept of the alpha shape is included to get accurate interpolated density within the non-convex hull enclosing all the samples for the highly deformed and elongated density distribution. The improved binning method increases the density accuracy by considering the variant nonlinearity of the density within each alpha shape triangulation, which calculates the joint and marginal density as the weighted sum of density weights per bin area and per bin width, respectively. The suitable sample number for the continuum method and the suitable grid number for performing the linear interpolation are selected by trading off the density accuracy and the computational effort. The superiority of the improved alpha shape-based continuum method is demonstrated for accurate and efficient density propagation in the context of the high-altitude and high area-to-mass ratio satellite long-term propagation.