  This paper compares the continuum evolution for density equation modelling
and the Gaussian mixture model on the 2D phase space long-term density
propagation problem in the context of high-altitude and high area-to-mass ratio
satellite long-term propagation. The density evolution equation, a pure
numerical and pointwise method for the density propagation, is formulated under
the influence of solar radiation pressure and Earth's oblateness using
semi-analytical methods. Different from the density evolution equation and
Monte Carlo techniques, for the Gaussian mixture model, the analytical
calculation of the density is accessible from the first two statistical moments
(i.e., the mean and the covariance matrix) corresponding to each sub-Gaussian
distribution for an initial Gaussian density distribution. An insight is given
into the phase space long-term density propagation problem subject to nonlinear
dynamics. The efficiency and validity of the density propagation are
demonstrated and compared between the density evolution equation and the
Gaussian mixture model with respect to standard Monte Carlo techniques.
