For the simple spherical case modeled by $M(t) = ho(r, heta, ext{phi}) ext{cdot} v(t)$, what must be true about the density term $ ho$?
It must be independent of the angular coordinates $ heta$ and $ ext{phi}$ across the entire surface.
The mathematical model describing mass ejection, $M(t) = ho(r, heta, ext{phi}) ext{cdot} v(t)$, specifies the conditions required for a perfect sphere. In this equation, $ ho$ represents the density and $v$ represents the velocity. For the resulting structure to be perfectly spherical, the mass loss must be isotropic in terms of density distribution. This means the density ($ ho$) cannot vary based on direction or position on the surface, which are represented by the angular coordinates $ heta$ and $ ext{phi}$. Any deviation in $ ho$ regarding these angles indicates an initial density asymmetry in the slow wind, which will later be dramatically revealed and amplified when the high-speed wind interacts with this uneven material.
