An Analytical Solution of Dynamics of Self-gravitating Spherical Gas-Dust Cloud

In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gas-dust cloud. We take two analytical approaches to study the dynamics of a gravitating system of a gasdust cloud. The first approach solves a set of non-linear equation of dynamics of a gravitating system. The second approach is a Cole-Hopf transformation, which is used to simplify the equations of dynamics and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The results found by the analytical method and the Cole-Hopf method are compared with each other, showing that both lead to the same result. The obtained results in this study are presented in plots. We used the Mathematica software package in performing calculation and plotting graphs.