Modelling the Dynamics of a Probe in Vicinity of Eross-433 With a Fourth-Order Polynomial Density Profile

In the present work, we study the motion of a probe in the gravitational field generated by an elongated geo-cruiser asteroid of irregular shape, which we model by an inhomogeneous mass distribution. We propose a model of inhomogeneous mass distribution with a symmetric polynomial density profile of order 4 and then establish the analytical expression of the gravitational potential generated by this segment. The Lagrangian formalism allowed us to establish the dynamic equations of motion of the probe in the gravitational field generated by this body, which we solved numerically.