Approximate Solution of Sensitivity Matrix with Final Velocity Constraint Using Linear Time-Varying Gravity Assumption

In this research, an approximate solution of the required velocity with final velocity constraint is derived using linear gravity assumption along the path of current position to the final position vectors. Moreover, an approximate solution for sensitivity matrix of the required velocity with respect to the position vector is obtained. The presented solutions are given for a predetermined final time. In this case, for the free final position, the analytical solution is rather more difficult than its fixed final position counterpart. Therefore, three approaches are utilized for approximation of the final position vector. Finally, the obtained solutions are compared to exact numerical one for the spherical- Earth model.