A frequent variational problem is one for which the fuel expenditure is to be minimized. In practice, approximate thrust steering schedules that vary bilinearly or linearly with time are introduced to reduce the multidimensional trials involved in attaining a numerical solution. The degree of approximation is established which is induced when these approximate programs are used for the correctional maneuver characterized by a small parameter which is related to the percentage change in orbital characteristics. For the maneuver the thrust magnitude is assumed to be constant and can be of the same order as the central force. It is proved that if there is an acceptable error in the minimum value of the burning time, then the bilinear program is applicable regardless of imposed end constraints. However for a special class of correctional maneuvers, defined by the property that boundary conditions are weakly dependent upon the circumferential displacement, one can utilize the simpler linear program with the same degree of accuracy. Numerical veri icati n of this theory is given by considering examples and comparing the results of burning time and terminal values of the dependent variables with exact solutions.