The method of nearby problems for estimation of numerical error in orbital-mechanics simulations

The method of nearby problems has previously been applied to validate the accuracy of numerical solutions of the problems in fluid dynamics. In this paper, the application of this method is extended to the problems in orbital mechanics. Using this method, the error in the numerical simulations of two-body and three-body equations of motion is estimated. A fixed step-size and a variable step-size numerical integration scheme are used for the simulations. The method of nearby problems is found to provide reliable error estimates and has advantages of cost efficiency and ease of use.