A software method used to control the degree in a polynomial computation of Hansen coefficients

The Hansen coefficients are widely used in the semi-analytical methods of elliptic orbital propagation. The generation of those coefficients, in computer software, was usually performed by means of recursion formulas, but this approach has some time penalties mainly if not all values are required. We developed a linear approach, which uses polynomials, and proved that the computation time was lower while the error was kept within acceptable limits. However, we found that, in some cases, due to the limitation of the data type of the programming language that we used (Java), the error was increasing when the degree of the polynomials used was bigger than 40 and we had to develop a method to decrease the degree of the polynomials while not losing the method advantages. This paper presents in detail the method that we used in order to decrease the degree of the polynomials and keep the computation error within acceptable limits.