Symbolic computing algorithm for the method of successive approximations for near-parabolic orbits

In this paper, an accurate algorithm for the method of successive approximations for near-parabolic orbits is established symbolically. Numerical applications are given for motion predictions at fifteen epochs between the years 66 to 1835 for Halley’s comet, and at fifteen epochs between the years 1417 to 1782 for Encke’s comet. Comparisons with the standard Gauss method [4] show that the present algorithm is very accurate and efficient for motion predications of near-parabolic orbits.