On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms

Many instances of hyperbolic orbits occur in the solar system and recently, among the artificial satellites, lunar and solar probes. Moreover, in some cases of orbit determination for an elliptic orbit, it may very well happen that during the solution process (usually iteration), the eccentricity e becomes greater than unity and the orbit becomes hyperbolic. Also, in the interplanetary transfer, the escape from the departure planet and the capture by the target planet involves hyperbolic orbits. On the other hand, in orbit determination of visual binaries provisional hyperbolic orbits are used to represent the periastron section of high-eccentricity orbits of long and indeterminate period. In fact, we should handle hyperbolic orbits frequently when integrating a perturbed motion with the initial condition of nearly parabolic orbits [1-3].