Optimal finite-thrust time-limited direct-ascent interception

Minimum-time and maximum final mass solutions are obtained for the problem of direct-ascent interception, from a launch point on the surface of the Earth, of a target in a circular orbit. The intercepting rocket is assumed to have finite thrust and is subject to aerodynamic forces including lift and drag. The effect of Earth rotation is included and an initial “coast arc” is allowed. The problem is formulated as an optimal control problem and direct collocation with nonlinear programming is used to find numerical solutions. Both time-open and time-fixed problems are considered. Optimal solutions include both posigrade and retrograde intercept trajectories. Solutions are obtained for a range of target orbit radii, inclinations, launch points, and initial target phase angles relative to the launch point.