A Method of Implementing Cutoff Conditions for Saturn V Lunar Missions Out of Earth Parking Orbit Assuming a Continuous Ground Launch Window
A method of implementing Saturn V lunar missions from an earth parking orbit is presented. The ground launch window is assumed continuous over a four and one-half hour period. The iterative guidance scheme combined with a set of auxiliary equations that define suitable S-IVB cutoff conditions, is the approach taken. The four inputs to the equations that define cutoff conditions are represented as simple third-degree polynomials as a function of ignition time. Errors at lunar arrival caused by the separate and combined effects of the guidance equations, cutoff conditions, hypersurface errors, and input representations are shown. Vehicle performance variations and parking orbit injection errors are included as perturbations. Appendix I explains how aim vectors were computed for the cutoff equations. Appendix II presents all guidance equations and related implementation procedures. Appendix III gives the derivation of the auxiliary cutoff equations. No error at lunar arrival was large enough to require a midcourse correction greater than one meter per second assuming a transfer time of three days and the midcourse correction occurs five hours after injection. Since this result is insignificant when compared to expected hardware errors, the implementation procedures presented are adequate to define cutoff conditions for Saturn V lunar missions.