Ballistic representation for kinematic access

This work uses simple two-body orbital dynamics to initially determine the kinematic access for a ballistic vehicle. Primarily this analysis was developed to assess when a rocket body might conjunct with an orbiting satellite platform. A family of access opportunities can be represented as a volume for a specific rocket relative to its launch platform. Alternately, the opportunities can be represented as a geographical footprint relative to aircraft or satellite position that encompasses all possible launcher locations for a specific rocket. A thrusting rocket is treated as a ballistic vehicle that receives all its energy at launch and follows a coasting trajectory. To do so, the rocket’s burnout energy is used to find its equivalent initial velocity for a given launcher’s altitude. Three kinematic access solutions are then found that account for spherical Earth rotation. One solution finds the maximum range for an ascent-only trajectory while another solution accommodates a descending trajectory. In addition, the ascent engagement for the descending trajectory is used to depict a rapid access scenario. These preliminary solutions are formulated to address ground-, sea-, or air-launched vehicles.