AN ALGORITHM FOR SOLVING SPACECRAFT REACHABLE DOMAIN WITH SINGLE-IMPULSE MANEUVERING IN ECEF COORDINATE SYSTEM

The spacecraft reachable domain (RD) is an effective tool in space situational awareness, which can be used in maneuver detection, threat assessment and collision warning. In particular, the RD in earth-centered earth-fixed (ECEF) coordinate system plays a significant role in analyzing the variation of maneuvering satellite’s subastral point and the reachable region of a maneuvering satellite in geostationary orbit (GEO). The majority of available literature provided the calculation of the absolute RD in earth-centered inertial (ECI) coordinate system. Nevertheless, the solution of RD in ECEF has not been studied before, which is still a hard nut to crack due to time coupling caused by the transformation of different coordinate systems. To solve this problem, an algorithm is developed in this paper by handling time constraint and accessibility constraint. The accessibility constraint of arbitrarily given orientation in ECI is firstly established by means of terminal velocity hyperbola in two-body orbital boundary-value problem. In addition, the coordinate transforming relation between ECEF and ECI is applied to construct the time constraint of the accessibility of arbitrarily given orientation in the ECEF coordinate system. Based on these two constraints, a solution model for solving the RD in ECEF is presented. The problem of determining the entire envelope of RD is consequently transformed into finding the extremum of spacecraft position vector in an accessible orientation. Then the RD in ECEF can be obtained by finding out the extremum of expression of position vector in any accessible orientation, which is derived by virtue of the variation of spacecraft's true anomaly in transfer orbit. Finally, the method proposed in this paper is verified by Monte Carlo simulation to show its feasibility and effectiveness.