Linear Model for Reentry Time Prediction of Spacecraft in Low-Eccentricity, Low Earth Orbits

Abstract

A linear model and associated algorithm for the time prediction of uncontrolled atmospheric reentries is presented for spacecraft in low-eccentricity, near-circular low Earth orbits, specifically at altitudes of 300 km and lower. The primary objective of the present research was to develop a comparatively high-accuracy reentry time prediction algorithm by reducing the complexity of the dynamics model, spacecraft physical model, and the overall computation methodology. As opposed to contemporary higher-fidelity prediction methods, reentry trajectories within the presented model are propagated with reduced three-degree-of-freedom equations of motion. In addition to two-line element data for initial orbit conditions, a solar-cycle-independent pseudo-exponential atmospheric density model with variable inverse scale height is used, coupled with coarse estimates for spacecraft aerodynamic characteristics and shape. The algorithm requires the execution of a series of parametric simulations to determine the reentry time for variations in spacecraft aerodynamic coefficients and drag reference area. When implemented, the linear model yields a mean time prediction accuracy deviation of less than 8 h approximately 5 days before reentry as shown by analysis of the Tiangong-1 reentry, as well as 5 additional example reentry cases from 1979 to 2018. All cases were selected to demonstrate the algorithm’s ability to deliver accurate reentry time predictions for spacecraft with varying physical size and mass, and reentering during different periods of solar cycle activity.