A MATLAB-based Numerical Orbital Decay Model for Undergraduate STEM Education

Abstract:

An undergraduate/community college level lab, requiring programming skills with MATLAB, is presented to predict the orbital decay of satellites. First, students learn to interpret the Two-Line Element sets and convert them to Kepler orbital elements. Next, several coordinate systems used to describe the motion of a satellites are computed: 1) The p-q orbital plane, 2) Earth Centered Inertial coordinates, 3) Earth Centered Earth Fixed (Rotating), and 4) Geodetic Latitude, Longitude, and Altitude. A 6-DOF Runge-Kutta scheme is used to propagate the orbit, with special perturbations that use the NRLMSIS00 (provided in MATLAB).

The example given is the July 11, 1979 deorbit of Skylab. This affords the opportunity to discuss the mission in general and how it contributed to Earth resources monitoring and learning to live and work in space as the natural follow-on of the Apollo missions. NASA had intended to service Skylab with the Space Shuttle, but budget related delays in the shuttle program coupled with unexpected solar storms resulting in increased density in the upper atmosphere lead to its decay. This computer exercise shows why space science and satellites monitoring the solar wind are critical to maintaining the health and safety of humans and resources in space. Students can use the model to ask what-if questions for different hypothetical satellite sizes, orbital elements, and solar wind drivers of the atmosphere to explore the impact of space weather on space assets.