Finite-burn De-orbit from Earth Orbit – SNOPT

Optimize a finite-burn maneuver that de-orbits a spacecraft from an initial circular or elliptical Earth orbit to a user-defined entry

This MATLAB script named fb_deorbit_snopt that can be used to compute the optimal finite-burn propulsive maneuver required to de-orbit a spacecraft from an initial circular or elliptical Earth orbit. The simulation assumes the propulsive maneuver is continuous, co-planar and modeled as a series of optimal discretized steering angles. This script attempts to minimize the thrust duration of the finite-burn while solving for user-defined orbital boundary conditions. Since the maneuver is continuous this is equivalent to minimizing the propellant required for the maneuver.

The user provides the classical orbital elements of the initial Earth orbit along with geodetic altitude and relative flight path angle boundary conditions at the entry interface (EI). These entry interface targets are computed with respect to an oblate, rotating Earth.

In this classic optimization problem, the maneuver thrust duration, the steering angle of the maneuver delta-v vector and the flight time from the maneuver to the entry interface are the control variables. The scalar magnitude of the finite-burn de-orbit is the objective function or performance index, and the geodetic altitude and relative flight path angle at the entry interface are treated as nonlinear equality mission constraints.

The fb_deorbit_snopt script uses the SNOPT nonlinear programming algorithm to solve this orbital mechanics problem. MATLAB versions of SNOPT for several computer platforms can be requested or purchased at Professor Philip Gill’s web site which is located at http://scicomp.ucsd.edu/~peg/. This web site also includes a PDF version of the software user’s guide.