Tethered aerobraking design for repeatable maneuvers

Highlights

• Analytic solutions for tether dynamics in an elliptical orbit.

• Efficient, robust computational algorithm for targeting tether libration angle and angular rate via tether length control.

• Demonstrates that repeated aerobraking maneuvers are possible with practical power requirements.

Abstract

An aerobraking maneuver performed with a tethered system has the benefit of increasing the drag for a given center of mass orbit by dropping the lower subsatellite into the denser atmosphere. While this concept has received significant attention in the literature, the exact means of controlling the attitude prior to the aerobraking fly-through has not been adequately treated. In particular, a scheme for repeated passes in elliptical orbits has not been developed, which would be required, for example, in a debris elimination system. This work uses tether reeling during the exoatmospheric flight in order to control the tether libration to target a desired state prior to the aerobraking trajectory. The design of the control law requires numerical solution of nonlinear equations, but newly developed analytics provide an estimate that reduces computational time and increases the robustness of the algorithm. The results show that the nearly periodic state that is required for successive passes can be achieved for practical tether lengths and power requirements.

Introduction

Momentum exchange tethers have been deeply studied as they are an efficient tool to introduce changes in the orbit of a satellite. For instance, for a system formed by two masses connected by a long cable, cutting the tether when the satellite is vertically orientated boosts the upper end-body into a higher elliptical orbit and the lower body into a lower energy one [1]. Recently, the idea has been applied to space debris [2,3]. A piece of debris is captured, reeled out along a long tether, and then released making use of the gravity gradient to deorbit the debris. This exchange of momentum between the debris and debris elimination satellite unfortunately places the latter into a higher orbit. After relatively few debris objects are deorbited, the debris elimination satellite is boosted above the LEO belt. The methodology developed in this paper can be implemented to counteract the increase in orbital energy caused by deorbiting a piece of debris, allowing for repeated deorbit of arbitrarily many debris objects without the use of propellant.

The salient interaction between tethered satellites and dense atmospheres has been extensively studied. Lorenzini et al. [4] studied the feasibility of a tethered system in a circular orbit around Mars ($e=0$), which investigated a sustained penetration of a probe into the Martian atmosphere. For hyperbolic orbits ($e>1$), Puig-Suari et al. [[5], [6], [7]] envisioned the satellite as a means to decelerate spacecraft and achieve an aerocapture. A practical analytical tool was provided to determine the initial conditions required for the transfer maneuver. However, the intermediate case of a system orbiting in an eccentric orbit ($0<e<1$) has not been adequately developed. In particular, a design for sustained, repeated aerobraking maneuvers (necessary for the debris removal concept described above) has not been accomplished.

Attitude control of the tether libration has also received much attention, in particular during the deployment and retrieval phase. Controlling the libration in elliptical orbits or to a non-vertical reference (both of which are required for this concept) have been topics of considerably less study. One exception is the work by Arnold in which he computes the nonzero equilibrium tether angle for a nearly circular orbit during deployment and retrieval [8]. He observes changes in the orbital elements due to the gravity gradient forces which can be seen in the results of this work. Martinez-Sanchez considers elliptical orbits, but has a nominal control law that is referenced to a vertical orientation [9]. Several papers treat the general case of large librational excursions in an elliptical orbit, but all of these develop a stabilizing control with a periodic reference motion [[10], [11], [12], [13]]. None of the work in the literature deals with targeting a specific non-equilibrium state at a given time in an elliptical orbit as is required for the aerobraking portion of this concept.

In this paper, a system formed by an orbiter and a probe connected by a long and thin tether that rotates around its center of mass in the plane of the orbit, is proposed as a means to efficiently reduce the orbital energy of a spacecraft in an eccentric orbit around the Earth (see Fig. 1). During the closest approach to the planet, the probe deeps down into the atmosphere to slow down the satellite. The work integrates previously developed theory for the aerobraking maneuvers with a new tether control law via tether reeling for targeting the desired initial tether libration state (angle and angular rate) for the aerobraking maneuver. This control scheme maintains the reusable nature of the system, allowing for an arbitrary number of atmospheric fly-throughs to decrease energy as additional debris is removed.