TAMU Sweeper with Sling-Sat for Space Debris Removal 1 and Daniele Mortari2

Jonathan Missel

Texas A&M University, College Station, TX, 77840 Low Earth Orbit is over cluttered by rogue objects. Traditional satellite missions are not ecient enough to collect an appreciable amount of debris due to the high cost of orbit transfers.

Many alternate proposals are politically controversial, costly, or

dependent on further technological advances. This paper proposes an ecient mission structure, TAMU Sweeper, and bespoke hardware, Sling-Sat, to de-orbit debris by capturing and appropriately expelling them. These are executed through plastic interactions, and the momentum exchange assists the satellite in transferring to subsequent debris with substantial fuel reduction! The proposed hardware also exploits existing momentum to save fuel. Capturing debris at the ends of a spinning satellite, adjusting angular rate, and then simply letting go at a specied time provides a simple mechanism for redirecting the debris to an Earth impacting trajectory or lower perigee. This paper provides initial system analyses and aspects of the control for debris collection.

Nomenclature

x

= magnitude

x

= vector

ˆ x

= unit-vector

PhD Student, 301B Reed McDonald, Aerospace Engineering, Texas A&M University, College Station, TX 77843, Tel.: (585) 298-1483 [email protected] 2 Professor, 746C H.R. Bright Building, Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, Tel.: (979) 845-0734, Fax: (979) 845-6051, AIAA Associate Fellow, IEEE Senior Member, mor1

[email protected]

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I.

Introduction

Low Earth Orbit (LEO) has become cluttered with lost and expired satellites, jettisoned components and collision shrapnel.

In 2009, Cosmos 2251 and Iridium 33 collided, marking the rst

signicant satellite accident in history [1]. Combined with the successful anti-satellite test conducted by China in 2007, the skies have become littered with debris [2]. Functioning orbiters are often burdened with avoidance maneuvers and impact damages as a result of the estimated 500,000 pieces of man-made clutter larger than 0.04 inches in LEO [3]. Actions for removal of this debris are necessary; unfortunately, this is a nontrivial task. This expansive problem spans a large range of orbits and changes with time, so it will likely take more than one specialized method to fully remedy. Traditional satellites and mission structures are not ecient enough to oer lasting improvements; successively transferring orbits to collect debris consumes excessive fuel. Also, the satellite's mass increases as debris are collected, requiring more fuel for each maneuver. Several ideas have been proposed to interact with debris at a distance (such as lasers and ion guns), which reduces the number of orbit transfers required [4]. However, these methods are controversial for fear of covert anti-satellite agendas [3]. Also, they often focus on large objects which take several months of beam impingement to de-orbit. Over this extended time, concerns have been raised regarding structural degradation of the material, and the possibility of creating more debris [5]. This paper introduces a new idea, called TAMU Sweeper, for a satellite mission that captures and then ejects debris to lower orbits that will eventually impact Earth. This technique uses the vastness of the space debris problem as part of its own solution by considering captures and expulsion as two free

∆V 's

the satellite can exploit while transferring orbits to encounter the next debris.

By keeping the mass of the satellite from increasing, and using the momentum exchanges from the debris, mission life will be signicantly extended. Moreover, the principles TAMU Sweeper is based on can be scaled and applied to a wide range of debris sizes in all orbits. There are two dominant parts to this concept, optimizing the sequence of debris interaction, and conceptualizing hardware that is bespoke to this mission. As the satellite interacts with debris, a logical concern is that the satellite will be pushed further from Earth as it launches debris down towards Earth. The resulting orbit might grow beyond the debris eld to be swept out. Accordingly,

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an analysis on how the satellite and debris orbits are inuenced is performed to nd the scenarios that will de-orbit debris while retaining control of the satellite's orbit.

To be clear, de-orbiting

debris does not necessarily mean causing it to directly impact Earth. As long as the perigee of the debris is lowered enough, atmospheric drag will cause its orbit to decay in time [6]. As this is a novel idea, there are concerns regarding the hardware for such a mission; these include mechanism development for capturing and expelling debris, and coping with unknown debris masses. This mission requires a craft that is light enough to be launched, robust enough to withstand repeated plastic collisions, dexterous enough to capture, aim, and expel debris, and stable enough to handle capture/ejection without tumbling.

The development of a suggested design is detailed

later. In short, it is a spinning satellite with collectors on the ends of variable-length arms that can adjust to control rotation rate, eectively controlling the debris ejection speed/direction when it is released. See Figs. 6 and 7 for illustrative references. This paper presents the key ideas of this novel debris removal technique, and discusses the results obtained by initial feasibility analyses.

Hardware,

and

Capture Control.

This paper is split into three sections:

Orbit Analysis,

The rst section investigates how the orbits of the debris and

satellite are aected by TAMU Sweeper interactions, the second proposes and analyzes conceptual designs for satellites that can execute such a mission, and the Capture Control section demonstrates an optimal controller for capturing debris.

II.

Orbit Analysis

One of the challenges in debris removal is that the mass of the objects are unknown. This is especially challenging to TAMU Sweeper because it depends on exploiting momentum exchange, which is intimately tied to mass and velocity.

Generating reliable a priori mass estimates is not

the focus of this research, so eorts to mitigating the uncertainties in momentum will be to have a healthy knowledge of the velocity related artifacts. Accordingly, much of the work presented in this section is devoted to gaining a fundamental background in the response to capturing and ejecting objects in orbit. The results presented throughout this section are primarily focused on the ejection process; however, these ndings translate to capturing debris as well.

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To visualize what debris ejection velocities are required for Earth impacting trajectories, a Monte Carlo simulation is provided. Starting from a satellite in polar orbit with

Vs = {5.62; 0; 0}T

km/s, debris was given a random ejection impulse

inertial ejection velocity is then

V = Vs + ∆V ,

r = {0; 0; 11, 100}T

∆V .

km,

Recognizing that the

the resulting perigee of the debris is determined

according to

RE ≥ RP = a (1 − e) where

RE

tricity

e

and

RP

are the Earth and perigee radii, respectively. The semimajor axis

a

and eccen-

can be evaluated from the energy and the eccentricity vector expressions

µr a= 2µ − r V 2

V × (r × V ) e= − rˆ µ

and

thus obtaining the condition for impact

  V × (r × V ) µr RE ≥ RP = − rˆ 1− 2µ − r V 2 µ Given 25,000 randomly chosen ejections impulses, Fig. 1 shows the point cloud marking the end points of those impulses which resulted in an impact.

In other words, each impulse vector

starts at the origin, and terminates at its respective point in the cloud.

The arrow points along

the satellite's inertial velocity, and the square at the origin marks the satellite's position.

Fig. 1 Impacting Velocities for LEO Example

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The

Fig. 2 Planar Ejection Perigee Mesh

orientation of the point cloud depends on the satellite's angular location above the Earth (right ascension and declination), and radial distortion increases with distance from Earth. The minimum impulse required to directly de-orbit debris is the point bounded by the cloud that is closest to origin. The outer surface of the hourglass shape represents the velocities that are exactly Earth-impacting,

RP = RE .

For this reason, knowing the equation of this surface is of interest to TAMU Sweeper;

however, the cross products used in determining the radius of perigee prevent a closed form solution from being readily backed out. To get around this, the two dimensional case has been analyzed, where ejected debris remains in the satellite's orbital plane. This is a relevant subset of trajectories, because ejecting out of the plane does not have any foreseeable advantage in de-orbiting debris. Considering only planar orbits (meaning the spacecraft is spinning with axis orthogonal to the orbit plane) provided a means to calculate the mesh in Fig.

2, which maps the radii of perigee

for various in-plane ejection velocities for the previously described orbit.

This surface changes

depending on the state of the satellite at ejection, but decomposing the impulses into radial and tangential directions clearly shows the expected trend for a large set of initial orbits. It should be noted that the tangential direction is orthogonal to the radial direction, and does not necessarily correspond to the velocity direction of the satellite.

The intersection of the vertical line and the

surface marks the zero impulse case (original orbit), with original perigee

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RP 0 = 8, 713

km. For

Fig. 3 Satellite Orbit Response to Ejection

Fig. 4 Debris Orbit Response to Ejection

ejections that directly impacted Earth, the constraint the impacting plane at

RP = 6, 378.1

RP ≥ RE

was enforced, which is evident by

km. Projected contours of this mesh are included to further

characterize the three dimensional surface. The contour corresponding to the leading edge of the impacting plane is the locus of all exactly Earth-impacting impulses in the orbital plane. Ejecting debris will have an important eect on the satellite's orbit, this is integral to the TAMU sweeper mission structure. Therefore, how the critical orbital elements of the satellite and

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Fig. 5 Saturated Orbit Comparison

debris are altered by ejection, has been analyzed. combined debris-satellite system, a xed energy

Starting from a specied initial orbit for the

∆E

was given for the expulsion.

Since

plastic

collisions do not conserve kinetic energy, the debris and satellite impulses are determined according r to

∆Vd =

2ms ∆E md (ms + md )

r and

∆Vs =

2md ∆E , ms (ms + md )

where subscripts

d

and

s

correspond to

the debris and satellite, respectively. Then, the apogee, perigee, semi-major axis, and eccentricity are calculated for both objects as the eccentric anomaly and ejection angle are fully swept. Figures 3 and 4 show the results for a qualitatively representative scenario in LEO. These two gures provide the areas where perigee radius, apogee radius, semi-major axis, and eccentricity parameters increase (in red) and where they decrease (in blue) for both, the satellite (Fig. 3) and the debris (Fig. 4). A concern with TAMU Sweeper was that reducing the perigee of the debris may expand the orbit of the satellite until it exceeds that of the debris eld. However, the white regions in Fig. 5 indicate places throughout the orbit where both the satellite and debris reduce their perigee (indicated by Rpd