The Removal of Large Space Debris
Using Tethered Space Tug
Samara State Aerospace University, Russia
Vladimir S. Aslanov and Vadim V. Yudintsev
5th Eucass - European Conference for Aerospace Sciences - Munich, Germany, 1-4 July 2013

1. Active debris removal techniques
2. Tethered space tug
3. Mathematical model
4. Numerical simulation and analysis
5. Results and conclusion
2
Outline

• Small debris (<10 cm)
– Magnetic field (<1 cm)
– Foams
– Lasers
– …
• Large Debris
– Solar sail
– Electrodynamic tether
– Tethered space tag
Source: J. Olympio, presentation at CNES Orbital Debris Removal Workshop, Paris, 22 June, 2010
Source: http://www.spacesafetymagazine.com
3
1. Active debris removal techniques

Large space debris body can be source of a lot of small debris.
Source: http://www.spacejunk3d.com/
4
1. Active debris removal techniques
So we consider the removal of a large space debris

1. Launch a space tug (“debritor”)
2. Catch a debris (attach a tether)
3.Decrease orbital velocity
4. Reentry
~100 km
5
2. Tethered space tug
Removal stages
Delta 2nd Stage Propellant
Tank
http://orbitaldebris.jsc.nasa.go
v/reentry/reentry.html

6
2. Tethered space tag
Large and heavy space debris can strongly
affect the motion of the space tug and to the
tether during the transportation process,
which can lead to the loss of control of the
tethered system.
The spatial motion of the orbital
debris relative to the tether and to
the space tug
should be investigated.

7
3. Mathematical model
General Provisions

Model = rigid body (large debris) + tether + material point (space tug)
Weightless viscoelastic
tether

1 1 1 1 1m m   a g T D F
2 2 2 2 2m m  a g T D
2
2
,j o j
d
dt
   a r ρ
,
[ , , ],
1,2
j o j
j j j jx y z
j
 


r r ρ
ρ
,0,0
1 cos
o
p
e 
 
   
r
3. Mathematical model
System center of mass equations
where
8
Space tug equation
Space debris equation
System’s center of mass vector:

( , , , , , )e p i  f
Orbital elements
9
3. Mathematical model
Orbit equations
Planetary equations are
used to describe motion of
the system’s center of mass
Space tug thrust force
projections
( , , , , , , , , )t x y z
d
e p i F F F
dt
  
f
f
 true anomaly
e eccentricity
p true anomaly
i inclination
 longitude of the ascending node
 argument of periapsis

Attitude motion of the space debris described by Euler equation
2 2 2 2 2 2  J ω ω J ω M
2 2 o ω Ω ω
sin sin( ) cos( )
sin cos( ) sin( )
cos
o
d di
i
dt dt
d di
i
dt dt
d d d
i
dt dt dt
   
   
 

  

 
 
 
 
   





 


 

ω
is an angular velocity vector of the orbital frame, is an angular velocity
of the orbital debris relative to the orbital frame Oxoyozo, J2 is a inertia tensor
of the space debris.
oω 2Ω
10
3. Mathematical model
Attitude motion of the space debris

• Gravitational force
• Aerodynamic drag
3
, 1,2.
j j
j j j
j
m
m j   
r
F g
r
11
1
, 1,2
2
j dj j rj rjc S V j  D V
3. Mathematical model
Forces
 atmosphere density
drag coefficients of the space tug (j=1) and the space debris (j=2)
reference areas of the space tug (j=1) and the space debris (j=2)
velocity of the space tug (j=1) and the space debris (j=2) relative to the Earth
atmosphere
djc
jS
rjV

1 2 Al   ρ ρ ρTether length
1 2
0 0( ) ( ) A
l T T
dl
H l l c l l d
dt l
  
    
 
ρ ρ ρ
TTether force
12
3. Mathematical model
Tether tension
0l is a tether free length, cT is a tether stiffness, dT is a tether damping, Hl(l-l0) is a
Heaviside step function.

• The net torque acting on the space debris is
• Tether torque is
• Gravitational torque
 
 
 
2 2
2 23
2
2 2
3
z y
z x
x y
g
C B
A C
B A
 

 
 
 
 
 


 
r
M
22 2
2 2 2
, ,
yx z
x y z  
 
  
r er e r e
r r r
2 T g M M M
T A M ρ T
13
3. Mathematical model
Torques
A2, B2, C2 are moments of inertia of the space debris; are unit
vectors of the basis O2x2y2z2.
, ,x y ze e e

Table 1 Parameters of the system
Parameter Value Parameter Value
Space tug mass m1 500 kg Orbital debris mass m2 3000 kg
Space tug force F [0; -20 N; 0] Axial moment of inertia A2 3000 kgm2
Space tug drag coefficient cd1 2 Moment of inertia B2=C2 15000 kgm2
Space tug reference area S1 1 m2 Orbital debris drag
coefficient cd2
2
Initial orbit height 500 km
Orbital debris reference
area S2
18 m2
Tether Young's modulus ET 1571 N/m Tether length l0 30 m
Tether damping dT 0…16 Ns/m
14
4. Numerical simulation and analysis
System parameters

15
4. Numerical simulation and analysis
Case 1. Tensioned tether
0(0) , 0, 0T Tl l c d  
/ 6 

Two modes of oscillation occur:
– a high frequency oscillation of the tether
– low frequency precess motion the space debris relative to the tether
due to the initial angular momentum of the orbital debris.
16
4. Numerical simulation and analysis
Tensioned tether
Time history of the angle ϑ and the tether elongation

17
4. Numerical simulation and analysis
Case 2. Slackened tether
0(0) , 0, 0T Tl l c d  
/ 6 

• The amplitude of the oscillation of the angle ϑ is higher than in the case 1.
• Greater tension of the tether is expected.
• A high oscillation of the angle ϑ during de-orbiting of the orbital debris
should be avoided. It can lead to the tether break or tether tangles.
18
4. Numerical simulation and analysis
Slackened tether
Time history of the angle ϑ and the tether elongation

19
4. Numerical simulation and analysis
Damped tether
0(0) , 0Tl l c 
/ 6  0Td 

• The amplitude of the oscillation of the angle is a smaller than in the case 2.
• Effect of the tether damping (d=16 N·s/m) on the oscillations of the orbital
debris relative to the tether is insignificant.
20
4. Numerical simulation and analysis
Damped tether
Time history of the angle ϑ and the tether elongation

• If tug’s thrust is low high amplitude oscillation of the tether can occur
relative to the r0 direction due to the action of the gravitational torque.
• The space tug control system should compensate these high oscillations of
the angle a by changing the direction of the thruster force vector F.
21
4. Numerical simulation and analysis
Action of the gravitational torque
F = [0, 0.2 N, 0 ]

Tether length as a function of orbit height
and the tug’s thrust
2.8F N450 ,h km
0 1500l m
If
22
4. Numerical simulation and analysis
Action of the gravitational torque
then tether length
should be

• Passive braking system produce low torque relative to the center of mass
23
4. Numerical simulation and analysis
Passive braking system
Drag force

Critical tether length as a function of orbit
height and the sphere radius
100sR m400 ,h km
0 3000l m
If
24
4. Numerical simulation and analysis
Passive braking system. Tether length
then tether length
should be

 min 1
2 1
1 1
F q h m
BC BC
 
  
 
The minimal space tug force
25
4. Numerical simulation and analysis
Motion near the atmosphere edge
1 2
1 2
0
D F D
m m

 
Collision avoidance condition
If BC1=250 kg/m2, BC2=3 kg/m2, h>98
km, Fmin=10 N.

1. The safe transportation process is possible when the space tug
force vector coincides with the direction of the tether and the
tether is always tensioned.
2. Tether damping device slightly reduces the amplitude oscillations of
the orbital debris.
3. The space tug has to keep sufficient level of the thruster force to
eliminate the high amplitude oscillations of the space tether
system.
4. There is the minimal height of the safe transportation below which
the space tug can come into collision with the connected orbital
debris.
5. Results and conclusion
26

Developed mathematical model can be
modified to investigate the influence of
the other properties of the system to the
motion of the space debris and the space
tug
• tether mass
• tether bending stiffness
• flexible properties of the space debris
The examples of simulation results made
with the modified models can be found
here
• http://www.youtube.com/watch?v=04iVJY1MzPY
• http://www.youtube.com/watch?v=CqbAOh0RxSA
5. Results and conclusion
27

Publications
28
1. V. S. Aslanov, V. V. Yudintsev Dynamics of Large Space Debris Removal
Using Tethered Space Tug. Acta Astronautica, 2013 (Accepted for
publication). doi: 10.1016/j.actaastro.2013.05.020
2. V. S. Aslanov, V. V. Yudintsev Dynamics of Large Debris Connected to
Space Tug by a Tether. Journal of Guidance, Control, and Dynamics. 2013
(Accepted for publication) doi: 10.2514/1.60976.

Thank you for your attention
Questions?
Presentation is available at
http://aslanov.ssau.ru
Contacts
aslanov@mail.ru
yudintsev@classmech.ru
29