SlideShare a Scribd company logo
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.

More Related Content

What's hot

Seminar report on GPS based Space Debris Removal System
Seminar report on GPS based Space Debris Removal SystemSeminar report on GPS based Space Debris Removal System
Seminar report on GPS based Space Debris Removal System
Sunil Ds
 
E1 - Introduction to the Universe
E1 - Introduction to the UniverseE1 - Introduction to the Universe
E1 - Introduction to the Universe
simonandisa
 
Chandryaan 2
Chandryaan 2Chandryaan 2
Chandryaan 2
AhmadAlImaad
 
Stars, Galaxies, and the Universe
Stars, Galaxies, and the UniverseStars, Galaxies, and the Universe
Stars, Galaxies, and the Universe
mlong24
 
WHAT IS SPACE DEBRIS????
WHAT IS SPACE DEBRIS????WHAT IS SPACE DEBRIS????
WHAT IS SPACE DEBRIS????
TANVEER SHAIKH
 
SPACE SCIENCE AND TECHNOLOGY FOR MANKIND
SPACE SCIENCE AND TECHNOLOGY FOR MANKINDSPACE SCIENCE AND TECHNOLOGY FOR MANKIND
SPACE SCIENCE AND TECHNOLOGY FOR MANKIND
Vishal Pandey
 
Space exploration
Space explorationSpace exploration
Space exploration
VisheshV
 
Space Debris
Space DebrisSpace Debris
Space Debris
Lokesh Parihar
 
The Space Junk
The Space JunkThe Space Junk
The Space Junk
MAGESHS41
 
Is Space Exploration Worth the Money (in 3d)
Is Space Exploration Worth the Money (in 3d)Is Space Exploration Worth the Money (in 3d)
Is Space Exploration Worth the Money (in 3d)
Rahul Jaiswal
 
Space travel
Space travelSpace travel
Space travel
Ksenia Tihomirova
 
Space Debris Removal System
Space Debris Removal SystemSpace Debris Removal System
Space Debris Removal System
Mohammad Shadab
 
Space exploration
Space explorationSpace exploration
Space exploration
sadasivuni datta sai
 
The History of Astronomy
The History of AstronomyThe History of Astronomy
The History of Astronomy
06426345
 
Junior solar system space quiz slideshare mar 2016
Junior solar system space quiz slideshare mar 2016Junior solar system space quiz slideshare mar 2016
Junior solar system space quiz slideshare mar 2016
Viewyonder
 
Space Waste Management
Space Waste ManagementSpace Waste Management
Space Waste Management
Abhishek Rajput
 
Asteroids and comets
Asteroids and cometsAsteroids and comets
Asteroids and comets
joverba
 
Satellites in Communication
Satellites in CommunicationSatellites in Communication
Satellites in Communication
Tejaswa Jain
 
Astrophysics Presentation
Astrophysics PresentationAstrophysics Presentation
Astrophysics Presentation
Akshay Sharma
 
Basics Of Astrophysics
Basics Of AstrophysicsBasics Of Astrophysics
Basics Of Astrophysics
Homam Hosseini
 

What's hot (20)

Seminar report on GPS based Space Debris Removal System
Seminar report on GPS based Space Debris Removal SystemSeminar report on GPS based Space Debris Removal System
Seminar report on GPS based Space Debris Removal System
 
E1 - Introduction to the Universe
E1 - Introduction to the UniverseE1 - Introduction to the Universe
E1 - Introduction to the Universe
 
Chandryaan 2
Chandryaan 2Chandryaan 2
Chandryaan 2
 
Stars, Galaxies, and the Universe
Stars, Galaxies, and the UniverseStars, Galaxies, and the Universe
Stars, Galaxies, and the Universe
 
WHAT IS SPACE DEBRIS????
WHAT IS SPACE DEBRIS????WHAT IS SPACE DEBRIS????
WHAT IS SPACE DEBRIS????
 
SPACE SCIENCE AND TECHNOLOGY FOR MANKIND
SPACE SCIENCE AND TECHNOLOGY FOR MANKINDSPACE SCIENCE AND TECHNOLOGY FOR MANKIND
SPACE SCIENCE AND TECHNOLOGY FOR MANKIND
 
Space exploration
Space explorationSpace exploration
Space exploration
 
Space Debris
Space DebrisSpace Debris
Space Debris
 
The Space Junk
The Space JunkThe Space Junk
The Space Junk
 
Is Space Exploration Worth the Money (in 3d)
Is Space Exploration Worth the Money (in 3d)Is Space Exploration Worth the Money (in 3d)
Is Space Exploration Worth the Money (in 3d)
 
Space travel
Space travelSpace travel
Space travel
 
Space Debris Removal System
Space Debris Removal SystemSpace Debris Removal System
Space Debris Removal System
 
Space exploration
Space explorationSpace exploration
Space exploration
 
The History of Astronomy
The History of AstronomyThe History of Astronomy
The History of Astronomy
 
Junior solar system space quiz slideshare mar 2016
Junior solar system space quiz slideshare mar 2016Junior solar system space quiz slideshare mar 2016
Junior solar system space quiz slideshare mar 2016
 
Space Waste Management
Space Waste ManagementSpace Waste Management
Space Waste Management
 
Asteroids and comets
Asteroids and cometsAsteroids and comets
Asteroids and comets
 
Satellites in Communication
Satellites in CommunicationSatellites in Communication
Satellites in Communication
 
Astrophysics Presentation
Astrophysics PresentationAstrophysics Presentation
Astrophysics Presentation
 
Basics Of Astrophysics
Basics Of AstrophysicsBasics Of Astrophysics
Basics Of Astrophysics
 

Viewers also liked

Attitude Dynamics of Re-entry Vehicle
Attitude Dynamics of Re-entry VehicleAttitude Dynamics of Re-entry Vehicle
Attitude Dynamics of Re-entry Vehicle
Theoretical mechanics department
 
1U-3U+ Cubesat Deployer by JSC SRC "Progress"
1U-3U+ Cubesat Deployer by JSC SRC "Progress"1U-3U+ Cubesat Deployer by JSC SRC "Progress"
1U-3U+ Cubesat Deployer by JSC SRC "Progress"
Theoretical mechanics department
 
The Dynamics of Tethered Debris With Flexible Appendages and Residual Fuel
The Dynamics of Tethered Debris With Flexible Appendages and Residual FuelThe Dynamics of Tethered Debris With Flexible Appendages and Residual Fuel
The Dynamics of Tethered Debris With Flexible Appendages and Residual Fuel
Theoretical mechanics department
 
Научно-исследовательская работа кафедры Теоретической механики
Научно-исследовательская работа кафедры Теоретической механикиНаучно-исследовательская работа кафедры Теоретической механики
Научно-исследовательская работа кафедры Теоретической механики
Руслан Пикалов
 
Deployers for nanosatellites
Deployers for nanosatellitesDeployers for nanosatellites
Deployers for nanosatellites
Theoretical mechanics department
 
Mathematical models and analysis of the space tether systems motion
Mathematical models and analysis of the space tether systems motion Mathematical models and analysis of the space tether systems motion
Mathematical models and analysis of the space tether systems motion
Theoretical mechanics department
 
On problems of active space debris removal using tethered towing
On problems of active space debris removal using tethered towingOn problems of active space debris removal using tethered towing
On problems of active space debris removal using tethered towing
Theoretical mechanics department
 
Space Debris and Present Active Debris Removal Techniques
Space Debris and Present Active Debris Removal TechniquesSpace Debris and Present Active Debris Removal Techniques
Space Debris and Present Active Debris Removal Techniques
V!vEk@nAnD S
 
Space debris
Space debrisSpace debris
Space debris
Vignesh Prasad
 
Модификация механизма Йо-Йо
Модификация механизма Йо-ЙоМодификация механизма Йо-Йо
Модификация механизма Йо-Йо
Theoretical mechanics department
 
Dynamics of Satellite With a Tether System
Dynamics of Satellite With a Tether SystemDynamics of Satellite With a Tether System
Dynamics of Satellite With a Tether System
Theoretical mechanics department
 
Chaotic motions of tethered satellites with low thrust
Chaotic motions of tethered satellites with low thrust Chaotic motions of tethered satellites with low thrust
Chaotic motions of tethered satellites with low thrust
Theoretical mechanics department
 
Написание научной статьи на английском языке
Написание научной статьи на английском языкеНаписание научной статьи на английском языке
Написание научной статьи на английском языке
Theoretical mechanics department
 
Casi Bench Test
Casi Bench TestCasi Bench Test
Casi Bench Test
andreipopov
 
GPS BASED DEBRIS REMOVAL SYSTEM
GPS BASED DEBRIS REMOVAL SYSTEMGPS BASED DEBRIS REMOVAL SYSTEM
GPS BASED DEBRIS REMOVAL SYSTEM
vanikkk
 
The Dynamics and Control of Axial Satellite Gyrostats of Variable Structure
The Dynamics and Control of Axial Satellite Gyrostats of Variable StructureThe Dynamics and Control of Axial Satellite Gyrostats of Variable Structure
The Dynamics and Control of Axial Satellite Gyrostats of Variable Structure
Theoretical mechanics department
 
Satellite dynamic and control
Satellite dynamic and controlSatellite dynamic and control
Satellite dynamic and control
Zuliana Ismail
 
The Operation Of Space Shuttle
The Operation Of Space ShuttleThe Operation Of Space Shuttle
The Operation Of Space Shuttle
Gokul Lakshmanan
 
Python. Обработка ошибок
Python. Обработка ошибокPython. Обработка ошибок
Python. Обработка ошибок
Theoretical mechanics department
 
GPS base Space Debris Removal System
GPS base Space Debris Removal SystemGPS base Space Debris Removal System
GPS base Space Debris Removal System
Sunil Ds
 

Viewers also liked (20)

Attitude Dynamics of Re-entry Vehicle
Attitude Dynamics of Re-entry VehicleAttitude Dynamics of Re-entry Vehicle
Attitude Dynamics of Re-entry Vehicle
 
1U-3U+ Cubesat Deployer by JSC SRC "Progress"
1U-3U+ Cubesat Deployer by JSC SRC "Progress"1U-3U+ Cubesat Deployer by JSC SRC "Progress"
1U-3U+ Cubesat Deployer by JSC SRC "Progress"
 
The Dynamics of Tethered Debris With Flexible Appendages and Residual Fuel
The Dynamics of Tethered Debris With Flexible Appendages and Residual FuelThe Dynamics of Tethered Debris With Flexible Appendages and Residual Fuel
The Dynamics of Tethered Debris With Flexible Appendages and Residual Fuel
 
Научно-исследовательская работа кафедры Теоретической механики
Научно-исследовательская работа кафедры Теоретической механикиНаучно-исследовательская работа кафедры Теоретической механики
Научно-исследовательская работа кафедры Теоретической механики
 
Deployers for nanosatellites
Deployers for nanosatellitesDeployers for nanosatellites
Deployers for nanosatellites
 
Mathematical models and analysis of the space tether systems motion
Mathematical models and analysis of the space tether systems motion Mathematical models and analysis of the space tether systems motion
Mathematical models and analysis of the space tether systems motion
 
On problems of active space debris removal using tethered towing
On problems of active space debris removal using tethered towingOn problems of active space debris removal using tethered towing
On problems of active space debris removal using tethered towing
 
Space Debris and Present Active Debris Removal Techniques
Space Debris and Present Active Debris Removal TechniquesSpace Debris and Present Active Debris Removal Techniques
Space Debris and Present Active Debris Removal Techniques
 
Space debris
Space debrisSpace debris
Space debris
 
Модификация механизма Йо-Йо
Модификация механизма Йо-ЙоМодификация механизма Йо-Йо
Модификация механизма Йо-Йо
 
Dynamics of Satellite With a Tether System
Dynamics of Satellite With a Tether SystemDynamics of Satellite With a Tether System
Dynamics of Satellite With a Tether System
 
Chaotic motions of tethered satellites with low thrust
Chaotic motions of tethered satellites with low thrust Chaotic motions of tethered satellites with low thrust
Chaotic motions of tethered satellites with low thrust
 
Написание научной статьи на английском языке
Написание научной статьи на английском языкеНаписание научной статьи на английском языке
Написание научной статьи на английском языке
 
Casi Bench Test
Casi Bench TestCasi Bench Test
Casi Bench Test
 
GPS BASED DEBRIS REMOVAL SYSTEM
GPS BASED DEBRIS REMOVAL SYSTEMGPS BASED DEBRIS REMOVAL SYSTEM
GPS BASED DEBRIS REMOVAL SYSTEM
 
The Dynamics and Control of Axial Satellite Gyrostats of Variable Structure
The Dynamics and Control of Axial Satellite Gyrostats of Variable StructureThe Dynamics and Control of Axial Satellite Gyrostats of Variable Structure
The Dynamics and Control of Axial Satellite Gyrostats of Variable Structure
 
Satellite dynamic and control
Satellite dynamic and controlSatellite dynamic and control
Satellite dynamic and control
 
The Operation Of Space Shuttle
The Operation Of Space ShuttleThe Operation Of Space Shuttle
The Operation Of Space Shuttle
 
Python. Обработка ошибок
Python. Обработка ошибокPython. Обработка ошибок
Python. Обработка ошибок
 
GPS base Space Debris Removal System
GPS base Space Debris Removal SystemGPS base Space Debris Removal System
GPS base Space Debris Removal System
 

Similar to The Removal of Large Space Debris Using Tethered Space Tug

Semi-Classical Transport Theory.ppt
Semi-Classical Transport Theory.pptSemi-Classical Transport Theory.ppt
Semi-Classical Transport Theory.ppt
VivekDixit100
 
kuramoto
kuramotokuramoto
Ch 1-3.ppt
Ch 1-3.pptCh 1-3.ppt
Ch 1-3.ppt
Rituparna Mitra
 
group 9 sec c3 .docx
group 9 sec  c3 .docxgroup 9 sec  c3 .docx
group 9 sec c3 .docx
MUSHFIQURSTUDENT
 
Design and characterization of a nano-Newton resolution thrust stand - RSI
Design and characterization of a nano-Newton resolution thrust stand - RSIDesign and characterization of a nano-Newton resolution thrust stand - RSI
Design and characterization of a nano-Newton resolution thrust stand - RSI
Jignesh Soni, PhD
 
Physics Sample Paper Class 11 - Studymate
Physics Sample Paper Class 11 - StudymatePhysics Sample Paper Class 11 - Studymate
Physics Sample Paper Class 11 - Studymate
studymateonline
 
seminar_final
seminar_finalseminar_final
seminar_final
Evgenia Virozub
 
Presentation
PresentationPresentation
Motion of the space elevator after the ribbon rupture
Motion of the space elevator  after the ribbon ruptureMotion of the space elevator  after the ribbon rupture
Motion of the space elevator after the ribbon rupture
Theoretical mechanics department
 
Master's presentation (English)
Master's presentation (English)Master's presentation (English)
Master's presentation (English)
Alexander Tsupko
 
Ch r ssm
Ch r ssmCh r ssm
Ch r ssm
Marta Díaz
 
Instantons in 1D QM
Instantons in 1D QMInstantons in 1D QM
Instantons in 1D QM
Scott Shermer
 
SVRS submission archive
SVRS submission archiveSVRS submission archive
SVRS submission archive
Timothy Chan
 
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...
Alexander Litvinenko
 
Control Synthesis for Marine Vessels in Case of Limited Disturbances
Control Synthesis for Marine Vessels in Case of Limited DisturbancesControl Synthesis for Marine Vessels in Case of Limited Disturbances
Control Synthesis for Marine Vessels in Case of Limited Disturbances
TELKOMNIKA JOURNAL
 
Platoon Control of Nonholonomic Robots using Quintic Bezier Splines
Platoon Control of Nonholonomic Robots using Quintic Bezier SplinesPlatoon Control of Nonholonomic Robots using Quintic Bezier Splines
Platoon Control of Nonholonomic Robots using Quintic Bezier Splines
Kaustav Mondal
 
Class 11 important questions for physics Friction in Soilds and Liquids
Class 11 important questions for physics Friction in Soilds and LiquidsClass 11 important questions for physics Friction in Soilds and Liquids
Class 11 important questions for physics Friction in Soilds and Liquids
Infomatica Academy
 
Q04605101105
Q04605101105Q04605101105
Q04605101105
IJERA Editor
 
IIT - JEE Main 2016 Sample Paper 3
IIT - JEE Main 2016 Sample Paper 3IIT - JEE Main 2016 Sample Paper 3
IIT - JEE Main 2016 Sample Paper 3
APEX INSTITUTE
 
Cyclones
CyclonesCyclones
Cyclones
ahkiaen
 

Similar to The Removal of Large Space Debris Using Tethered Space Tug (20)

Semi-Classical Transport Theory.ppt
Semi-Classical Transport Theory.pptSemi-Classical Transport Theory.ppt
Semi-Classical Transport Theory.ppt
 
kuramoto
kuramotokuramoto
kuramoto
 
Ch 1-3.ppt
Ch 1-3.pptCh 1-3.ppt
Ch 1-3.ppt
 
group 9 sec c3 .docx
group 9 sec  c3 .docxgroup 9 sec  c3 .docx
group 9 sec c3 .docx
 
Design and characterization of a nano-Newton resolution thrust stand - RSI
Design and characterization of a nano-Newton resolution thrust stand - RSIDesign and characterization of a nano-Newton resolution thrust stand - RSI
Design and characterization of a nano-Newton resolution thrust stand - RSI
 
Physics Sample Paper Class 11 - Studymate
Physics Sample Paper Class 11 - StudymatePhysics Sample Paper Class 11 - Studymate
Physics Sample Paper Class 11 - Studymate
 
seminar_final
seminar_finalseminar_final
seminar_final
 
Presentation
PresentationPresentation
Presentation
 
Motion of the space elevator after the ribbon rupture
Motion of the space elevator  after the ribbon ruptureMotion of the space elevator  after the ribbon rupture
Motion of the space elevator after the ribbon rupture
 
Master's presentation (English)
Master's presentation (English)Master's presentation (English)
Master's presentation (English)
 
Ch r ssm
Ch r ssmCh r ssm
Ch r ssm
 
Instantons in 1D QM
Instantons in 1D QMInstantons in 1D QM
Instantons in 1D QM
 
SVRS submission archive
SVRS submission archiveSVRS submission archive
SVRS submission archive
 
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...
 
Control Synthesis for Marine Vessels in Case of Limited Disturbances
Control Synthesis for Marine Vessels in Case of Limited DisturbancesControl Synthesis for Marine Vessels in Case of Limited Disturbances
Control Synthesis for Marine Vessels in Case of Limited Disturbances
 
Platoon Control of Nonholonomic Robots using Quintic Bezier Splines
Platoon Control of Nonholonomic Robots using Quintic Bezier SplinesPlatoon Control of Nonholonomic Robots using Quintic Bezier Splines
Platoon Control of Nonholonomic Robots using Quintic Bezier Splines
 
Class 11 important questions for physics Friction in Soilds and Liquids
Class 11 important questions for physics Friction in Soilds and LiquidsClass 11 important questions for physics Friction in Soilds and Liquids
Class 11 important questions for physics Friction in Soilds and Liquids
 
Q04605101105
Q04605101105Q04605101105
Q04605101105
 
IIT - JEE Main 2016 Sample Paper 3
IIT - JEE Main 2016 Sample Paper 3IIT - JEE Main 2016 Sample Paper 3
IIT - JEE Main 2016 Sample Paper 3
 
Cyclones
CyclonesCyclones
Cyclones
 

More from Theoretical mechanics department

Космический мусор
Космический мусорКосмический мусор
Космический мусор
Theoretical mechanics department
 
Основы SciPy
Основы SciPyОсновы SciPy
Основы NumPy
Основы NumPyОсновы NumPy
Python. Объектно-ориентированное программирование
Python. Объектно-ориентированное программирование Python. Объектно-ориентированное программирование
Python. Объектно-ориентированное программирование
Theoretical mechanics department
 
Python: ввод и вывод
Python: ввод и выводPython: ввод и вывод
Python: ввод и вывод
Theoretical mechanics department
 
Python: Модули и пакеты
Python: Модули и пакетыPython: Модули и пакеты
Python: Модули и пакеты
Theoretical mechanics department
 
Основы Python. Функции
Основы Python. ФункцииОсновы Python. Функции
Основы Python. Функции
Theoretical mechanics department
 
Основы языка Питон: типы данных, операторы
Основы языка Питон: типы данных, операторыОсновы языка Питон: типы данных, операторы
Основы языка Питон: типы данных, операторы
Theoretical mechanics department
 
Машинная арифметика. Cтандарт IEEE-754
Машинная арифметика. Cтандарт IEEE-754Машинная арифметика. Cтандарт IEEE-754
Машинная арифметика. Cтандарт IEEE-754
Theoretical mechanics department
 
Docking with noncooperative spent orbital stage using probe-cone mechanism
Docking with noncooperative spent orbital stage using probe-cone mechanismDocking with noncooperative spent orbital stage using probe-cone mechanism
Docking with noncooperative spent orbital stage using probe-cone mechanism
Theoretical mechanics department
 
Алгоритмы и языки программирования
Алгоритмы и языки программированияАлгоритмы и языки программирования
Алгоритмы и языки программирования
Theoretical mechanics department
 
CubeSat separation dynamics
CubeSat separation dynamicsCubeSat separation dynamics
CubeSat separation dynamics
Theoretical mechanics department
 
Chaotic Behavior of a Passive Satellite During Towing by a Tether
Chaotic Behavior of a Passive Satellite During Towing by a TetherChaotic Behavior of a Passive Satellite During Towing by a Tether
Chaotic Behavior of a Passive Satellite During Towing by a Tether
Theoretical mechanics department
 
Основы MATLAB. Численные методы
Основы MATLAB. Численные методыОсновы MATLAB. Численные методы
Основы MATLAB. Численные методы
Theoretical mechanics department
 
Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+
Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+
Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+
Theoretical mechanics department
 
Методы решения нелинейных уравнений
Методы решения нелинейных уравненийМетоды решения нелинейных уравнений
Методы решения нелинейных уравнений
Theoretical mechanics department
 
Наноспутники формата кубсат
Наноспутники формата кубсатНаноспутники формата кубсат
Наноспутники формата кубсат
Theoretical mechanics department
 
Отделение створок головного обтекателя
Отделение створок головного обтекателяОтделение створок головного обтекателя
Отделение створок головного обтекателя
Theoretical mechanics department
 
Метод Кейна
Метод КейнаМетод Кейна
Метод Кейна
Theoretical mechanics department
 
Метод отдельных тел
Метод отдельных телМетод отдельных тел
Метод отдельных тел
Theoretical mechanics department
 

More from Theoretical mechanics department (20)

Космический мусор
Космический мусорКосмический мусор
Космический мусор
 
Основы SciPy
Основы SciPyОсновы SciPy
Основы SciPy
 
Основы NumPy
Основы NumPyОсновы NumPy
Основы NumPy
 
Python. Объектно-ориентированное программирование
Python. Объектно-ориентированное программирование Python. Объектно-ориентированное программирование
Python. Объектно-ориентированное программирование
 
Python: ввод и вывод
Python: ввод и выводPython: ввод и вывод
Python: ввод и вывод
 
Python: Модули и пакеты
Python: Модули и пакетыPython: Модули и пакеты
Python: Модули и пакеты
 
Основы Python. Функции
Основы Python. ФункцииОсновы Python. Функции
Основы Python. Функции
 
Основы языка Питон: типы данных, операторы
Основы языка Питон: типы данных, операторыОсновы языка Питон: типы данных, операторы
Основы языка Питон: типы данных, операторы
 
Машинная арифметика. Cтандарт IEEE-754
Машинная арифметика. Cтандарт IEEE-754Машинная арифметика. Cтандарт IEEE-754
Машинная арифметика. Cтандарт IEEE-754
 
Docking with noncooperative spent orbital stage using probe-cone mechanism
Docking with noncooperative spent orbital stage using probe-cone mechanismDocking with noncooperative spent orbital stage using probe-cone mechanism
Docking with noncooperative spent orbital stage using probe-cone mechanism
 
Алгоритмы и языки программирования
Алгоритмы и языки программированияАлгоритмы и языки программирования
Алгоритмы и языки программирования
 
CubeSat separation dynamics
CubeSat separation dynamicsCubeSat separation dynamics
CubeSat separation dynamics
 
Chaotic Behavior of a Passive Satellite During Towing by a Tether
Chaotic Behavior of a Passive Satellite During Towing by a TetherChaotic Behavior of a Passive Satellite During Towing by a Tether
Chaotic Behavior of a Passive Satellite During Towing by a Tether
 
Основы MATLAB. Численные методы
Основы MATLAB. Численные методыОсновы MATLAB. Численные методы
Основы MATLAB. Численные методы
 
Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+
Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+
Транспортно-пусковой контейнер для наноспутников типоразмера 3U, 3U+
 
Методы решения нелинейных уравнений
Методы решения нелинейных уравненийМетоды решения нелинейных уравнений
Методы решения нелинейных уравнений
 
Наноспутники формата кубсат
Наноспутники формата кубсатНаноспутники формата кубсат
Наноспутники формата кубсат
 
Отделение створок головного обтекателя
Отделение створок головного обтекателяОтделение створок головного обтекателя
Отделение створок головного обтекателя
 
Метод Кейна
Метод КейнаМетод Кейна
Метод Кейна
 
Метод отдельных тел
Метод отдельных телМетод отдельных тел
Метод отдельных тел
 

Recently uploaded

From Natural Language to Structured Solr Queries using LLMs
From Natural Language to Structured Solr Queries using LLMsFrom Natural Language to Structured Solr Queries using LLMs
From Natural Language to Structured Solr Queries using LLMs
Sease
 
Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...
Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...
Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...
manji sharman06
 
Christine's Supplier Sourcing Presentaion.pptx
Christine's Supplier Sourcing Presentaion.pptxChristine's Supplier Sourcing Presentaion.pptx
Christine's Supplier Sourcing Presentaion.pptx
christinelarrosa
 
MySQL InnoDB Storage Engine: Deep Dive - Mydbops
MySQL InnoDB Storage Engine: Deep Dive - MydbopsMySQL InnoDB Storage Engine: Deep Dive - Mydbops
MySQL InnoDB Storage Engine: Deep Dive - Mydbops
Mydbops
 
The Microsoft 365 Migration Tutorial For Beginner.pptx
The Microsoft 365 Migration Tutorial For Beginner.pptxThe Microsoft 365 Migration Tutorial For Beginner.pptx
The Microsoft 365 Migration Tutorial For Beginner.pptx
operationspcvita
 
Day 2 - Intro to UiPath Studio Fundamentals
Day 2 - Intro to UiPath Studio FundamentalsDay 2 - Intro to UiPath Studio Fundamentals
Day 2 - Intro to UiPath Studio Fundamentals
UiPathCommunity
 
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk
"Frontline Battles with DDoS: Best practices and Lessons Learned",  Igor Ivaniuk"Frontline Battles with DDoS: Best practices and Lessons Learned",  Igor Ivaniuk
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk
Fwdays
 
Must Know Postgres Extension for DBA and Developer during Migration
Must Know Postgres Extension for DBA and Developer during MigrationMust Know Postgres Extension for DBA and Developer during Migration
Must Know Postgres Extension for DBA and Developer during Migration
Mydbops
 
AWS Certified Solutions Architect Associate (SAA-C03)
AWS Certified Solutions Architect Associate (SAA-C03)AWS Certified Solutions Architect Associate (SAA-C03)
AWS Certified Solutions Architect Associate (SAA-C03)
HarpalGohil4
 
"Scaling RAG Applications to serve millions of users", Kevin Goedecke
"Scaling RAG Applications to serve millions of users",  Kevin Goedecke"Scaling RAG Applications to serve millions of users",  Kevin Goedecke
"Scaling RAG Applications to serve millions of users", Kevin Goedecke
Fwdays
 
What is an RPA CoE? Session 2 – CoE Roles
What is an RPA CoE?  Session 2 – CoE RolesWhat is an RPA CoE?  Session 2 – CoE Roles
What is an RPA CoE? Session 2 – CoE Roles
DianaGray10
 
A Deep Dive into ScyllaDB's Architecture
A Deep Dive into ScyllaDB's ArchitectureA Deep Dive into ScyllaDB's Architecture
A Deep Dive into ScyllaDB's Architecture
ScyllaDB
 
PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx
PRODUCT LISTING OPTIMIZATION PRESENTATION.pptxPRODUCT LISTING OPTIMIZATION PRESENTATION.pptx
PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx
christinelarrosa
 
Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf
Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdfLee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf
Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf
leebarnesutopia
 
Demystifying Knowledge Management through Storytelling
Demystifying Knowledge Management through StorytellingDemystifying Knowledge Management through Storytelling
Demystifying Knowledge Management through Storytelling
Enterprise Knowledge
 
GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...
GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...
GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...
GlobalLogic Ukraine
 
"Choosing proper type of scaling", Olena Syrota
"Choosing proper type of scaling", Olena Syrota"Choosing proper type of scaling", Olena Syrota
"Choosing proper type of scaling", Olena Syrota
Fwdays
 
QA or the Highway - Component Testing: Bridging the gap between frontend appl...
QA or the Highway - Component Testing: Bridging the gap between frontend appl...QA or the Highway - Component Testing: Bridging the gap between frontend appl...
QA or the Highway - Component Testing: Bridging the gap between frontend appl...
zjhamm304
 
Apps Break Data
Apps Break DataApps Break Data
Apps Break Data
Ivo Velitchkov
 
Y-Combinator seed pitch deck template PP
Y-Combinator seed pitch deck template PPY-Combinator seed pitch deck template PP
Y-Combinator seed pitch deck template PP
c5vrf27qcz
 

Recently uploaded (20)

From Natural Language to Structured Solr Queries using LLMs
From Natural Language to Structured Solr Queries using LLMsFrom Natural Language to Structured Solr Queries using LLMs
From Natural Language to Structured Solr Queries using LLMs
 
Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...
Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...
Call Girls Chandigarh🔥7023059433🔥Agency Profile Escorts in Chandigarh Availab...
 
Christine's Supplier Sourcing Presentaion.pptx
Christine's Supplier Sourcing Presentaion.pptxChristine's Supplier Sourcing Presentaion.pptx
Christine's Supplier Sourcing Presentaion.pptx
 
MySQL InnoDB Storage Engine: Deep Dive - Mydbops
MySQL InnoDB Storage Engine: Deep Dive - MydbopsMySQL InnoDB Storage Engine: Deep Dive - Mydbops
MySQL InnoDB Storage Engine: Deep Dive - Mydbops
 
The Microsoft 365 Migration Tutorial For Beginner.pptx
The Microsoft 365 Migration Tutorial For Beginner.pptxThe Microsoft 365 Migration Tutorial For Beginner.pptx
The Microsoft 365 Migration Tutorial For Beginner.pptx
 
Day 2 - Intro to UiPath Studio Fundamentals
Day 2 - Intro to UiPath Studio FundamentalsDay 2 - Intro to UiPath Studio Fundamentals
Day 2 - Intro to UiPath Studio Fundamentals
 
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk
"Frontline Battles with DDoS: Best practices and Lessons Learned",  Igor Ivaniuk"Frontline Battles with DDoS: Best practices and Lessons Learned",  Igor Ivaniuk
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor Ivaniuk
 
Must Know Postgres Extension for DBA and Developer during Migration
Must Know Postgres Extension for DBA and Developer during MigrationMust Know Postgres Extension for DBA and Developer during Migration
Must Know Postgres Extension for DBA and Developer during Migration
 
AWS Certified Solutions Architect Associate (SAA-C03)
AWS Certified Solutions Architect Associate (SAA-C03)AWS Certified Solutions Architect Associate (SAA-C03)
AWS Certified Solutions Architect Associate (SAA-C03)
 
"Scaling RAG Applications to serve millions of users", Kevin Goedecke
"Scaling RAG Applications to serve millions of users",  Kevin Goedecke"Scaling RAG Applications to serve millions of users",  Kevin Goedecke
"Scaling RAG Applications to serve millions of users", Kevin Goedecke
 
What is an RPA CoE? Session 2 – CoE Roles
What is an RPA CoE?  Session 2 – CoE RolesWhat is an RPA CoE?  Session 2 – CoE Roles
What is an RPA CoE? Session 2 – CoE Roles
 
A Deep Dive into ScyllaDB's Architecture
A Deep Dive into ScyllaDB's ArchitectureA Deep Dive into ScyllaDB's Architecture
A Deep Dive into ScyllaDB's Architecture
 
PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx
PRODUCT LISTING OPTIMIZATION PRESENTATION.pptxPRODUCT LISTING OPTIMIZATION PRESENTATION.pptx
PRODUCT LISTING OPTIMIZATION PRESENTATION.pptx
 
Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf
Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdfLee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf
Lee Barnes - Path to Becoming an Effective Test Automation Engineer.pdf
 
Demystifying Knowledge Management through Storytelling
Demystifying Knowledge Management through StorytellingDemystifying Knowledge Management through Storytelling
Demystifying Knowledge Management through Storytelling
 
GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...
GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...
GlobalLogic Java Community Webinar #18 “How to Improve Web Application Perfor...
 
"Choosing proper type of scaling", Olena Syrota
"Choosing proper type of scaling", Olena Syrota"Choosing proper type of scaling", Olena Syrota
"Choosing proper type of scaling", Olena Syrota
 
QA or the Highway - Component Testing: Bridging the gap between frontend appl...
QA or the Highway - Component Testing: Bridging the gap between frontend appl...QA or the Highway - Component Testing: Bridging the gap between frontend appl...
QA or the Highway - Component Testing: Bridging the gap between frontend appl...
 
Apps Break Data
Apps Break DataApps Break Data
Apps Break Data
 
Y-Combinator seed pitch deck template PP
Y-Combinator seed pitch deck template PPY-Combinator seed pitch deck template PP
Y-Combinator seed pitch deck template PP
 

The Removal of Large Space Debris Using Tethered Space Tug

  • 1. 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
  • 2. 1. Active debris removal techniques 2. Tethered space tug 3. Mathematical model 4. Numerical simulation and analysis 5. Results and conclusion 2 Outline
  • 3. • 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
  • 4. 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
  • 5. 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. 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. 7 3. Mathematical model General Provisions  Model = rigid body (large debris) + tether + material point (space tug) Weightless viscoelastic tether
  • 8. 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:
  • 9. ( , , , , , )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
  • 10. 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
  • 11. • 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
  • 12. 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.
  • 13. • 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
  • 14. 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. 15 4. Numerical simulation and analysis Case 1. Tensioned tether 0(0) , 0, 0T Tl l c d   / 6 
  • 16. 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. 17 4. Numerical simulation and analysis Case 2. Slackened tether 0(0) , 0, 0T Tl l c d   / 6 
  • 18. • 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. 19 4. Numerical simulation and analysis Damped tether 0(0) , 0Tl l c  / 6  0Td 
  • 20. • 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
  • 21. • 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 ]
  • 22. 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
  • 23. • Passive braking system produce low torque relative to the center of mass 23 4. Numerical simulation and analysis Passive braking system Drag force
  • 24. 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
  • 25.  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.
  • 26. 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
  • 27. 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
  • 28. 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.
  • 29. Thank you for your attention Questions? Presentation is available at http://aslanov.ssau.ru Contacts aslanov@mail.ru yudintsev@classmech.ru 29