Commercial Strategy for Addressing Growing Orbit Debris as Private Firm

Commercial Strategy for Addressing Orbit
Debris Problem as A Private Firm
February 8, 2016
1

Control Number 54097
Contents
1 Introduction 3
2 Problem Statement 4
2.1 Definition of space debris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Effect of space debris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Theoretical Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 The space junk removal concept 5
4 Economic Analysis of Space Junk Removal Program 7
5 VaR Analysis of Orbits 8
5.1 Deduced Value of Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.2 Cost-Benefit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.3 Comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6 Cost Estimation Technique 10
6.1 Estimated cost per kg deorbited . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.2 Estimate Cost per Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.3 Advanced Missions Cost Model Brady Kalb . . . . . . . . . . . . . . . . . . . . 11
6.4 Cost Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.5 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7 Sensitive Analysis of the profit 13
8 Conclusion 14

Abstract
In this report, we embark on finding the most efficient strategy or combination
of strategies of the space junk Removal program using VaR Analysis and Cost
Estimation Technique. Above all, there are some commercial opportunities
in this area after the logical economic analysis of this program. Moreover,
some mature and available methods can be used here as the solid technological
background to run this project. After searching and analysing data from official
organization using our models, the costs and benefits can be approximately
estimated respectively as the items of final profit model. Although there are
quit expensive for the equipment and it seems impossible at the moment, the
cost will be reduced along with the development of the relevant technique.
This program can generate considerable benefit from our analysis of models. In
conclusion, we recommend private firm to consider running this program as a
long-term commercial program.
1 Introduction
In 2010, the U.S. President Barack Obamas National Space Policy was pub-
lished. It simply directs NASA and the Defense Department to perform re-
search and development of technologies and techniques to mitigate and remove

on-orbit debris, reduce hazards, and increase understanding of the current and
future debris environment[12]. In June 2014, NASA adopted a policy to sup-
port development of orbital debris removal technology. According to NASA
spokesman Joshua Buck in an emailed response to a question about the policy
on June 8, there is no viable technological or economically affordable approach
that is sufficiently mature to justify technology demonstration at present[3].
In Switzerland, engineers at the cole Polytechnique Fdrale de Lausanne are de-
signing Clean Space One, a spacecraft to catch a cubesat and move it to Earths
atmosphere. Astroscale, a startup based in Singapore, is preparing to launch a
dual-satellite Active Debris Removal System in 2017. The German Aerospace
Center, DLR, plans to begin servicing spacecraft in orbit and removing debris
through its Deutsche Orbital Servicing Mission scheduled to launch in 2018[12].
In this report, we are going to evaluate the economic viability of the devel-
oping SOLDIER vehicle project. The concept of the project and the principle
how the SOLDIER vehicle works are included at first. Then, the Value at Risk
Model and Advanced Mission Cost Model are employed to check the benefit
and the cost of the project respectively[8]. Furthermore, a sensitive analysis of
the whole profit is performed to show the viability.
2 Problem Statement
2.1 Definition of space debris
The collection of defunct artificial objects in orbit around Earth is called space
debris such as old satellites, exhausted rocket stages, and fragments from dis-
integration, erosion, and collisions including those caused by debris itself.
NASA (the National Aeronautics and Space Administration) defines space de-
bris as all man-made objects in orbit about the Earth which no longer serve a
useful purpose[13].
2.2 Effect of space debris
A small piece of space debris could blow the satellite into thousands of frag-
ments, due to the huge energy, which is released during the process when debris
with high velocities crashes satellite. After such an accident, a thousand pieces
of debris will be generated, which increases the probabilities of occurrence of
such potential crash events[2]. Although these pieces of debris will be clustered

at the beginning, overtime, they will disperse due to the regression of node.
After the impact of the gravitational force from sun, moon and earth, and they
will almost completely encircle the earth within one year; which implies the
worldwide risk caused by the fragmentation event[11].
2.3 Theoretical Backgrounds
The Six Kepler Elements:
In order to define the position and velocity for the space object, it is normal
to use set of orbital parameters. We will use the six Kepler elements in our
simulation: a: the semimajor axis;
e: the eccentricity;
i: the inclination;
Ω The right ascension of ascending node;
ω : The argument of perigee;
M: the mean anomaly[11].
Kepler’s Laws
In astronomy, Keplers laws of planetary motion are three scientific laws describ-
ing the motion of planets around the sun. The orbit of a planet is an ellipse
with the sun at one of the two foci. A line segment joining a planet and the
sun sweeps out equal areas during equal intervals of time. The square of the
orbital period of a planet is proportional to the cube of the semi-major axis of
its orbit[4].
The Classical Equation For Kinetic Energy
In this model, the classical equation for kinetic energy for the satellite indicated
by the space junk is as follow:
Ek =
1
2
mSDv2
pas (1)
where Ek[J] is the kinetic energy, mSD is the mass of the Space Debris, and
vpas is the speed between the satellite and the space debris.
3 The space junk removal concept
The risk of orbital debris has been highlighted as a major forthcoming issue for
space vehicle safety and operations. According to NASA, five derelict satellites
must be safely removed from low Earth orbit (LEO) every year in order to keep
the risk of orbital debris from escalating. To solve this problem, SOLDIER

was designed as a concept vehicle to respond to these growing needs[5]. The
SOLDIER vehicle is a small one-time use satellite, which is launched to target
a single derelict satellite, performs close proximity operations around the target
satellite, attaches to the target using a tethered lance and then re-enters with
the attached target to dispose of it safely[6]. This section will cover the gen-
eral design of the SOLDIER concept and its primary functionality as a ’large
category orbital debris remover’. At the same time, the issue of capturing the
rotating targets will be investigated.
The SOLDIER concept was developed to remove large size space junks such as
spacecraft and large remains of launch operations or in-orbit breakups. Since
there are still lots of small size space junks, it can not solve the problem of orbit
debris completely[6]. However, it can be applied to the area of the problem with
a high benefit to-cost ratio. In this way, this concept may not only be a good
approach for the governments but also could become an economically viable
business case. Once the large size space junks are removed, it will effectively
reduce the risk of collision of large size space junks. Hence, it will reduce the
amount of the small size space junks generated by collision which are hard to
detect and remove[6]. From this aspect, there are considerable benefits in the
long term.
This part will move on to show how this SOLDIER vehicle works. The SOL-
DIER vehicle uses a tethered lance or harpoon to catch the target. A simple
simulation of the capture will be carried out in the following context[6].
Parameters denoted:
θ1= Yaw angle between cable and target capture plane
θ2= Pitch angle between cable and target capture plane
ω1=Yaw rate
ω2=Pitch rate
H1=Yaw component target momentum
H2=Pitch component target momentum
FT = Force on target
rt = Distance from target center of gravity to capture point
I = Target moment of inertia
Assumption
1. The capture mechanism is connected securely and it hits the target.
2. Thrusters are actuated immediately upon contact (the cable is always under

tension)
3. The SOLDIER vehicle is controlled to be relatively stationary to the target
debris.
4. The target is a cube with evenly distributed mass and the rotation about
the axis of the cable is ignored.


H1
H2

 = cos


θ1
θ2

 FT rt (2)


ω1
ω2

 =


H1
H2

 /I (3)


θ1
θ2

 = cos


ω1
ω2

 (4)
The equations above represent the dynamic model showing that the force acts
oppositely to the direction of rotation as a corrective or stabilizing force. The
purpose of the simulation is to show that the angular momentum of the target
debris can be controlled via this cable under tension[3]. Because the model
is simple, a simple controller (proportional momentum controller) is used to
throttle the thrust and damp the momentum.
We want to show the simulated cable angle from normal with debris target over
the ﬁrst 30 minutes of capture. (simulation outcome)
4 Economic Analysis of Space Junk Removal Program
Figure 1

In the wake of developments in science and technology, the amount of the
launched spacecraft increases rapidly, bringing about 300,000 pieces of debris
which has enough size to destroy the satellite[8]. While insurance fees can be
used as reference for this project, the insurance premium against space risk
was up to $800 million in 2011 and losses due to damage valued $600 million.
Based on this situation, there may be some economic opportunities for private
firm to dig out new profit target[1]. In this section, we will analyse the value
of this potential commercial opportunity, and conclude some efficient strategy
or combination of strategies for private company to make profits in space junk
removal Program.
The purpose of this report is to dig out the possible maximum profits of Space
Junk Removal Program by considering expected cost and benefit under possi-
ble risk conditions. Since this program aims to eliminate the possible threat
of satellites, then the profits are achieved from the revenue of the global satel-
lite revenue in 2014, which valued totally $195.2 billion[1]. By considering the
possible risk percentage and the global satellites’ revenue, the benefit can be
estimated and predicted by using following models based on the past several
years’ data.
Next step is to minimize the cost of our mission. It’s conventional wisdom
that there are three orbits including Low Earth orbit (LEO) with altitudes
up to 2,000 km, Medium Earth orbit (MEO) with altitudes from 2,000 km to
35,786 km, and High Earth orbit above the altitude of geosynchronous orbit.
Since the majority of satellites circled around LEO, it’s efficient just to consider
removing space junk with short distance from earth surface. From this aspect,
the cost can be reduced and the profit can be increased[10]. As for the following
sections, the models are established only for orbit debris in LEO.
5 VaR Analysis of Orbits
5.1 Deduced Value of Orbits
It’s a conventional wisdom that the cost of active removal for orbital junk is
really expensive, and the debris is useless. Based on the futility of debris itself,
the risk of its removal and reduction missions seem significant to be considered.
The focus here is not who is the purchaser here, however, space systems com-

panies, government and inter-governmental agencies, and insurance companies
can be considered as the possible responsible party for payment.
The aim of this method is to supply measurement for impact of system like
SOLDIER acting on the debris management. Two models involved in this
measurement including a value model and a risk model. Specifically, the value
model emphasizes the measure of the benefits obtained from a space system
or group of systems. For instance, Eq.(5) is a value model over time with the
value - v obtained from the space asset, and v is treated as a constant over the
life of the space asset or assets. Moreover, the potential loss can be caused by
some risk to this asset, which can decrease the expected value over time. The
less anticipated value in the future is valued when the some specific scenario
occur. Then exponential decay can be used here to represent this value, which
is also called discount rate of future return[6].
V (t) = [1 − R(t)]ve−dt
(5)
R(t) = 1 − e−γt
(6)
As for this model, the risk could be measured as a value between 0 and 1 rep-
Figure 2
resenting the probability of mission-ending collision, which increases with the
growth parameter γ. The limitation of this model is that it doesn’t consider
the additional secondary affections of space junk[8]. The first threat is that it

will collide with a functioning space asset if the decrepit satellites are left in
a congesting space. The second threat is that the added smaller debris cloud
after break up could cause threat for satellites in the closed orbital regime[6].
The amount of anticipated value increase is the metric for the success of space
waste, which is caused by the decrease of risk growth parameter.
5.2 Cost-Benefit Analysis
Applying the value and risk models above, it’s obvious that the anticipative
value could change based on the reduction of the risk growth parameter γ. It
is assumed that the value for γ and d are 0.05 and 6% respectively. Obviously
the null hypothesis is that there is no risk in this case, the yellow line can be
obtained in Figure 1 as the changes of the value over time. If the value of γ is
0.05 (the maximum risk parameter), the blue line can be used to instead the
changes. By reducing γ by 0.01 each time, the expected value will lie in the
area between yellow and blue line. For example, the assumed value of γ is 0.04
and this value yields red line as the new anticipative value[6].
In this design reference condition, this figure also can indicate the alterations
in value curve over the lifetime of the notional space substance. Following the
growth of the risk, the expected value reduces along with time. Moreover, the
present value of future profits will be discounted for some rate. However, the
risk will decline with decreasing amount of the debris, while total value will
increase at this case[1].
5.3 Comment
Since this model doesn’t consider the secondary effects of the space junk, the
risk parameter is the same as primary value all the time, which is generated
by the exciting space waste. This model can be improved by considering the
secondary impact of the collision of the debris itself as the new parameter for
further more precise modelling.
6 Cost Estimation Technique
There are mainly two methods to estimate the cost which is estimated cost per
mission and estimated cost per kg deorbited.

6.1 Estimated cost per kg deorbited
The estimated cost per kg de-orbited (ECD) is a measure of the cost in the re-
lation to the missions capability. ECD will define the cost-effectiveness for the
analysed missions. The Active Debris Removal projects are sometimes accused
to be not efficient[7].
6.2 Estimate Cost per Mission
The estimate cost per mission (ECM) is a measure of the total cost of the mis-
sion.
We will mainly focus on the estimate cost per mission (ECM) to estimate
the cost of the system. In the following sections, Advanced Missions Cost
Model is introduced. AMCM provides a useful method for quick turnaround,
rough-order-of-magnitude estimating. The model can be used for estimating the
development and production cost of spacecraft, space transportation systems,
aircraft, missiles, ships, and land vehicles[7].
6.3 Advanced Missions Cost Model Brady Kalb
The parameters involved in the models are denoted as below
α = 5.56 x 10−4
β = 0.5941
Ξ = 0.6604
δ = 80.599
ε = 3.8085 x 10−55
ϕ = -0.3553
γ = 1.5691
= Quantity
M = Dry Mass (lbs)
S = Specification
IOC = Initial Operating Capability
B = Block Number
D = Difficulty
Table 1 AMCM Variable Descriptions

Variable Description
Q Quantity Number of vehicles to be produced
M Mass Dry mass of the vehicle in pounds, does not include fuel or consumables
S Specification Value that designates type of mission
IOC Initial Operating Capability Systems first year of operation
B Block Number Represents level of design inheritance
D Difficulty Number ranging from -2.5 to 2.5 representing difficulty of production
The formula expression is :
Cost = α β
MΞ
δs
ε
1
IOC−1900 Bϕ
γD
(7)
This cost estimation technique can be used to determine the overall cost of
the project. It was developed at NASA Johnson, and has been used on nearly
every major NASA project in the last 15 years. The advanced mission model
is driven mainly by the dry mass of the vehicle. The variables involved in the
formula is shown in the table above with brief descriptions[7].
6.4 Cost Estimation Results
Subsystem Mass (kg)
Payload 100
Structure 50
Thermal 11
Attitude Control 20
Power 66
Communication 13
Propulsion(dry) 16
Propellant 275
Total 551
From the AMCM model, the estimated total cost is $47 million.
CostPerY ear = A(10F2
− 20F3
+ 10F4
) + B(10F3
− 20F4
+ 10F5
) + 5F4
− 4F5
) (8)
In order for the project to be feasible, the cost in any given year must not
exceed the proposed yearly budget. NASA currently having a yearly budget of
approximately $15 Billion. The cost per year schedule shown above was found
using a 60% Beta Curve. The equation for the 60% Beta Curve is shown as
Eq.(8), where A is 0.32, B is 0.68, and F, the time fraction, is the percentage
of the project development completed in a given year.

6.5 Comments
Although some portions of the spacecraft have not been included in this cost
analysis (storage section, fuel tanks, and propellant costs), these costs are mini-
mal, and will not greatly affect the estimated cost. The storage section and fuel
tanks are essentially cylinders, which can be constructed with great simplicity.
While the amount of fuel used in the mission is quite large, fuel is relatively
inexpensive when compared to the development and production costs of the
spacecraft.
7 Sensitive Analysis of the profit
In the beginning, it is assumed that the project lasted 5 years. From the
outcome simulated by Matlab, the total benefit is gained. At the same time,
according to the AMCM calculator, the total cost is estimated to be 47 millions.
Then a sensitive analysis of the profit is performed and three different cases are
considered. 1. In the optimistic case, if the derived value of the project without
risk model is considered, the total benefit of the project is estimated to be 225
million dollars. The profit is estimated to be 178 million dollars.
2. In the normal case, if the derived value of the project with the risk growth
parameter 0.04, the total benefit of the project is estimated to be 180 million
dollars. The profit is estimated to be 133 million dollars.
3. In the pessimistic case, if the derived value of the project with the risk
growth parameter 0.05, the total benefit of the project is estimated to be 180
million dollars. The profit is estimated to be 128 million dollars.
The estimations are listed in the following table:
Scenarios Profit (million dollars )
Optimistic 178
Normal 133
Pessimistic 128
To sum up, there exists a commercial opportunity for the private firm even in
the pessimistic case. The estimated profit of the firm is between the interval
128-178 million dollars with risk growth parameter from 0 to 0.05. However,
many other complex situations are still needed to be considered which can make
the result more accurate.

8 Conclusion
From the simulation results, it is concluded that there exists a viable commer-
cial opportunity which will bring about profits of million dollars. Although it
seems impractical in the real world at present, this space debris removal tech-
nology tends to be viable and profitable in the near future. Going forward,
the US government needs to work closely with the commercial sector in this
endeavor, focusing on removing pieces of US debris with the greatest potential
to contribute to future collisions[3]. In the meantime, it may also keep its space
debris removal system as open and transparent as possible to allow for future
international cooperation in this field. According to the United Nations 1967
Outer Space Treaty, space-based objects including spent rocket boosters and
satellite fragments, belong to the nation or nations that launched them. Hence,
international coordination would be required for any sustained effort to capture
and remove debris because many nations have contributed to the problem[9].
Although leadership in space debris removal will entail certain risks, investing
early in preserving the near-Earth space environment is necessary to protect the
satellite technology that is so vital to US military and day-to-day operations
of the global economy. By instituting global space debris removal measures, a
critical opportunity exists to mitigate and minimize the potential damage of
space debris and ensure the sustainable development of the near-Earth space
environment.

References
[1] Alexander William Salter (2015), A Law and Economics Analysis of the
Orbital Commons. 3434 WashingtonBlvd, 4th Floor, Arlington, Virginal:
George Mason University.
[2] Allianz, Space Risks: A New Generation of Challenges 2 (Allianz Global
Corporate and Specialty, Working Paper No. WP/IC/0612, 2012),
https://www.allianz.com/v1342876324000/media/press/document/agcsspacerisk
[3] Esa (2013) DEBRIS REMOVAL,
Available at:http://www.esa.int/Our Activities/Operations/Space Debris/
(Accessed: 31th January 2016).
[4] James Mason, Jan Stupl, William Marshall and Creon Levit (2011), Orbital
Debris-Debris Collision Avoidance.Cornell University Library.
[5] J.-C. Liou (2010) An Assessment of the Current LEO Debris Environment
and the Need for Active Debris Removal. HoustonTexas: NASA Orbital
Debris Program Office Johnson Space Center.
[6] Joshua J. Loughman (2010) Overview and Analysis of the SOLDIER Satel-
lite Concept for Removal of Space Debris. Orbital Sciences Corporation,
Gilbert: Orbital Sciences Corporation.
[7] Larson, Wiley J. and Pranke, Linda K. (2004) Human Spaceflight Mission
Analysis and Design. New York: McGraw Hill.
[8] Matteo Emanuelli et al. (2013) CONCEPTUALIZING AN ECONOMI-
CALLY, LEGALLY AND POLITICALLY VIABLE ACTIVE DEBRIS
REMOVAL OPTION. Beijing, China, 64th International Astronautical
Congress.
[9] ]Megan Ansdell (2010) ACTIVE SPACE DEBRIS REMOVAL: NEEDS,
IMPLICATION, AND RECOMMENDATIONS FOR TODAY’S GEOPO-
LITICAL ENVIRONMENT. Journal of Public and International Affairs.
[10] KNASA Orbital Debris Program Office (2012) Orbital Debris
http://orbitaldebris.jsc.nasa.gov/faqs.html (Accessed: 31th Jan-
uary 2016).
[11] Thomas Iversen Bredeli (2013) Modeling and simulation of space debris
distribution. Narvik University College.

[12] Debra Werner (2015). NASAs Interest in Removal of Orbital Debris
Limited to Tech Demos
http://spacenews.com/nasas-interest-in-removal-of-orbital-debris-limite
02/01/2016)
[13] KNASA Orbital Debris Program Oﬃce (2012) Orbital Debris
http://orbitaldebris.jsc.nasa.gov/faqs.html (Accessed: 31th Jan-
uary 2016
[14] Stephen Messenger (2012) Self-Destructing Janitor Satellite to Clean Up
Space
http://www.treehugger.com/clean-technology/outer-space-no-one-can-hear-
(Accessed: 1st January 2016).

Appendix
For VaR Model
r1=0.05;r2=0.04;r3=0;
% risk model growth parameter
d=0.06;
% value model discount parameter
v=300000000;
% commmerial satellite revenue
t=0:20;
% 20 years with interval 1 year
R1=1-exp(-r1.*t); % risk model
V1=(1-R1).*v.*exp(-d.*t); % value model
R2=1-exp(-r2.*t);
V2=(1-R2).*v.*exp(-d.*t);
R3=1-exp(-r3.*t);
V3=(1-R3).*v.*exp(-d.*t);
plot(t,V1,t,V2,t,V3,'LineWidth',4)
grid on
xlabel('Time[yrs]')
ylabel('Present[$]')
title('Value Effect on Debris Risk Reduction')
legend('Derived Value','Derived Value with Reduced Risk','Derived Value without risk mo
For Cost Estimation Technique
alpha = 5.56 * 10ˆ(-4);
beta = 0.5941;
xi = 0.6604;
delta = 80.599;
epsilon = 3.8085 * 10ˆ(-55);
Psi = -0.3553;
Gamma = 1.5691;
Q= input('Input Q please:');
M= input('Input M please:');
S= input('Input S please:');
IOC= input('Input IOC please:');
B= input('Input B please:');
D= input('Input D please:');
Cost = alpha* Qˆbeta*Mˆxi*deltaˆS*epsilonˆ(1/(IOC-1900))*BˆPsi*GammaˆD;
disp(Cost)
A = 0.32;
B = 0.68;
F = input('Input F please:'); % time fraction
CostPerYear = A*(10*Fˆ2-20*Fˆ3+10*Fˆ4)+B*(10*Fˆ3-20*Fˆ4+10*Fˆ5)+5*Fˆ4-4*Fˆ5;
disp(CostPerYear) % every year's percentage of the whole cos

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