Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions Full Presentation and Report with Appendices

U S A F A
Space
Systems
Research
Center
Kinetic Energy Transfer of Near-Earth Objects for
Interplanetary Manned Missions
C1C Winston Sanks
United States Air Force Academy
Department of Astronautics
1Unclassified -- Distribution A. Approved for Public Release. Distribution Unlimited.

U S A F A
Space
Systems
Research
Center
Overview
 Introduction
• Interplanetary Travel
• Energy Requirements
• Transfer Opportunities
 Kinetic Energy Transfer
• Near Earth Object - Bennu
• Procedures
 Future Applications
• Mission Candidates
 Conclusion
Near-Earth Asteroid 2012 DA14 (Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Interplanetary Travel
 Reasons for traveling
• Scientific development
• Resource utilization
• Sustainment of the Human Race on
other celestial bodies
 Terminal Destinations
• Mars
• Moon
• Titan
• Europa
Jupiter’s sixth closest moon, Europa (Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Interplanetary Travel
 Travel Constraints
• Time
• Environmental Control and Life
Support System (ECLSS)
limitations of interplanetary
spacecraft
• Radiation exposure
• Effects of prolonged low-
gravity environment
• Psycho-social impact of
prolonged isolation of crew
• Energy-propulsion
restrictions
• Monetary Support
• Political Consideration
Wernher Von Braun’s 1948-1952 Mars Expedition plan,
involving 10 spacecraft and seventy astronauts
(Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Trans Mars Injection
Energy Requirements
 Energy required for Trans Mars
Injection
• 7.45x1013 - 1.97x1014 Joules
• Roughly equivalent to 8-10
Saturn V Rockets
• Energy required dependent on
trajectory chosen and mass of
the space vehicle(s)
• Values based on NASA Mars
Design Reference Architecture
Mission 5.0
• 250 - 500 metric tons spacecraft
mass
• Bennu’s approximate mean
kinetic energy is 2.3x1019 Joules
NASA Mars Design Reference Architecture 5.0
Theoretical Manned Spacecraft (Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Mars Transfer
Opportunities
 Opposition Class Trajectory
• Short surface stays
• About 40 days
• Best Departure Dates
• 4 September 2017
– ∆V=7588 meters/second
– Bennu approach 0.317 AU
• 12 September 2023
– Outbound Venus Flyby
Opposition - Class Trajectory
Correct phasing occurs every 26 months
(Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Mars Transfer
Opportunities
 Conjunction Class Trajectory
• Long surface stays
• Greater than 500 days
• Best Departure Date
• 11 May 2018
Conjunction - Class Trajectory
Correct phasing occurs every 26 months
(Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Bennu
 101955 Bennu (1999 RQ36)
• Every six years, Bennu’s orbit
takes it near the Earth
• 2017, 2018, and 2023 are next
close approaches at 0.317 AU,
0.35 AU, and 0.471 AU
• During 2175 to 2199 timeframe,
approaches to within two Earth
radii
• The mean orbital speed of
Bennu is 27.8 km/s
• 480 to 511 m diameter
• Made of carbonaceous material
• Target of upcoming OSIRIS-
REx mission
(Courtesy NASA)
Orbit of 101955 Bennu (Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Kinetic Energy Transfer
Date Class Relative KE
available from
Bennu (Joules)
∆KE needed
for Transfer
(Joules)
∆V needed
Outbound
(km/s)
Maximum fuel
saved due to
transfer (kg)
4-Sept-2017
Opposition
2.93x1019 1.25x1014
7.49 2.69x106
11-May-2018 Conjunction 1.60x1019 5.53x1013
3.51 1.10x106
12-Sept-2023
Opposition-
Outbound
Venus Flyby 3.19x1019 7.03x1013
4.40 1.34x106

U S A F A
Space
Systems
Research
Center
NEO Capture Procedures
Net and Inertial Reel
Conceptual design of Net and Inertial Reel capture system
(Courtesy Space Junk 3D, LLC)

U S A F A
Space
Systems
Research
Center
Net and Inertial Reel
Reel Mass (kg)
Anticipated
Spacecraft Mass (kg)
4.16 x107 5 x105
6.29 x107 5 x105
 The spacecraft mass budget
prohibits a Net-and-Reel
system as a viable capture
method
Date ∆V needed
Outbound
(km/s)
∆V Max Net
and Reel
Capture
(km/s)
∆t Capture
at 10g (s)
Cross
Sectional
Area of
Reel (cm2)
Length of
Reel (km)
Total Net and
Reel System
Mass (kg)
4-Sept-2017 7.49 2.97 30.29 203.25 947 4.16x107
12-Sept-2023 4.40 5.62 44.82 203.25 1433 6.29x107

U S A F A
Space
Systems
Research
Center
Asteroid Station and Mass Driver
Conceptual design of Asteroid Station and Mass Driver
(Courtesy Bryan Versteeg / Spacehabs.com)

U S A F A
Space
Systems
Research
Center
Conceptual design of Spacecraft Mass Collector (Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Date Firing
Velocity
(km/s)
Slug Mass
(kg)
Muzzle
Energy
(Joules)
Total Mass
Transfer
(kg)
Acceleration of
SC per Slug
Capture (m/s2)
Mass of SC
Mass
Collector
(kg)
Number
of
Firings
4-Sept-2017 1.0 64 3.2x107 2.41x105
1.18 1480 3767
11-May-2018 1.0 64 3.2x107 1.91x105 1.99 1261 2976
12-Sept-2023 1.0 64 3.2x107
1.25x105 2.26 952 1947

U S A F A
Space
Systems
Research
Center
 Reasonable method of
momentum exchange
• Mass Transfer differences are
dependent on required
transfer ∆V and relative
velocities of Earth and Bennu
at the time of transfer
Departure
Date
Asteroid Station
Mass (kg)
Total Mass
Transfer (kg)
4-Sep-17 2.02 x106 2.41 x105
11-May-18 2.02 x106 1.91 x105
12-Sep-23 2.02 x106 1.25x105

U S A F A
Space
Systems
Research
Center
Safety
 Safety is a priority
• Perturbation risk within Bennu’s
orbit
• Could result in inaccurate
rendezvous location predictions
• Possibility of collision with the
spacecraft
• In late 22nd century Bennu’s orbit
becomes a potential hazard to Earth
• Possibility of collision with Earth
• G-limit restrictions of the spacecraft
and its occupants during an
acceleration by the asteroid
NASA Mars Theoretical Positron Reactor Powered
Spacecraft (Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Safety
 Perturbation risk within Bennu’s
orbit
• Bennu has a well-determined orbit
due primarily to 12 years of radar
ranging
• Accuracy of the orbit determined for
Bennu will increase dramatically by
the planned departure dates in the
late 22nd century
 In late 22nd century Bennu’s orbit
becomes a potential hazard to
Earth
• Study found that transfer with one
500,000kg spacecraft would not
cause a collision that wasn’t going
to happen otherwise.
 G-limit restrictions of the
spacecraft and its occupants
during an acceleration by the
asteroid
• The maximum spacecraft
acceleration is limited to 10g
• Ensured in the Net and Inertial
Reel architecture through the
inertial reel itself
• In the Mass Driver
architecture, each 64kg slug
capture by the spacecraft
contributes a maximum
acceleration of roughly 2 m/s

U S A F A
Space
Systems
Research
Center
Future Candidates
 (285263) 1998 QE2
• Binary asteroid system (primary
body has a moonlet)
• Orbital period of 3.77 years
• Diameter calculated at 2.75
kilometers
• The next notable close approach
predicted May 27, 2221, the
asteroid will pass Earth at
0.038 AU
(Courtesy NASA)

U S A F A
Space
Systems
Research
Center
Conclusion
 Introduction
• Interplanetary Travel
• Energy Requirements
• Transfer Opportunities
 Kinetic Energy Transfer
• Near Earth Object - Bennu
• Procedures
 Future Applications
• Mission Candidates
 Conclusion

U S A F A
Space
Systems
Research
Center
Acknowledgements

U S A F A
Space
Systems
Research
Center
Questions?
21
Unclassified -- Distribution A.
Approved for Public Release.
Distribution Unlimited

Sanks 1
Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions
(KETNEO-FIMM)
C1C Winston A. Sanks
Department of Astronautics, 2354 Vandenberg Drive, Suite 5B57,PO Box 4303, U.S. Air Force Academy, CO 80841
C15Winston.Sanks@Usafa.edu
This report outlines the rationale, procedures, technical feasibility, risk assessment, and cost-benefit
analysis of utilizing a Near-Earth Object, 101955 Bennu (provisional designation 1999 RQ36 - the target of
the OSIRIS-REx mission), as a source of energy to minimize the propulsion requirements of an
interplanetary spacecraft. The planet Mars is the target body in this study and the outbound Trans-Mars
injection in the years between 2175 and 2199 will be analyzed (within this timeframe Bennu’s orbit is
predicted to approach Earth within two Earth radii on at least 80 occasions). The Mars orbit insertion burn,
Trans-Earth injection burn, and Earth orbit insertion burn are assumed to be achieved with propulsive
maneuvers outlined in standard manned interplanetary mission architectures. To accomplish this mission,
two methods of transferring kinetic energy are examined: direct capture and release of the asteroid by a
spacecraft using a Kevlar net and an inertial reel, and indirect capture by establishing a station on the
asteroid to manufacture compressed material from the carbonaceous regolith in order to fire a mass stream
to be captured by the spacecraft. This mission architecture analysis takes into account the associated safety
risks of perturbations within Bennu’s orbit (which could result in inaccurate rendezvous location
predictions), the implications of altering the orbit of 101955 Bennu after transferring a portion of its energy
(since there is a possibility of collision with Earth in the late 22nd
century if the asteroid is slowed too
significantly), g-limit restrictions of the spacecraft and its occupants during an acceleration by the asteroid,
and the possibility of a collision between Bennu and the spacecraft. In addition, the cost-benefit
considerations of this mission architecture are weighed. This examination concludes that a direct capture Net
and Reel system aboard the spacecraft is not a viable capture method due to an insufficient maximum ∆V
available through a best-case perfectly elastic collision (capture) with the asteroid, as well as a prohibitive
weight penalty aboard the spacecraft due to the Net and Reel system. However, this report finds that the
method of establishing a station on Bennu with the capability to separate mass from the asteroid and fire it at
a spacecraft is a plausible (if costly) means of transferring a significant ∆V. A KETNEO-FIMM Asteroid
Station mission architecture could also be used in subsequent interplanetary missions providing cost-sharing
over many decades for future interplanetary missions.
I. Nomenclature and Acronyms
a = Semi-major axis (km)
ε = Specific mechanical energy (km2
/s2
)
Isp = Specific impulse (s)
g0 = Earth’s gravitational acceleration (m/s2
)
KE = Kinetic energy (Joules)
σ = Normal stress (Pascal)
∆V = Change in velocity (km/s)
μ = Universal gravitational constant times the mass of the central body (km2
/s2
)
ADACS - Attitude Determination and Control System
ECLSS - Environmental Control and Life Support System
EOI - Earth Orbit Insertion
MOI -Mars Orbit Insertion
SSME – Space Shuttle Main Engine
TEI - Trans-Earth Injection
TOF – Time of Flight
TMI – Trans-Mars Injection

Sanks 2
II. Introduction
The ability to travel to large distances within the solar system is a high priority for the global community
due to available opportunities for scientific development, extraterrestrial resource utilization, and the sustainment of
the human race on other celestial bodies. However, manned efforts to reach Mars or other superlunary destinations
are severely impeded by the hostile environment that interplanetary space offers: high energy radiation exposure, the
psychosocial impact of the prolonged isolation of a crew, and in particular, the ECLSS requirements of a long-
duration interplanetary transfer. All of these factors conspire to create a mission requirement of a heavy spacecraft
and a large ∆V. Manned interplanetary missions are examined in this study specifically because these constraints are
much less demanding (or nonexistent) for unmanned missions and a kinetic energy assist by an asteroid may not be
necessary. However, this mission architecture could potentially be applied to an unmanned interplanetary mission as
well. The technical feasibility of designing a spacecraft capable of supporting a manned trans-Martian (or beyond)
mission is limited due to the above requirements. Even using mitigating techniques such as in-situ resource
utilization to manufacture fuel for a return trip, the total mass for a crewed interplanetary vehicle and cargo could
measure upwards of 500 metric tons, based on the most recent NASA Mars Design Reference Architecture1
. This
study will use the best case scenario of a Class B manned spacecraft with a mass of 500,000kg (this mass is the total
spacecraft mass following Earth launch, reaching the rendezvous point, and prior to the TMI ∆V) utilizing the Ares
V cargo vehicle equipped with SSMEs2
as the launch element (this is the same launch configuration used in
NASA’s Mars Design Reference Architecture).
III. 101955 Bennu (1999 RQ36)
101955 Bennu, an Apollo class carbonaceous asteroid roughly 550 meters in diameter at its widest point,
has a synodic period of roughly six years in relation to Earth3
(every six years, Bennu’s orbit takes it near the Earth).
Bennu has a stable and predictable orbit making it a suitable choice for an asteroid sampling mission as well as the
KETNEO-FIMM mission architecture. 101955 Bennu is the target of the Origins Spectral Interpretation Resource
Identification Security - Regolith Explorer (OSIRIS-REx) asteroid sample return mission led by the University of
Arizona, NASA's Goddard Space Flight Center, Lockheed Martin Space Systems of Denver, and NASA's Marshall
Space Flight Center4
. According to OSIRIS-REx team member Steven Chesley of the Jet Propulsion Laboratory,
“The new orbit for … 1999 RQ36 is the most precise asteroid orbit ever obtained.”5
Important orbital and physical
characteristics of Bennu are outlined in Figure 1 and 2 below.
Figure 1: Properties of 101955 Bennu6 7
1
Drake, Bret. "NASA Mars Design Reference Architecture 5.0." NASA, July 2009. Web. Apr 2014. Page 27.
<http://www.nasa.gov/pdf/373665main_NASA-SP-2009-566.pdf>.
2
"Return to SSME – Ares V undergoes evaluation into potential switch." NASASpaceFlight.com, July 2009. Web.
Apr 2014.
<http://www.nasaspaceflight.com/2008/12/ssme-ares-v-undergoes-evaluation-potential-switch/>.
3
"JPL Small-Body Database Browser." Apr 2013. Web. Apr 2014.
<http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=bennu&orb=1>.
4
"OSIRIS-REx." Web. Apr 2014. <http://www.asteroidmission.org/>.
5
Dunbar, Brian. "Asteroid Nudged by Sunlight: Most Precise Measurement of Yarkovsky Effect." NASA, 24 May
2012. Web. Apr. 2014. <http://www.nasa.gov/topics/universe/features/yarkosky-asteroid_prt.htm>.
6
"OSIRIS-REx Fact Sheet." Web. Apr. 2014.
<http://www.nasa.gov/centers/goddard/pdf/552572main_OSIRIS_REx_Factsheet.pdf>.
7
Chelsey, Steven, and David Farnocchia. "Orbit and Bulk Density of the OSIRIS-REx Target Asteroid (101955)
Bennu." Cornell University Library. 23 Feb. 2014. Web. Apr. 2014. <http://arxiv.org/abs/1402.5573>.
Orbital Period
(days)
Semi-Major Axis
(AU)
Mean Orbital Velocity
(km/s)
Estimated Mass
(kg)
Estimated Density
(g/cm3
)
436.6 1.126 27.8 6.0x1010
1.26

N
both the N
average kin
the energy
trajectory c
C). By ren
spacecraft
required to
savings wo
spacecraft
assist the c
be mitigate
T
26 months
associated
examined
Examples
8
Farnocch
<http://pos
9
"101955
<http://neo
10
Drake, B
<http://ww
11
"Mars E
<http://mar
Note that the de
Net and Reel
netic energy of
y needed for a
chosen and the
ndezvousing w
and the astero
o reach destina
ould allow for
could be used
crew’s psycho-
ed.
The correct pha
11
. These oppo
time of flight,
in this study: C
of these transfe
hia, David. "Tra
stdocs.jpl.nasa
Bennu (1999 R
o.jpl.nasa.gov/r
Bret. "NASA M
ww.nasa.gov/pd
xploration Rov
rsrover.nasa.go
Figure
ensity of Bennu
and Mass Dri
f Bennu9
(relat
spacecraft to
e mass of the sp
with Bennu du
oid - it is possi
ations within th
r a much lighte
d to bolster the
-social well-be
asing for a spe
ortunities for tr
surface stay d
Conjunction cl
ers are outlined
ajectory analys
a.gov/files/ura
RQ36) Impact
risk/a101955.h
Mars Design Re
df/373665main
ver Mission: Te
ov/technology/
2: Orbit of 101
u is only slight
iver energy tra
tive to a spacec
travel to Mars
pacecraft and l
uring a close a
ible to decelera
he solar system
er overall vehi
e radiation cou
eing). The maj
III. Tran
ecific ballistic t
ransfer are clas
duration, and E
lass, Oppositio
d in figures 3 a
sis of the poten
a/Trajectory_a
Risk." 3 Mar. 2
html>, and appe
eference Archi
n_NASA-SP-20
echnology." W
/bb_propulsion
1955 Bennu (C
tly greater than
ansfer method
craft orbiting E
s (between 7.0
aunch vehicles
approach to E
ate 101955 Be
m, reducing the
icle to be built
untermeasures,
or concerns of
sfer Opportun
trajectory betw
ssified by the t
Earth return tim
on class, and O
and 4.
ntially hazardou
analysis_of_th
2014. Web. Ap
endix A
tecture 5.0." N
009-566.pdf>,
Web. Apr. 2014
n.html>.
Courtesy NASA
n that of water
dologies (pleas
Earth) is 2.3x1
03x1013
and 1
s10
- please see
Earth - with a
ennu and accel
e propellant ma
t, and the avai
ECLSS system
f interplanetary
nities
ween Earth and
total ∆V requi
me of flight. Th
Opposition clas
us asteroid (10
he_potentially_
pr 2014.
NASA, July 200
and appendice
4.
SA)8
– this property
se see section
019
Joules - sev
1.25x1014
Joul
e figure 7 and a
velocity diffe
lerate a spacec
ass needed at la
ilable excess v
ms, and living
y manned spac
d Mars occurs
ired to accomp
hree Earth-Mar
ss with an Out
01955) Bennu."
_hazardous_as
09. Web. Apr 2
es A, B, and C
S
y will be explo
V.a. and V.b
veral thousand
les dependent
appendices A, B
erential betwe
raft along the
aunch. These w
volume on boa
g space (which
ce travel woul
approximately
plish the transf
rs trajectories w
tbound Venus
" Web. Apr. 20
steroid_Bennu
2014. Page 27.
anks 3
oited in
). The
d times
on the
B, and
en the
vector
weight
ard the
h could
ld then
y every
fer, the
will be
Flyby.
014.
u.pdf>
.

Sanks 4
Figure 3: Conjunction Class Trajectory Example (Courtesy NASA)12
Figure 4: Opposition Class Trajectory with an Inbound Venus Flyby Example (Courtesy NASA)13
However, the KETNEO-FIMM architecture requires a date of departure with the conditions of both a
desirable Earth-Mars transfer phasing and a Bennu-Earth close approach. The orbits of Bennu, Earth, and Mars can
be extrapolated to the desired dates of departure in the late 22nd
century with only a modicum of accuracy; therefore
in order to accomplish an accurate concept study, three suitable dates of departure that occur within the next decade
will be examined:
12
Williams, David. "A Crewed Mission to Mars...." 25 Apr. 2005. Web. Apr. 2014.
<http://nssdc.gsfc.nasa.gov/planetary/mars/marsprof.html>.
13
Williams, David. "A Crewed Mission to Mars...." 25 Apr. 2005. Web. Apr. 2014.
<http://nssdc.gsfc.nasa.gov/planetary/mars/marsprof.html>.

Sanks 5
Figure 5: Table of Spacecraft-Bennu Rendevous Opportunity ∆V Requirements17 18
The most important consideration for this study is the outbound ∆V needed and the relative velocities of
Earth and Bennu on the date of departure. These factors will drive the technical feasibility of a KETNEO-FIMM
mission architecture. Multiple considerations must be weighed in selecting a suitable departure date for the mission
as a whole – the total mission ∆V needed incorporating MOI, TEI, and EOI burns is a driving requirement due to the
corresponding propellant mass required to satisfy the total change in velocity (although, propellant mass
requirements can be mitigated through the use of in-situ resource utilization on Mars to manufacture fuel for the
return trip). In addition, the TOF and surface stay durations will dominate ECLSS mass requirements of the
spacecraft, making total mission length an extremely important consideration as well.
Figure 6: Table of Spacecraft-Bennu Rendevous Opportunity TOF Requirements
This study focuses only on the suitability of a kinetic energy transfer to be used on the TMI; therefore, no
single date of departure will be selected for this report and all three dates of departure will be analyzed. However, in
addition to the findings and recommendations made in the remainder of this mission architecture analysis, the
considerations stated above would need to be synthesized at a systems engineering level to determine the best date
of departure.
14
Using the tangential velocities approximation stated in the assumptions section
15
Assuming an atmospheric deceleration upon return to Earth
16
During the 11 May 2018 approach Bennu has a Sun-relative velocity that is lower than the Earth’s – making it
suitable only for the Mass Cannon energy transfer method, see figures 5 and 7
17
Larson, Wiley J. Human spaceflight: mission analysis and design. New York: McGraw-Hill, 2000. Print. Pages
257-264
18
Ishimatsu, Takuto , Jeffrey Hoffman, and Olivier de Weck. "Interplanetary Trajectory Analysis for 2020-2040
Mars Missions including Venus Flyby Opportunities." 14 Sept. 2009. Web. Apr. 2014. Pages 7-8.
<http://www.enu.kz/repository/2009/AIAA-2009-6470.pdf>.
Date Bennu Approach
Distance (AU)
Relative Earth-Bennu
Velocity14
(km/s)
Class ∆V Outbound
(km/s)
∆V MOI
(km/s)
∆V TEI
(km/s)
∆V EOI15
(km/s)
∆V Total
(km/s)
4-September-2017 0.317 1.486 Opposition 7.488 4.454 4.556 0 16.498
11-May-201816
0.35 -6.686 Conjunction 3.507 2.230 2.466 0 8.203
12-September-2023 0.471 2.812
Opposition-
Outbound
Venus Flyby 4.397 4.454 2.234 0 11.085
Date Time of Flight
Outbound (days)
Surface Stay (days) Time of Flight
Return (days)
Total Mission
Duration (days)
4-September-2017 260 40 170 470
11-May-2018 204 553 190 947
12-September-2023 300 14 290 604

Sanks 6
IV. Assumptions
To carry out this analysis, several assumptions were made to simplify calculations and to provide a baseline
from which a more detailed study could be carried out. A two body assumption was made for all orbits (suitable as
the orbits of the bodies in question are being considered for short periods of time); the orbits of Mars, Bennu, and
Earth are approximated as tangential and coplanar (all orbits are assumed to lie on the plane of the ecliptic) at the
time of momentum exchange in order to forego vector analysis (which would yield minimally increased accuracy -
all orbit velocities are dominated in a direction within the plane of the ecliptic); a best-case perfectly elastic collision
is assumed for the Net and Reel capture method (i.e. no energy is lost to heat or light in the momentum exchange);
all changes in velocity are assumed instantaneous and tangential (except for the Mass Driver architecture, which
cannot transfer momentum all at once, see section V.b.); Bennu is approximated as a spherical body; the Asteroid
Station is assumed to be nuclear powered and capable of manufacturing dense slugs from Bennu’s carbonaceous
regolith - the mass and power requirements of this system will be approximated to a modern tunnel boring system19
(9.25x105
kg and 3.4 x106
Volt-Amperes); the density of slugs in the Mass Driver architecture is assumed to be made
roughly that of limestone (2.0 g/cm3
); the Mars orbit insertion burn, Trans-Earth injection burn, and Earth orbit
insertion burn are assumed to be achieved with propulsive maneuvers outlined in standard manned interplanetary
mission architectures (such as the NASA Mars Design Reference Architecture 5.0); the ∆V needed from Earth
launch is dominated by burnout velocity, therefore the velocity contributions from the rotation of the Earth and the
velocity penalties due to drag and gravity are not incorporated into calculations; Earth is a point mass during the
spacecraft’s rendezvous with Bennu (i.e. J2, drag, and other perturbations will not affect the spacecraft’s orbit
through its rendezvous with the asteroid); and the time of flight from launch to the rendezvous location is assumed
to be 2 hours for all scenarios (this assumption uses the very close predicted approach of 2 Earth Radii on 9
September 218820
) – this assumption is due to the lack of accuracy in orbital prediction over several decades.
In the late 22nd
century, when very close Earth-Bennu approaches will take place, the ∆V required for
interplanetary transfer, relative velocities between the Earth and Bennu, and other parameters will be similar to the
values that are used in this report for the upcoming dates of departure in the next decade. Therefore in order to
accomplish an accurate concept study, even though the true date of departure would occur between 2175 and 2199,
the three suitable dates of departure that occur within the next decade will be examined
V. Transfer Methodologies Data Reduction and Math Techniques
Two transfer methodologies were examined in this study: utilizing a Kevlar net and an inertial reel attached
to the spacecraft to directly capture the Bennu (or a portion of it) thereby decelerating the asteroid and accelerating
the spacecraft, and establishing a nuclear powered station on the asteroid to manufacture compressed material from
the carbonaceous regolith in order to fire mass from the asteroid to be captured by the spacecraft - similarly
decelerating the asteroid and accelerating the spacecraft due to the mass transfer. Both of these methods would also
allow the extraction of chemical energy from the asteroid depending on the suitability of the asteroid material as a
fuel - the composition of which will be accurately determined in the upcoming OSIRIS-REx mission21
.
The following calculations are outlined in Appendices A, B, and C. First, the specific mechanical energy of
Bennu, Earth, and a 500,000kg Spacecraft orbiting Earth was determined using equation 1 and the given values for
semi-major axis of the bodies being examined using the JPL HORIZONS Database22
. The radius of perigee for the
spacecraft was chosen to be 6878.137km (500km altitude) and the radius of apogee was used as the Earth-Bennu
approach distance on the date of departure23
. Using the orbital energy of each body, the relative velocities of the
bodies in relation to the Sun were calculated using the orbital velocity equation.
19
"Tunnel Boring Machine Fact Sheet." Web. Page 2.
<http://media.metro.net/projects_studies/eastside/images/ee_factsheet_03_tunnelboring.pdf>, and appendix A
20
"101955 Bennu (1999 RQ36) Impact Risk." 3 Mar. 2014. Web. Apr 2014.
<http://neo.jpl.nasa.gov/risk/a101955.html>, and appendix A
21
"OSIRIS-REx Fact Sheet." Web. Apr. 2014.
22
"HORIZONS Web-Interface." Web. <http://ssd.jpl.nasa.gov/horizons.cgi#top>.
23
"JPL Small-Body Database Browser." Apr 2013. Web. Apr 2014.
<http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=bennu&orb=1>.

Sanks 7
a2

  (1)
Equation 1: Specific Mechanical Energy Equation
)(2 


R
V Sun
(2)
Equation 2: Orbital Velocity Equation
Where R is the distance from the Sun to the body in question. Next, the kinetic energies for Bennu and the
spacecraft were calculated using the Kinetic Energy Equation, and the kinetic energy needed for the spacecraft to
achieve the transfer ∆V was computed.
2
2
mv
KE  (3)
Equation 3: Kinetic Energy Equation
The ideal rocket equation was used to determine the maximum amount of fuel that could be saved through
kinetic energy transfer with the required interplanetary transfer ∆V using current rocket technology (SSMEs) where
mf is the spacecraft mass after the TMI burn (500,000kg). Figure 7 outlines Kinetic energy and velocity exchange
data yielded through these calculations.
)ln(0
f
i
sp
m
m
gIV  (4)
Equation 4: Ideal Rocket Equation
Figure 7: Table of Spacecraft-Bennu KE available, KE needed, ∆V needed, and fuel savings data
24
Assuming the spacecraft would otherwise use SSME engines for interplanetary ∆V, see appendices A, B, and C
25
During the 11 May 2018 approach Bennu has a Sun-relative velocity that is lower than the Earth’s – making it
suitable only for the Mass Cannon energy transfer method, see figures 5 and 7
Date Class Relative KE available
from Bennu (Joules)
∆KE needed for
Transfer (Joules)
∆V needed
Outbound (km/s)
Maximum fuel saved
due to transfer (kg)24
4-September-2017 Opposition 2.93x1019
1.25x1014
7.49 2.69x106
11-May-201825
Conjunction 1.60x1019
5.53x1013
3.51 1.10x106
12-September-2023
Opposition-
Outbound
Venus Flyby 3.19x1019
7.03x1013
4.40 1.34x106

Sanks 8
Bennu’s kinetic energy (and thus its velocity) is not significantly reduced in a momentum exchange due to
its mass that is much greater than the spacecraft mass. The trajectory of Bennu is likewise infinitesimally altered26
and will likely not have Earth-impact implications in the late 22nd
century. This possibility will be discussed in detail
in section VI, Safety. Using the rocket equation once again, the maximum fuel saved due to energy transfer was
calculated. This value was based on the assumption of current rocket technology, and represents a significant mass
savings. An interplanetary transfer ∆V achieved through a momentum exchange avoids a mass penalty that would
have otherwise required a spacecraft design orders of magnitude larger and heavier to accommodate the extra fuel –
adding significant complexity and cost to the launch element of the interplanetary mission.
V.a Direct Capture –Net and Inertial Reel
In the Direct Capture methodology, a Kevlar net connected to an inertial reel will provide the means to
accomplish the kinetic energy exchange. The inertial reel would be a hydraulically or electromagnetically damped
reel around which the Kevlar would spool. The reel would control the rate of unreeling to ensure the acceleration of
the spacecraft remained within calculated parameters during the capture of Bennu. Kevlar was chosen as the Net and
Reel material due to its high tensile strength, low density, and ability to be produced in mass quantities27
. A
conceptual design of the Net and Inertial Reel capture system is outlined in figure 8.
Figure 8: Conceptual design of Net and Inertial Reel capture system (Courtesy Space Junk 3D, LLC)28
The force of the spacecraft being accelerated by the asteroid at a chosen maximum of 10g was calculated to
find the mass of an inertial reel system capable of sustaining the momentum transfer. 10g was chosen as the
acceleration limit based on experimental data of human horizontal g-load tolerances (“eyeballs in”) over the length
of time of the anticipated acceleration29
(30.29s to 44.82s, see figure 9). An analysis of a perfectly elastic collision
was carried out using equations 5 and 6 to determine if utilizing the Net and Reel capture architecture could deliver
the required ∆V. For the departures in 2017 and 2018, the Net and Reel capture system cannot provide the ∆V
needed for the interplanetary transfer in full (in 2018, this mission architecture cannot be used at all due to the
negative relative velocity of Bennu to Earth30
).
26
See appendices A, B, and C
27
"Technical Guide, Kevlar, Aramid Fiber." Dupont. Web. Apr. 2014. Page II-1 and II-2.
<http://www2.dupont.com/Kevlar/en_US/assets/downloads/KEVLAR_Technical_Guide.pdf>.
28
<http://i.space.com/images/i/000/025/507/i02/space-fishing-net.jpg?1359135870>
29
Creer, Brent, Harald Smedal, and Rodney Wingrove. "CENTRIFUGE STUDY OF PILOT TOLERANCE TO
ACCELERATION PILOT PERFORMANCE." 1 Nov. 1960. Web. Apr. 2014. Figure 10.
<http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980223621.pdf>.
30
See figure 5

Sanks 9
iif
v
mm
m
v
mm
mm
v 2
21
2
1
21
21
1
2




 (5)
Equation 5: Perfectly Elastic Collision Equation - Velocity of Body 1
iif
v
mm
m
v
mm
mm
v 1
21
1
2
21
12
2
2




 (6)
Equation 6: Perfectly Elastic Collision Equation - Velocity of Body 2
The necessary cross sectional area of the Kevlar reel was determined using the tension force provided by an
accelerating spacecraft, and the tensile yield strength of Kevlar (a factor of safety under the Class B manned mission
assumption was applied - the Kevlar yield tensile strength used was 1.5 times weaker than the true Kevlar yield
tensile strength), and equation 7.


F
A
A
F
 ; (7)
Equation 7: Normal Stress Equation
Next, the length of the reel was calculated through a work-energy analysis. The force of the spacecraft on
the inertial reel is assumed to be constant and in the same direction of the velocity of the spacecraft. Therefore the
work done on the spacecraft is equal to the total kinetic energy transfer during the capture, which is also equal to the
constant force multiplied by the distance traveled during the 10g acceleration of the spacecraft. This distance is the
length that the inertial reel must accommodate.
  Fxdxf
mv
KE
2
2
(8)
Equation 8: Kinetic Energy and Work Equations (constant force)
Using this length of the reel, the calculated cross sectional area of the reel, and the density of the material in
question (1.44 gram/cm2
for Kevlar31
) a mass estimate for a Net and Reel system could be generated. The Net and
Reel system total mass is estimated as 1.5 times the mass of the reel itself.
Figure 9: Table of Direct Capture Net and Reel Architecture Properties
As can be seen in the table above, the mass of the reel system is very heavy – two orders of magnitude
heavier than the spacecraft mass budget - even in the 4 September 2017 scenario with a reduced mission ∆V (less
than the total needed for the interplanetary transfer).
31
"Technical Guide, Kevlar, Aramid Fiber." Dupont. Web. Apr. 2014. Page II-1 and II-2.
<http://www2.dupont.com/Kevlar/en_US/assets/downloads/KEVLAR_Technical_Guide.pdf>.
Date ∆V needed
Outbound (km/s)
∆V Max Net and
Reel Capture (km/s)
∆t Capture
at 10g (s)
Cross Sectional
Area of Reel (cm2
)
Length of Reel
(km)
Total Net and Reel
System Mass (kg)
4-September-2017 7.49 2.97 30.29 203.25 947 4.16x107
12-September-2023 4.40 5.62 44.82 203.25 1433 6.29x107

Fi
expending
Bennu), or
by cleaving
Reel syste
significant
prohibitive
system tha
Fig
W
mission wa
withstand a
5000kg un
415,800kg
outweigh t
Bennu will
V
In
mission w
minimal ve
be nuclear
requiremen
mass35
of a
mass drive
spacecraft.
system ma
structure. T
32
See appe
33
Appendi
34
Appendi
35
"Tunnel
<http://med
36
"Polyeth
<http://ww
igure 10 plots
additional pro
r by arresting a
g off only a se
em mass of 3
ly reduced ∆V
e – the spacecr
at is 670% of th
gure 10: Grap
While this study
as carried out
a greater accel
nmanned space
. Even with th
the total spacec
l not be viable
V.b Indirect Ca
n the Indirect
ill be flown to
elocity differen
r powered an
nts of this Ast
at least 9.25x1
er). The mass
The spacecra
ade of a tough
This mass coll
endix E
ix E
ix F
Boring Machi
dia.metro.net/p
hylene (Low D
ww.bpf.co.uk/P
smaller ∆V op
opellant to rend
a smaller portio
ection of the as
.35x106
kg wo
V requirement,
raft mission d
he total spacecr
ph of Net and R
y focuses on m
to test the fea
eration34
. Usin
e system capab
his comparativ
craft mass tens
(and is unsuita
apture –Aster
Capture Aster
o rendezvous a
ntial using prox
nd capable of
teroid Station
05
kg (due to t
slugs would th
aft would be e
h low-density
ection system
ne Fact Sheet."
projects_studie
ensity) LDPE,
lastipedia/Poly
ptions against th
dezvous with th
on of mass of t
steroid during c
uld be require
the weight pen
design architect
raft mass.
Reel system ma
manned interp
asibility of this
ng the 4 Septem
ble of sustaini
vely light unm
s of times. The
able to be appli
roid Station an
roid Station an
an unmanned s
ximity operatio
f manufacturin
will be approx
the nuclear rea
hen be acceler
equipped to ca
plastic such
would contrib
" Web. Page 2
es/eastside/ima
LLDPE." Plas
ymers/LDPE.as
he resultant Ne
he asteroid at a
the asteroid (ea
capture). To ac
ed32
– 670%
nalty of a Net
ture used for t
ass versus ∆V
planetary missi
s transfer meth
mber 2017 depa
ing 100g, the m
manned spacec
e Net and Reel
ied to a manne
nd Mass Drive
nd Mass Drive
station with th
ons - the inten
ng dense slug
ximated to a m
actor, regolith t
rated from the
apture these m
as polyethylen
ute a reasonab
ges/ee_factshe
stipedia: The P
spx>.
et and Reel sys
a higher veloci
asily achievab
chieve a ∆V of
of the availab
and Reel captu
this study can
options – 4 Sep
ions, an analys
hod with a spac
arture date, the
mass of an in
craft, the mass
kinetic energy
ed or an unman
er
er methodolog
he asteroid (thi
nt is not to cap
gs from Benn
modern tunnel
tunnel boring m
asteroid by an
mass slugs wit
ne36
- reinforc
ble mass penalt
eet_03_tunnelb
Plastics Encyclo
stem mass (thi
ity (and a lesse
le due to the lo
f 0.25km/s a co
ble spacecraft
ure system abo
nnot accommod
eptember 2017
sis of an unma
cecraft of a lo
e maximum ∆V
nertial reel was
s of an inertial
y transfer missi
nned mission).
gy, a mission p
is is a standard
pture the astero
nu’s carbonac
l boring system
machine, mass
n electric mas
thin an expand
ced with a ho
ty (roughly 10
boring.pdf>, an
opedia. Web. A
San
s can be achiev
er relative velo
ow density of B
orresponding I
mass. Even w
oard the spacec
date a Net and
7 Departure33
anned interpla
ower mass that
V of 2.971km/s
s found to red
l reel system
ion architectur
prior to the m
d rendezvous
oid). This statio
ceous regolith
m with an esti
s compactor, a
s driver towar
dable mass co
oneycomb com
000kg, see figu
nd appendix A
Apr 2014.
nks 10
ved by
city to
Bennu
Inertial
with a
craft is
d Reel
anetary
t could
, and a
duce to
would
re with
manned
with a
on will
h. The
imated
and the
rds the
llector
mposite
ure 13)

Sanks 11
to the spacecraft37
. The slugs would be decelerated in the mass collection system apparatus similar in design to the
Net and Reel concept – however the acceleration involved38
would be so minimal that no inertial reel would be
necessary, and thus the mass penalty would be negligible. A conceptual design of the Asteroid Mass Driver Station
and the Spacecraft Mass Collector system is outlined in figures 11 and 12.
Figure 11: Conceptual design of Asteroid Station and Mass Driver
(Courtesy Bryan Versteeg / Spacehabs.com)39
Figure 12: Conceptual design of Spacecraft Mass Collector (Courtesy NASA)40
The Asteroid Station would need to encapsulate at least half of the asteroid surface area in order to restrict
the loosely packed material of Bennu from shifting during the operation of the station. This can be achieved by the
use of a thin, flexible, reinforced plastic sheeting similar to the spacecraft mass collection system. This sheeting
would blanket half of Bennu and be secured into the station – disallowing the escape of any asteroid mass during
slug manufacturing (compression) or firing. This mass restriction system would contribute a significant mass
penalty41
(1.09x106
kg) bringing the total Asteroid Station system mass42
to 2.02x106
kg. The impact of this penalty
37
Appendix A, B, and C
38
See figure 13
39
http://www.spacehabs.com/357373/asteroid-mining-gallery/
40
Kaufman, Marc "NASA Announces Plan for Capturing Asteroid." National Geographic, Apr. 2013. Web. 1 Apr.
2014. <http://news.nationalgeographic.com/news/2013/04/130410-asteroid-recovery-nasa-space-budget-science/>
41
See appendix A

Sanks 12
on the mission will be discussed in section VII, conclusion. In order to find the total mass that a Mass Driver system
would need to fire to achieve the desired spacecraft interplanetary ∆V, a slug firing velocity of 1 km/s was chosen
based on power capabilities of modern nuclear reactors43
and achievable velocities of modern naval-based rail
guns44
(while the intended projectile in this study is non-ferrous, and a carriage would need to be utilized to propel a
slug, the power usage and achievable velocity values are assumed to be roughly equivalent). By the year 2175 these
technologies can be anticipated to grow even more powerful while weighing less and consuming less power. Using
the Kinetic Energy Equation, the chosen slug ∆V of 1 km/s, and the ∆V needed for the interplanetary transfer, the
total mass needed to transfer from Bennu to the spacecraft was calculated (1.25x105
kg to 2.41x105
kg – between
roughly half of and equal to the mass of the first Space Launch System rocket45
). With the total mass of the
momentum exchange determined, the volume of the mass collector on the spacecraft could then be found using the
relation for the definition of density and the assumption that the density of the slugs are made to be slightly less than
that of limestone46
(2.0 g/cm3
). The mass of each slug was found using the achievable muzzle energy of current rail
guns47
(about 32 mega joules) and the chosen firing velocity of the Mass Driver - once again using kinetic energy
relations. The number of total firings was then found using the mass of each slug and the total mass needed for the
energy exchange. The data yielded through this analysis is presented in figure 13 below.
Figure 13: Table of Indirect Capture Mass Driver Architecture Properties
Since the mass transfer between Bennu and the spacecraft must happen in multiple firings, the
instantaneous and tangential ∆V assumption being used throughout this study cannot apply in this mission
architecture case. Therefore, a more complex analysis to determine the astrodynamic specifications of the kinetic
energy transfer would need to be conducted – which is beyond the scope of this study (for example, the relative
velocities, distances, and trajectories of each body will change after each slug firing and capture – thereby changing
the net kinetic energy needed for the transfer and creating a new problem to be solved through iteration). This
method would require an extremely accurate attitude determination and control system (ADACS) on both the
spacecraft and the Asteroid Station with precise pointing stability acting in conjunction with a highly dynamic (and
equally accurate) telemetry, tracking, and command (TT&C) network. These systems must be able to precisely
adjust the attitude of the two bodies for the correct firing and capture orientation as well as predict the new trajectory
of the spacecraft and Asteroid Station after each mass transfer.
42
See appendix A
43
"How much electricity does a typical nuclear power plant generate?" U.S. Energy Information Administration, 3
Dec 2013. Web. Apr 2014. <http://www.eia.gov/tools/faqs/faq.cfm?id=104&t=3>.
44
Ellis, Roger. "Electromagnetic Railgun." Office of Naval Research. Web. Apr. 2014.
<http://www.onr.navy.mil/media-center/fact-sheets/electromagnetic-railgun.aspx>.
45
Gerbis, Nicholas. "How the Space Launch System Will Work." HowStuffWorks. HowStuffWorks.com, 11 Oct
2011. Web. Apr 2014. <http://science.howstuffworks.com/space-launch-system1.htm>.
46
"Rock Types and Specific Gravity." Rock Types and Specific Gravity. Web. Apr 2014.
<http://www.edumine.com/xtoolkit/tables/sgtables.htm>.
47
Ellis, Roger. "Electromagnetic Railgun." Office of Naval Research. Web. Apr. 2014.
<http://www.onr.navy.mil/media-center/fact-sheets/electromagnetic-railgun.aspx>.
48
Assuming a capture ∆t of 1s, see appendices A, B, and C
Date Firing Velocity
(km/s)
Slug Mass
(kg)
Muzzle Energy
(Joules)
Total Mass Transfer
(kg)
Acceleration of SC per
Slug Capture (m/s2
)48
Mass of SC Mass
Collector (kg)
Number of
Firings
4-September-2017 1.0 64 3.2x107
2.41x105
1.18 1480 3767
11-May-2018 1.0 64 3.2x107
1.91x105
1.99 1261 2976
12-September-2023 1.0 64 3.2x107
1.25x105
2.26 952 1947

Sanks 13
VI. Safety
Safety is a priority in this mission architecture as the already grave risks of manned spaceflight are
compounded by the risks inherent in a momentum transfer. The risk of inaccurate rendezvous location predictions
due to perturbations within Bennu’s orbit is a concern as there is a possibility of mass collision with the spacecraft in
an area not designed to withstand an impact. This safety concern is addressed by the extremely accurate TT&C
systems outlined in the Mass Driver architecture that would characterize Bennu’s orbit for years before a transfer
attempt was made in addition to the selection of Bennu as the source of kinetic energy. As stated above in section II,
Bennu has a stable and predictable orbit making it a suitable choice for the KETNEO-FIMM mission architecture.
According to the report Orbit and Bulk Density of the OSIRIS-REx Target Asteroid (101955) Bennu by the OSIRIS-
Rex research team49
, Bennu has a well-determined orbit due primarily to 12 years of radar ranging – the accuracy of
the orbit determined for Bennu will increase dramatically by the planned departure dates in the late 22nd
century.
In this same timeframe – the late 22nd
century – Bennu’s orbit becomes a potential hazard to Earth.
Between 2175 and 2199 Bennu’s orbit is predicted to approach Earth within two Earth radii on at least 80
occasions50
making the date range of these close approaches an excellent time to pursue a KETNEO-FIMM
interplanetary mission. However, it is possible that if the energy of Bennu’s orbit was lowered to a certain degree its
orbit could potentially collide with the Earth. In the analysis found through this study, the kinetic energy transfer to
accelerate one 500,000kg spacecraft would not be enough to alter its trajectory such that an Earth collision (that
wasn’t going to happen otherwise) would occur. However, if multiple missions of this sort were undertaken, it
would be possible to have a degree of control over Bennu’s trajectory – if Bennu’s energy was lowered significantly
enough through the KETNEO-FIMM architecture, its trajectory could be brought under the Earth (relative to the
Sun) during the 2175-2199 close approaches, mitigating Bennu’s collision potential. The mass required to effect this
change would need to be analyzed closer to the dates of departure in order to accurately determine a trajectory offset
plan (as it stands, Bennu is predicted to have a 1 in 2700 chance of an impact with Earth in the late 22nd
century51
-
the lines of variance predicting Bennu’s and Earth’s orbit 170 years from now are not yet precise enough).
The G-limit restrictions of the spacecraft and its occupants during acceleration by the asteroid have been
addressed in this study by limiting the maximum spacecraft acceleration to 10g. This is ensured in the Net and
Inertial Reel architecture through the inertial reel itself – this would be a hydraulically or electromagnetically
damped reel which would control the rate of unreeling to ensure the acceleration of the spacecraft remained within
the calculated parameters during the capture of Bennu. In the Mass Driver architecture, each 64kg slug capture by
the spacecraft contributes an acceleration of roughly52
1m/s to 2 m/s (assuming a capture ∆t of 1s), far below the
safe acceleration value that the astronauts and spacecraft could be designed for.
VII. Conclusion
This report aimed to analyze the rationale, procedures, technical feasibility, risk assessment, and cost-
benefit analysis of utilizing a Near-Earth Object, 101955 Bennu (provisional designation 1999 RQ36 - the target of
the OSIRIS-REx mission), as a source of energy to minimize the propulsion requirements of an interplanetary
spacecraft. The planet Mars was the target body in this study and only the outbound Trans-Mars injection in the
years between 2175 and 2199 was examined. The Mars orbit insertion burn, Trans-Earth injection burn, and Earth
orbit insertion burn were assumed to be achieved with propulsive maneuvers outlined in standard manned
interplanetary mission architectures (such as the NASA Mars Design Reference Architecture 5.0). Two methods of
transferring kinetic energy were considered: direct capture and release of the asteroid by a spacecraft using a Kevlar
net and an inertial reel, and establishing a station on the asteroid to manufacture compressed material from the
carbonaceous regolith in order to fire a mass stream to be captured by the spacecraft.
This examination concludes that a direct capture Net and Reel system aboard the spacecraft is not a viable
capture method due to an insufficient maximum ∆V available through a best-case perfectly elastic collision with
(capture of) the asteroid, as well as a prohibitive weight penalty aboard the spacecraft due to the Net and Reel
49
Bennu." Cornell University Library. 23 Feb. 2014. Web. Apr. 2014. Page 22. <http://arxiv.org/abs/1402.5573>.
50
"101955 Bennu (1999 RQ36) Impact Risk." 3 Mar. 2014. Web. Apr 2014.
<http://neo.jpl.nasa.gov/risk/a101955.html>.
51
Bennu." Cornell University Library. 23 Feb. 2014. Web. Apr. 2014. Page 2. <http://arxiv.org/abs/1402.5573>.
52
See figure 13 and appendices A, B, and C

Sanks 14
system. As well, the Net and Reel system is unsuitable to be applied to an unmanned mission - even if an unmanned
5000kg space system was capable of sustaining 100g, the mass of the corresponding inertial reel system would
measure 415,800kg53
. The mass of an inertial reel system would still outweigh the total spacecraft mass several
times. Unfortunately, the Net and Inertial Reel mission architecture would not be suitable for any interplanetary
mission architecture.
However, this report finds that the method of establishing a station on Bennu with the capability to separate
mass from the asteroid and fire it at a spacecraft is a plausible means of transferring a significant ∆V to a spacecraft.
The fuel savings per mission could measure up to 2.7x106
kg of propellant54
depending on the ∆V required and the
relative velocities of Earth and Bennu at the time of transfer. To accomplish this mission, a station with an estimated
mass55
of at least 2.02x106
kg (due to the polyethylene mass restriction system, nuclear reactor, regolith tunnel
boring machine, mass compactor, and the mass driver) would be rendezvoused with the asteroid at significant ∆V
using a standard propulsion system – enough to match Bennu’s velocity on the date of departure (as stated above, a
Net and Reel capture method could not be used to provide the ∆V to rendezvous the station with the asteroid).
Effectively, the launch of the Asteroid Station mission would be capable of reaching Mars on its own. Therefore, the
KETNEO-FIMM Asteroid Station mission architecture would require three times the amount of mass (and the
according amount of propellant) that a standard non-kinetic energy transferring interplanetary mission architecture
would require. However, the KETNEO-FIMM Asteroid Station and Mass Driver mission architecture could also be
used in subsequent interplanetary missions providing cost-sharing over many decades. Based on the available kinetic
energy of Bennu on the dates of departure used in this study, between 200,000 and 450,000 missions could be
propelled through a KETNEO-FIMM architecture before Bennu’s orbit decayed to the point of being unusable56
.
This opportunity to provide ∆V for future missions could provide low cost access to Mars very frequently over the
entirety of the close approach time frame from 2175 to 2199 with a return on investment that could measure
hundreds of the initial station cost (depending on the number of missions carried out).
VIII. Acknowledgements
I would like to express my deep gratitude to the following individuals for their help in fact-checking,
reviewing, and revising this report – without their help this project would have not been possible. Colonel (ret) Gary
Payton, Lieutenant Colonel Sean Londrigan, and Lieutenant Colonel Thomas Joslyn - professors at the U.S. Air
Force Academy assisted me in the formative ideas of this report and kept me tempered in its technical feasibility.
Mr. Russ Anarde and Mr. Jim Przybysz of Northrop Grumman vetted the foundational concepts involved in the
momentum transfer proposal. Mr. Todd Merrill and Major Marc Fulson of the Space and Missile Systems Center
thoroughly assisted in the grammatical and stylistic format of the report. Dr. Dante Lauretta (OSIRIS-Rex principal
investigator) and Ms. Evelyn Hunten of the University of Arizona discussed with me the proper phasing required to
accomplish the mission as well as the suitability of Bennu as an energy transfer target. Ms. Rachel Weiss, Mr.
Wayne Hallman, and Mr. David Garza of Aerospace Corporation and the Jet Propulsion Laboratory reviewed
trajectory options and provided the JPL HORIZONS tool which was pivotal in the completion of the research. The
following professors, scientists, students, and mentors were likewise invaluable in their contributions to the analysis:
Col (ret.) Jack Anthony, Col James Dutton, Col Robert Kraus, Lt Col David French, Lt Col David Barnhart, Lt Col
David Richie, Lt Col Scott Putnam, Major Douglas Kaupa, Captain Jason Christopher, Capt Brian Crouse, Capt
Joseph Robinson, Capt Pamela Wheeler, Capt Blythe Andrews, Dr. James Solti, Dr. Robert Brown, Michael
Schmidhuber (AIAA), Supreet Vijay, C1C Miguel Barrios, C1C Julian Rojas, C1C Ryan Good, and C2C David
Emanuel. Finally, I wish to thank my Mother, Deatrice Angela Sanks; my Grandmother, Rosemary Sanks; my
Grandfather, Royce Sanks; my Uncle, Royce Sanks Jr, and my cousin, Starr Sanks or their support and
encouragement throughout my studies.
53
Appendix F
54
See figure 7
55
Appendix A and "Tunnel Boring Machine Fact Sheet." Web. Page 2.
<http://media.metro.net/projects_studies/eastside/images/ee_factsheet_03_tunnelboring.pdf>.
56
Appendices A, B, and C

Sanks 15
Appendices:
A – Energy Transfer Calculations for 4 September 2017 Date of Departure and Asteroid Station Mass Restriction
System Calculations
B – Energy Transfer Calculations for 11 May 2018 Date of Departure
C – Energy Transfer Calculations for 12 September 2023 Date of Departure
D – Rendezvous Time of Flight and Fuel Calculations for 4 September 2017 and 9 September 2188 Dates of
Departure
E – Net and Inertial Reel Mass Calculations for minimized ∆V options on 4 September 2017 Date of Departure
F – Energy Transfer Calculations for 4 September 2017 Date of Departure for Unmanned System

−Appendix A
System
A S/C conducting an kinetic energy transfer (with a velocity differential) with 101955 Bennu on 4 September 2017
Given
S/C exchanges with Bennu at closest approach distance to Earth (47,272,927.1km); Semi-major axis Bennu
1.126AU=168 505 699km; Sun distance to Bennu 1.005AU=150 345 860km; Earth distance to Sun 1 AU=149 597
871km; Bennu distance to Earth 0.317AU=47 422 525km; 10g acceleration limit of a 500000kg spacecraft; Kevlar
yield tensile strength 3620MPa; Kevlar density 1.44 g/cm^3; Kevlar factor of safety of 1.5 (Class B manned
experimental mission); Net and Reel System mass = 1.5*Reel mass; Asteroid Station Mass Restriction System
mass = 1.5*Polyethylene Sheeting mass; Density of Cannon fired mass ~ limestone =2.0g/cm^3
−Assumptions Equations
Two Body assumption for all orbits; Mars, Bennu, and Earth orbits are tangential and coplanar (all orbits are
on the plane of the ecliptic) at time of energy exchange; Approximate Earth-Sun distance on date of transfer
1AU; Perfectly Elastic Collsion for Net and Reel Capture; Instantaneous tangential delta V; Earth is a point
mass for S/C rendevous with Bennu; delta V needed for launch to rendevous coordinates is dominated by
burnout velocity
＝((1)) σ ―
F
A
(Normal Stress Equation)
＝((2)) ε ――
−μ
2 a
(Specific Mechanical Energy Equation)
＝((3)) V
‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+―
μ
R
ε
⎞
⎟
⎠
(Orbital Velocity Equation)
＝((4)) ΔV ⋅⋅Isp g0 ln
⎛
⎜
⎝
――
mi
mf
⎞
⎟
⎠
(Ideal Rocket Equation)
(Kinetic Energy and Work Equations - True if force is
constant and in the same direction as travel -which it is
for SC during Net and Reel capture)
＝＝＝((5)) KE ――
mv2
2
⌠
⌡ df x ⋅F dx
＝((6)) v1f +
⎛
⎜
⎝
――――
⎛⎝ −m1 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v2i (Perfectly Elastic Collision
Equation - Velocity of Body 1)
＝((7)) v2f +
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ −m2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
Find
1) Net Kinetic Energy Transfer for the Opposition Class delta V of 7.488km/s on 4 September 2017;
2) Mass of Kevlar Net and Reel System; 3) Mass and Firing Velocity of Cannon Tranfer; 4)Mass of a SC Mass Collector system
Created with Mathcad Express. See www.mathcad.com for more information.

Solve
≔μSun ⋅1.327 1011
――
3
2
≔μEarth 398600.5 ――
3
2
≔SSMEIsp 453.2
≔BennuMass ⋅6.0 1010
≔ρBennu 1.26 ――3
≔g0 9.81 ―2
≔SCMass =500000 ⎛⎝ ⋅5 105 ⎞⎠ ≔SCaccelconstantlimit =⋅((10)) g0 98.1 ―2
≔RpSCRelEarth
(( +500 6378.137)) ≔RaSCRelEarth 47272927.1
≔aSCRelEarth =――――――――
+RaSCRelEarth RpSCRelEarth
2
⎛⎝ ⋅2.364 107 ⎞⎠ ≔aEarthRelSun 149597871
≔aBennuRelSun 168505699 ≔RBennuRelSun 150345860
≔εBennuRelSun =―――――
−μSun
2 aBennuRelSun
−393.755 ――
2
2
≔εEarthRelSun =―――――
−μSun
2 aEarthRelSun
−443.522 ――
2
2
≔εSCRelEarth =――――
−μEarth
2 aSCRelEarth
−0.008 ――
2
2
≔BennuVelocityRelSun =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
RBennuRelSun
εBennuRelSun
⎞
⎟
⎠
31.269 ―― ≔BennuAvgVelocityRelSun 27.8 ――
≔BennuKineticEnergyRelSun =―――――――――――――
⎛⎝ ⋅BennuMass ⎛⎝BennuVelocityRelSun2 ⎞⎠⎞⎠
2
⎛⎝ ⋅2.933 1019⎞⎠ ≔BennuAvgKineticEnergyRelSun =―――――――――――――――
⎛⎝ ⋅BennuMass ⎛⎝BennuAvgVelocityRelSun2 ⎞⎠⎞⎠
2
⎛⎝ ⋅2.319 1019⎞⎠
≔EarthVelocityRelSun =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
aEarthRelSun
εEarthRelSun
⎞
⎟
⎠
29.783 ――
≔SCVelocityApogeeRelEarth =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+――――
μEarth
RaSCRelEarth
εSCRelEarth
⎞
⎟
⎠
0.002 ――
(The Spacecraft velocity relative to Earth is negligible)
≔SCVelocityRelSun =EarthVelocityRelSun 29.783 ――
≔SCKineticEnergyRelSun =―――――――――――
⋅((SCMass)) ⎛⎝SCVelocityRelSun2 ⎞⎠
2
⎛⎝ ⋅2.218 1014⎞⎠
≔BennuVelocityPerfectElasticCollision =+
⎛
⎜
⎝
――――――――――――――――
⋅(( −BennuMass SCMass)) BennuVelocityRelSun
(( +BennuMass SCMass))
⎞
⎟
⎠
⎛
⎜
⎝
――――――――
(( ⋅2 SCMass))
⎞
⎟
⎠
SCVelocityRelSun 31.269 ――
≔SCVelocityPerfectElasticCollision =+
⎛
⎜
⎝
―――――――――――――
⋅(( ⋅2 BennuMass)) BennuVelocityRelSun
⎞
⎟
⎠
⎛
⎜
⎝
――――――――――――――
⋅(( −SCMass BennuMass)) SCVelocityRelSun
⎞
⎟
⎠
32.755 ――
≔ΔVNeededOpposition 7.488 ―― ≔ΔVMaxNetReelCapture =−SCVelocityPerfectElasticCollision SCVelocityRelSun 2.971 ――

(For a Net-and-Reel capture method, the maximum
delta V is limited due to the maximum energy transfer
available in a perfectly elastic collision)
≔ΔtCapture =―――――――
ΔVMaxNetReelCapture
SCaccelconstantlimit
30.29
≔SCMassPropellantSavedIdeal =⋅
⎛
⎜
⎝
⎛
⎜⎝
―――――((ΔVNeededOpposition))
(( ⋅SSMEIsp g0))
⎞
⎟⎠
⎞
⎟
⎠ SCMass ⎛⎝ ⋅2.694 106 ⎞⎠
≔SCMassPropellantSavedMaxNetReelCapture =⋅
⎛
⎜
⎝
⎛
⎜⎝
―――――((ΔVMaxNetReelCapture))
(( ⋅SSMEIsp g0))
⎞
⎟⎠
⎞
⎟
⎠ SCMass ⎛⎝ ⋅9.755 105 ⎞⎠
≔SCKineticEnergyOppositionNeeded =―――――――――――――――――
⋅((SCMass))
⎛
⎝⎛⎝ +SCVelocityRelSun ΔVNeededOpposition
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅3.473 1014⎞⎠
≔SCKineticEnergyPostNetReelRelSun =――――――――――――――――――
⋅((SCMass))
⎛
⎝⎛⎝ +SCVelocityRelSun ΔVMaxNetReelCapture
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅2.682 1014⎞⎠
≔NetKineticEnergyTransferMaxNetReel =−SCKineticEnergyPostNetReelRelSun SCKineticEnergyRelSun ⎛⎝ ⋅4.646 1013⎞⎠
≔NetKineticEnergyTransferOpposition =−SCKineticEnergyOppositionNeeded SCKineticEnergyRelSun ⎛⎝ ⋅1.255 1014⎞⎠
≔BennuKineticEnergyPostNetReelRelSun =−BennuKineticEnergyRelSun NetKineticEnergyTransferMaxNetReel ⎛⎝ ⋅2.933 1019⎞⎠
≔BennuVelocityPostNetReelRelSun =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――――――――
(( ⋅BennuKineticEnergyPostNetReelRelSun 2))
BennuMass
31.269 ――
≔SCVelocityPostNetReelRelSun =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
――――――――――――――
(( ⋅SCKineticEnergyPostNetReelRelSun 2))
SCMass
32.755 ――
≔σKevlarYield 3620 ≔σKevlarYieldSafety =――――
σKevlarYield
1.5
⎛⎝ ⋅2.413 103 ⎞⎠
≔ForceFromSC =⋅SCMass SCaccelconstantlimit ⎛⎝ ⋅4.905 107 ⎞⎠ ≔ρKevlar 1.44 ――3
≔CrossSectionalAreaKevlarReel =―――――
ForceFromSC
σKevlarYieldSafety
203.246 2
≔LengthKevlarReel =―――――――――――――
NetKineticEnergyTransferMaxNetReel
ForceFromSC
947.141
≔VolumeKevlarReel =⋅LengthKevlarReel CrossSectionalAreaKevlarReel ⎛⎝ ⋅1.925 104 ⎞⎠
3
≔MassKevlarReel =⋅VolumeKevlarReel ρKevlar
⎛⎝ ⋅2.772 107 ⎞⎠
≔MassNetReelSystem =⋅MassKevlarReel 1.5 ⎛⎝ ⋅4.158 107 ⎞⎠
≔FiringVelocityCannonTransfer 1 ―― ≔ρCannonMass 2.0 ――3
≔MuzzleEnergy ⋅32 106

≔MassCannonTransfer =―――――――――――――――――――
(( ⋅2 ((NetKineticEnergyTransferOpposition))))
(( +BennuVelocityRelSun FiringVelocityCannonTransfer))
2
⎛⎝ ⋅2.411 105 ⎞⎠
≔VelocityCannonTransferMass =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
――――――――――――――
(( ⋅NetKineticEnergyTransferOpposition 2))
MassCannonTransfer
32.269 ――
≔VolumeSCMassCollector =――――――――
MassCannonTransfer
ρCannonMass
120.549 3
≔HeightSCMassCollector 3
≔RadiusCylindricalSCMassCollector =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――
VolumeSCMassCollector
⋅HeightSCMassCollector
3.576
≔SurfaceAreaSCMassCollector =+⋅⋅⋅2 RadiusCylindricalSCMassCollector HeightSCMassCollector ⋅RadiusCylindricalSCMassCollector2
107.596 2
≔ThicknessPolyethyleneSheetingSC 1 ≔ρPolyethylene 0.917 ――3
≔VolumePolyethyleneSheetingSC =⋅ThicknessPolyethyleneSheetingSC SurfaceAreaSCMassCollector 1.076 3
≔MassPolyethyleneSheetingSC =⋅ρPolyethylene VolumePolyethyleneSheetingSC 986.659
≔MassTotalReinforcedStructureSC =⋅MassPolyethyleneSheetingSC 1.5 ⎛⎝ ⋅1.48 103 ⎞⎠
≔MassSlug =―――――――――――
(( ⋅((MuzzleEnergy)) 2))
FiringVelocityCannonTransfer2
64
≔NumberOfFirings =――――――――
MassCannonTransfer
MassSlug
⋅3.767 103
≔accelPerSlug =―――――――
―――――――
⎛⎝ΔVNeededOpposition
⎞⎠
((NumberOfFirings))
1
1.988 ―2
≔NumberOfPotentialMissions =―――――――――――――
BennuKineticEnergyRelSun
NetKineticEnergyTransferOpposition
⋅2.337 105
≔AsteroidTunnelCompactorandDriverMass =2050000 ――
g0
⎛⎝ ⋅9.295 105 ⎞⎠ (From Tunnel Boring
Machine Fact Sheet)
≔VolumeBennu =――――
BennuMass
ρBennu
⎛⎝ ⋅4.762 107 ⎞⎠
3
≔RadiusSphericalBennu =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
3
⋅((VolumeBennu)) ――
⎛
⎜
⎝
―
3
4
⎞
⎟
⎠
224.852
≔SurfaceAreaCircularBennu =⋅RadiusSphericalBennu2 ⎛⎝ ⋅1.588 105 ⎞⎠
2

≔ThicknessStationPolyethyleneSheeting 0.5
≔VolumePolyethyleneStationSheeting =⋅ThicknessStationPolyethyleneSheeting SurfaceAreaCircularBennu 794.172 3
≔MassPolyethyleneStationSheeting =⋅ρPolyethylene VolumePolyethyleneStationSheeting ⎛⎝ ⋅7.283 105 ⎞⎠
≔MassTotalReinforcedStructureStation =⋅MassPolyethyleneStationSheeting 1.5 ⎛⎝ ⋅1.092 106 ⎞⎠
≔AsteroidStationTotalMass =+AsteroidTunnelCompactorandDriverMass MassTotalReinforcedStructureStation ⎛⎝ ⋅2.022 106 ⎞⎠
Test
The mass of the Reel system is far too heavy - multiple orders of magnitude too heavy - even with the
reduced delta V inherent in the Net and Reel system. Capture through inertial reels will not be viable. A
reasonable amount of mass may be fired from the asteroid and recieved by the spacecraft at 1 km/s in order
to acheive the required mission delta V. The asteroid station mass restriction system is extremely heavy.

−Appendix B
System
A S/C conducting an kinetic energy transfer (with a velocity differential) with 101955 Bennu on 11 May 2018
Given
1.126AU=168 505 699km; Sun distance to Bennu 1.343AU=200 909 940km; Earth distance to Sun 1
AU=149 597 871km; Bennu distance to Earth 0.35AU=52 359 254.7km; 10g acceleration limit of a
500000kg spacecraft; Kevlar yield tensile strength 3620MPa; Kevlar density 1.44 g/cm^3; Kevlar factor of
safety of 1.5 (Class B manned experimental mission); Asteroid Station Mass Restriction System mass =
1.5*Polyethylene Sheeting mass; Net and Reel System mass = 1.5*Reel mass; Density of Cannon fired mass
~ limestone =2.0g/cm^3
Two Body assumption for all orbits; Mars, Bennu, and Earth orbits are tangential and coplanar (all orbits
are on the plane of the ecliptic) at time of energy exchange; Approximate Earth-Sun distance on date of
transfer 1AU; Perfectly Elastic Collsion for Net and Reel Capture; Instantaneous tangential delta V;
Earth is a point mass for S/C rendevous with Bennu; delta V needed for launch to rendevous coordinates
is dominated by burnout velocity
＝((1)) σ ―
F
A
＝((2)) ε ――
−μ
2 a
＝((3)) V
‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+―
μ
R
ε
⎞
⎟
⎠
＝((4)) ΔV ⋅⋅Isp g0 ln
⎛
⎜
⎝
――
mi
mf
⎞
⎟
⎠
＝＝＝((5)) KE ――
mv2
2
⌠
⌡ df x ⋅F dx
＝((6)) v1f +
⎛
⎜
⎝
――――
⎛⎝ −m1 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
＝((7)) v2f +
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ −m2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠

Find
1) Net Kinetic Energy Transfer for the Conjunction Class delta V of 3.507km/s on 11 May 2018;
2) Mass of Kevlar Net and Reel System; 3) Mass and Firing Velocity of Cannon Tranfer; 4)Mass of a SC Mass Collector
Solve
≔μSun ⋅1.327 1011
――
3
2
≔μEarth 398600.5 ――
3
2
≔SSMEIsp 453.2
≔ρBennu 1.26 ――3
≔g0 9.81 ―2
≔SCMass 500000 ≔SCaccelconstantlimit =⋅((10)) g0 98.1 ―2
≔RpSCRelEarth
(( +500 6378.137)) ≔RaSCRelEarth 52359254.7
2
⎛⎝ ⋅2.618 107 ⎞⎠ ≔aEarthRelSun 149597871
−μSun
2 aBennuRelSun
−393.755 ――
2
2
−μEarth
2 aSCRelEarth
−0.008 ――
2
2
−μSun
2 aEarthRelSun
−443.522 ――
2
2
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
RBennuRelSun
εBennuRelSun
⎞
⎟
⎠
23.097 ――
2
⎛⎝ ⋅1.6 1019⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
aEarthRelSun
εEarthRelSun
⎞
⎟
⎠
29.783 ――
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+――――
μEarth
RaSCRelEarth
εSCRelEarth
⎞
⎟
⎠
0.001 ――
2
⎛⎝ ⋅2.218 1014⎞⎠

⎛
⎜
⎝
――――――――――――――――
⎞
⎟
⎠
⎛
⎜
⎝
――――――――
(( ⋅2 SCMass))
⎞
⎟
⎠
⎛
⎜
⎝
―――――――――――――
⎞
⎟
⎠
⎛
⎜
⎝
――――――――――――――
⎞
⎟
⎠
16.411 ――
≔ΔVNeededConjunction 3.507 ―― ≔ΔVMaxNetReelCapture =−SCVelocityPerfectElasticCollision SCVelocityRelSun −13.372 ――
−136.311
⎛
⎜
⎝
⎛
⎜⎝
―――――((ΔVNeededConjunction))
(( ⋅SSMEIsp g0))
⎞
⎟⎠
⎞
⎟
⎠ SCMass ⎛⎝ ⋅1.1 106 ⎞⎠
≔SCKineticEnergyConjunctionNeeded =――――――――――――――――――
⋅((SCMass))
⎛
⎝⎛⎝ +SCVelocityRelSun ΔVNeededConjunction
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅2.771 1014⎞⎠
⋅((SCMass))
⎛
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅6.733 1013⎞⎠
≔NetKineticEnergyTransferMaxNetReel =−SCKineticEnergyPostNetReelRelSun SCKineticEnergyRelSun ⋅−1.544 1014
≔NetKineticEnergyTransferConjunction =−SCKineticEnergyConjunctionNeeded SCKineticEnergyRelSun ⎛⎝ ⋅5.53 1013⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――――――――
BennuMass
23.097 ――
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
――――――――――――――
SCMass
16.411 ――
σKevlarYield
1.5
⎛⎝ ⋅2.413 103 ⎞⎠
ForceFromSC
σKevlarYieldSafety
31.503 2
ForceFromSC
⋅−1.956 103

≔VolumeKevlarReel =⋅LengthKevlarReel CrossSectionalAreaKevlarReel ⋅−6.399 104 3
≔MassKevlarReel =⋅VolumeKevlarReel ρKevlar ⋅−9.215 107
≔MassNetReelSystem =⋅MassKevlarReel 1.5 ⋅−1.382 108
≔FiringVelocityCannonTransfer 1 ―― ≔MuzzleEnergy ⋅32 106
≔ρCannonMass 2.0 ――3
(( ⋅2 ((NetKineticEnergyTransferConjunction))))
2
⎛⎝ ⋅1.905 105 ⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――――――――
(( ⋅NetKineticEnergyTransferConjunction 2))
MassCannonTransfer
24.097 ――
MassCannonTransfer
ρCannonMass
95.234 3
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――
3.179
91.663 2
≔MassTotalReinforcedStructureSC =⋅MassPolyethyleneSheetingSC 1.5 ⎛⎝ ⋅1.261 103 ⎞⎠
≔MassSlug =―――――――――――
64

MassCannonTransfer
MassSlug
⋅2.976 103
―――――――
⎛⎝ΔVNeededConjunction
⎞⎠
((NumberOfFirings))
1
1.178 ―2
≔NumberOfPotentialMissions =―――――――――――――
NetKineticEnergyTransferConjunction
⋅2.894 105
Test
The Net and Reel system is completely unfeasible here - the asteroid is moving slower than the spacecraft. The asteroid station
needs less total mass transferred in this scenario even with the unfavorable relative velocities between Earth and Bennu due to the
low delta V required for the transfer. A reasonable amount of mass may be fired from the asteroid and recieved by the spacecraft at
1 km/s in order to acheive the required mission delta V. The asteroid station mass restriction system is extremely heavy.

−Appendix C
System
A S/C conducting an kinetic energy transfer (with a velocity differential) with 101955 Bennu on 12 September 2023
Given
S/C exchanges with Bennu at closest approach distance to Earth (70 460 597.1 km); Semi-major axis
Bennu 1.126AU=168 505 699km; Sun distance to Bennu 0.959AU=143 464 358km; Earth distance to
Sun 1 AU=149 597 871km; Bennu distance to Earth 0.471AU=70 460 597.1km; 10g acceleration limit
of a 500000kg spacecraft; Kevlar yield tensile strength 3620MPa; Kevlar density 1.44 g/cm^3; Kevlar
factor of safety of 1.5 (Class B manned experimental mission); Asteroid Station Mass Restriction
System mass = 1.5*Polyethylene Sheeting massNet and Reel System mass = 1.5*Reel mass; Density of
Cannon fired mass ~ limestone =2.0g/cm^3
Two Body assumption for all orbits; Mars, Bennu, and Earth orbits are tangential and coplanar (all
orbits are on the plane of the ecliptic) at time of energy exchange; Approximate Earth-Sun distance on
date of transfer 1AU; Perfectly Elastic Collsion for Net and Reel Capture; Instantaneous tangential
delta V; Earth is a point mass for S/C rendevous with Bennu; delta V needed for launch to rendevous
coordinates is dominated by burnout velocity
＝((1)) σ ―
F
A
＝((2)) ε ――
−μ
2 a
＝((3)) V
‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+―
μ
R
ε
⎞
⎟
⎠
＝((4)) ΔV ⋅⋅Isp g0 ln
⎛
⎜
⎝
――
mi
mf
⎞
⎟
⎠
＝＝＝((5)) KE ――
mv2
2
⌠
⌡ df x ⋅F x
＝((6)) v1f +
⎛
⎜
⎝
――――
⎛⎝ −m1 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
＝((7)) v2f +
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ −m2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠

Find
1) Net Kinetic Energy Transfer for the Venus Flyby Class delta V of 4.397km/s on 12 September 2023;
2) Mass of Kevlar Net and Reel System; 3) Mass and Firing Velocity of Cannon Tranfer; 4)Mass of a SC Mass Collector
Solve
≔μSun ⋅1.327 1011
――
3
2
≔μEarth 398600.5 ――
3
2
≔SSMEIsp 453.2
≔ρBennu 1.26 ――3
≔g0 9.81 ―2
≔SCMass 500000 ≔SCaccelconstantlimit =⋅((10)) g0 98.1 ―2
≔RpSCRelEarth
(( +500 6378.137)) ≔RaSCRelEarth 70460597.1
2
⎛⎝ ⋅3.523 107 ⎞⎠ ≔aEarthRelSun 149597871
−μSun
2 aBennuRelSun
−393.755 ――
2
2
−μSun
2 aEarthRelSun
−443.522 ――
2
2
−μEarth
2 aSCRelEarth
−0.006 ――
2
2
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
RBennuRelSun
εBennuRelSun
⎞
⎟
⎠
32.595 ――
2
⎛⎝ ⋅3.187 1019⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
aEarthRelSun
εEarthRelSun
⎞
⎟
⎠
29.783 ――
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+――――
μEarth
RaSCRelEarth
εSCRelEarth
⎞
⎟
⎠
0.001 ――
(The Spacecraft velocity relative to Earth is negligible and
is assumed perpendicular to direction of asteroid travel)
2
⎛⎝ ⋅2.218 1014⎞⎠

⎛
⎜
⎝
――――――――――――――――
⎞
⎟
⎠
⎛
⎜
⎝
――――――――
(( ⋅2 SCMass))
⎞
⎟
⎠
⎛
⎜
⎝
―――――――――――――
⎞
⎟
⎠
⎛
⎜
⎝
――――――――――――――
⎞
⎟
⎠
35.406 ――
≔ΔVNeededVenusFlyby 4.397 ――
≔ΔVMaxNetReelCapture =−SCVelocityPerfectElasticCollision SCVelocityRelSun 5.623 ――
delta V is limited based on the maximum energy
transfer available in a perfectly elastic collision)
ΔVNeededVenusFlyby
44.822
≔SCMassPropellantSaved =⋅
⎛
⎜
⎝
⎛
⎜⎝
―――――((ΔVNeededVenusFlyby))
(( ⋅SSMEIsp g0))
⎞
⎟⎠
⎞
⎟
⎠ SCMass ⎛⎝ ⋅1.344 106 ⎞⎠
≔SCKineticEnergyVenusFlybyNeeded =――――――――――――――――――
⋅((SCMass))
⎛
⎝⎛⎝ +SCVelocityRelSun ΔVNeededVenusFlyby
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅2.921 1014⎞⎠
⋅((SCMass))
⎛
⎝⎛⎝ +SCVelocityRelSun ΔVNeededVenusFlyby
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅2.921 1014⎞⎠
≔NetKineticEnergyTransferVenusFlyby =−SCKineticEnergyVenusFlybyNeeded SCKineticEnergyRelSun ⎛⎝ ⋅7.031 1013⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――――――――
BennuMass
32.595 ――
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
――――――――――――――
SCMass
34.18 ――
σKevlarYield
1.5
⎛⎝ ⋅2.413 103 ⎞⎠
ForceFromSC
σKevlarYieldSafety
203.246 2
ForceFromSC
⎛⎝ ⋅1.433 103 ⎞⎠

≔VolumeKevlarReel =⋅LengthKevlarReel CrossSectionalAreaKevlarReel ⎛⎝ ⋅2.913 104 ⎞⎠
3
⎛⎝ ⋅4.195 107 ⎞⎠
≔FiringVelocityCannonTransfer 1 ―― ≔ρCannonSlug 2.0 ――3
(( ⋅2 ((NetKineticEnergyTransferVenusFlyby))))
2
⎛⎝ ⋅1.246 105 ⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
――――――――――――――
(( ⋅NetKineticEnergyTransferVenusFlyby 2))
MassCannonTransfer
33.595 ――
MassCannonTransfer
ρCannonSlug
62.299 3
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――
2.571
69.229 2
≔MassTotalReinforcedStructureSC =⋅MassPolyethyleneSheetingSC 1.5 952.246
≔MassSlug =―――――――――――
64
MassCannonTransfer
MassSlug
⋅1.947 103

―――――――
⎛⎝ΔVNeededVenusFlyby
⎞⎠
((NumberOfFirings))
1
2.259 ―2
≔NumberofPotentialMissions =―――――――――――――
NetKineticEnergyTransferVenusFlyby
⋅4.533 105
Test
The Net and Reel system is more feasible here - the available delta V available thorugh direct capture exceeds the
required transfer delta V. However capture through inertial reels will still not be viable due to the mass of a Net
and Reel system still being too high. The asteroid station needs the least mass of all scenarios due to favorable
relative velocities between Earth and Bennu. A reasonable amount of mass may be fired from the asteroid and
recieved by the spacecraft at 1 km/s in order to acheive the required mission delta V. The asteroid station mass
restriction system is extremely heavy.

−Appendix D
System
A S/C conducting an kinetic energy transfer (with a velocity differential) with 101955 Bennu
on 4 September 2017 and 9 September 2188
Given
Semi-major axis Bennu 1.126AU=168 505 699km; Sun distance to Bennu 1.005AU=150 345 860km;
Earth distance to Sun 1 AU=149 597 871km; Bennu distance to Earth 0.317AU=47 422 525km on 4
September 2017; Bennu distance to Earth = 12 760km on 9 September 2188;
Two Body assumption for all orbits; Instantaneous tangential delta V; Earth is a point mass for S/C
rendevous with Bennu; delta V needed for launch to rendevous coordinates is dominated by burnout
velocity
＝((1)) Period 2
‾‾‾
―
a3
μ
(Period of Orbit Equation)
＝((2)) ε ――
−μ
2 a
＝((3)) V
‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+―
μ
R
ε
⎞
⎟
⎠
＝((4)) ΔV ⋅⋅Isp g0 ln
⎛
⎜
⎝
――
mi
mf
⎞
⎟
⎠
Find
1) Fuel needed and time of flight of a spacecraft conducting an kinetic energy transfer (with a
velocity differential) with 101955 Bennu on 4 September 2017
2) Fuel needed and time of flight of a spacecraft conducting an kinetic energy transfer (with a
velocity differential) with 101955 Bennu on 9 September 2188
Solve
≔μEarth 398600.5 ――
3
2
≔SSMEIsp 453.2 ≔SCMass 500000 ≔g0 9.81 ―2
≔RpSCRelEarth4Sept2017
(( +500 6378.137)) ≔RaSCRelEarth4Sept2017 47272927.1
≔aSCRelEarth4Sept2017 =―――――――――――――
+RaSCRelEarth4Sept2017 RpSCRelEarth4Sept2017
2
⎛⎝ ⋅2.364 107 ⎞⎠
≔εSCRelEarth4Sept2017 =―――――――
−μEarth
2 aSCRelEarth4Sept2017
−0.008 ――
2
2
≔SCVelocityPerigeeRelEarth4Sept2017 =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+――――――
μEarth
RpSCRelEarth4Sept2017
εSCRelEarth4Sept2017
⎞
⎟
⎠
10.765 ――
≔SCPropellantMassFraction4Sept2017 =
⎛
⎜⎝
――――――――((SCVelocityPerigeeRelEarth4Sept2017))
(( ⋅SSMEIsp g0))
⎞
⎟⎠ 11.261

≔MassInitial4Sept2017 =⋅SCMass SCPropellantMassFraction4Sept2017
⎛⎝ ⋅5.631 106 ⎞⎠
≔MassFuel4Sept2017 =−MassInitial4Sept2017 SCMass ⎛⎝ ⋅5.131 106 ⎞⎠
≔SCTOFtoRendevousRelEarth4Sept2017 =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――
⎛⎝aSCRelEarth4Sept2017
⎞⎠
3
μEarth
18.124
(A capture in the near future with an approach point of approximately 0.316AU such as in the example
above will not be feasible due to the very long time of flight to rendevous with the asteroid as well as the
massive amount of propellant that would be required to reach the rendevous point)
≔RaSCRelEarth9Sept2188 ⋅((6378.137)) 2 ≔RpSCRelEarth9Sept2188
(( +500 6378.137))
≔aSCRelEarth9Sept2188 =―――――――――――――
+RpSCRelEarth9Sept2188 RaSCRelEarth9Sept2188
2
⎛⎝ ⋅9.817 103 ⎞⎠
≔εSCRelEarth9Sept2188 =―――――――
−μEarth
2 aSCRelEarth9Sept2188
−20.301 ――
2
2
≔SCVelocityPerigeeRelEarth9Sept2188 =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+――――――
μEarth
RpSCRelEarth9Sept2188
εSCRelEarth9Sept2188
⎞
⎟
⎠
8.678 ――
≔SCPropellantMassFraction9Sept2188 =
――――――――((SCVelocityPerigeeRelEarth9Sept2188))
(( ⋅SSMEIsp g0)) 7.042
≔MassInitial9Sept2188 =⋅SCMass SCPropellantMassFraction9Sept2188
⎛⎝ ⋅3.521 106 ⎞⎠
≔MassFuel9Aug2188 =−MassInitial9Sept2188 SCMass ⎛⎝ ⋅3.021 106 ⎞⎠
≔SCTOFtoRendevousRelEarth9Sept2188 =
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――
⎛⎝aSCRelEarth9Sept2188
⎞⎠
3
μEarth
1.344
Test
A capture in the late 22nd century with an approach point of approximately 2 times the radius of Earth such
as in the example above will be feasible due to the short time of flight needed to rendevous with the asteroid
as well as the more reasonable amount of propellant that would be required to reach the rendevous point.

AppendixEDeltaV(m/s)CaptureSystemMass(kg)
04Sep172503.35E+06
5006.72E+06
7501.01E+07
10001.36E+07
12501.70E+07
15002.05E+07
74881.12E+08
0.00E+00
2.00E+06
4.00E+06
6.00E+06
8.00E+06
1.00E+07
1.20E+07
1.40E+07
1.60E+07
1.80E+07
2.00E+07
2.20E+07
01002003004005006007008009001000110012001300140015001600
Mass(kg)
DeltaV(m/s)
InertialReelSystemMass(kg)vsDeltaV(m/s)
4September2017Departure

−Appendix F
System
An unmanned S/C conducting an kinetic energy transfer (with a velocity differential) with 101955 Bennu on 4
September 2017
Given
1.126AU=168 505 699km; Sun distance to Bennu 1.005AU=150 345 860km; Earth distance to Sun 1 AU=149 597
871km; Bennu distance to Earth 0.317AU=47 422 525km; 100g acceleration limit of a 5000kg spacecraft; Kevlar
yield tensile strength 3620MPa; Kevlar density 1.44 g/cm^3; Kevlar factor of safety of 1.5 (Class B manned
experimental mission); Net and Reel System mass = 1.5*Reel mass; Asteroid Station Mass Restriction System
mass = 1.5*Polyethylene Sheeting mass; Density of Cannon fired mass ~ limestone =2.0g/cm^3
Two Body assumption for all orbits; Mars, Bennu, and Earth orbits are tangential and coplanar (all orbits are
on the plane of the ecliptic) at time of energy exchange; Approximate Earth-Sun distance on date of transfer
1AU; Perfectly Elastic Collsion for Net and Reel Capture; Instantaneous tangential delta V; Earth is a point
mass for S/C rendevous with Bennu; delta V needed for launch to rendevous coordinates is dominated by
burnout velocity
＝((1)) σ ―
F
A
＝((2)) ε ――
−μ
2 a
＝((3)) V
‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+―
μ
R
ε
⎞
⎟
⎠
＝((4)) ΔV ⋅⋅Isp g0 ln
⎛
⎜
⎝
――
mi
mf
⎞
⎟
⎠
＝＝＝((5)) KE ――
mv2
2
⌠
⌡ df x ⋅F dx
＝((6)) v1f +
⎛
⎜
⎝
――――
⎛⎝ −m1 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m2
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
＝((7)) v2f +
⎛
⎜
⎝
――――
⎛⎝ ⋅2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
v1i
⎛
⎜
⎝
――――
⎛⎝ −m2 m1
⎞⎠
⎛⎝ +m1 m2
⎞⎠
⎞
⎟
⎠
Find
1) Net Kinetic Energy Transfer for the Opposition Class delta V of 7.488km/s on 4 September 2017;
2) Mass of Kevlar Net and Reel System; 3) Mass and Firing Velocity of Cannon Tranfer; 4)Mass of a SC Mass Collector system

Solve
≔μSun ⋅1.327 1011
――
3
2
≔μEarth 398600.5 ――
3
2
≔SSMEIsp 453.2
≔ρBennu 1.26 ――3
≔g0 9.81 ―2
≔SCMass =5000 ⎛⎝ ⋅5 103 ⎞⎠ ≔SCaccelconstantlimit =⋅((100)) g0 981 ―2
≔RpSCRelEarth
(( +500 6378.137)) ≔RaSCRelEarth 47272927.1
2
⎛⎝ ⋅2.364 107 ⎞⎠ ≔aEarthRelSun 149597871
−μSun
2 aBennuRelSun
−393.755 ――
2
2
−μSun
2 aEarthRelSun
−443.522 ――
2
2
−μEarth
2 aSCRelEarth
−0.008 ――
2
2
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
RBennuRelSun
εBennuRelSun
⎞
⎟
⎠
31.269 ―― ≔BennuAvgVelocityRelSun 27.8 ――
2
⎛⎝ ⋅2.933 1019⎞⎠ ≔BennuAvgKineticEnergyRelSun =―――――――――――――――
⎛⎝ ⋅BennuMass ⎛⎝BennuAvgVelocityRelSun2 ⎞⎠⎞⎠
2
⎛⎝ ⋅2.319 1019⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
⋅2
⎛
⎜
⎝
+――――
μSun
aEarthRelSun
εEarthRelSun
⎞
⎟
⎠
29.783 ――
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
2
⎛
⎜
⎝
+――――
μEarth
RaSCRelEarth
εSCRelEarth
⎞
⎟
⎠
0.002 ――
2
⎛⎝ ⋅2.218 1012⎞⎠
⎛
⎜
⎝
――――――――――――――――
⎞
⎟
⎠
⎛
⎜
⎝
――――――――
(( ⋅2 SCMass))
⎞
⎟
⎠
⎛
⎜
⎝
―――――――――――――
⎞
⎟
⎠
⎛
⎜
⎝
――――――――――――――
⎞
⎟
⎠
32.755 ――
≔ΔVNeededOpposition 7.488 ―― ≔ΔVMaxNetReelCapture =−SCVelocityPerfectElasticCollision SCVelocityRelSun 2.971 ――

3.029
⎛
⎜
⎝
⎛
⎜⎝
―――――((ΔVNeededOpposition))
(( ⋅SSMEIsp g0))
⎞
⎟⎠
⎞
⎟
⎠ SCMass ⎛⎝ ⋅2.694 104 ⎞⎠
≔SCMassPropellantSavedMaxNetReelCapture =⋅
⎛
⎜
⎝
⎛
⎜⎝
―――――((ΔVMaxNetReelCapture))
(( ⋅SSMEIsp g0))
⎞
⎟⎠
⎞
⎟
⎠ SCMass ⎛⎝ ⋅9.755 103 ⎞⎠
≔SCKineticEnergyOppositionNeeded =―――――――――――――――――
⋅((SCMass))
⎛
⎝⎛⎝ +SCVelocityRelSun ΔVNeededOpposition
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅3.473 1012⎞⎠
⋅((SCMass))
⎛
⎞⎠
2 ⎞
⎠
2
⎛⎝ ⋅2.682 1012⎞⎠
≔NetKineticEnergyTransferOpposition =−SCKineticEnergyOppositionNeeded SCKineticEnergyRelSun ⎛⎝ ⋅1.255 1012⎞⎠
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
―――――――――――――――
BennuMass
31.269 ――
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
――――――――――――――
SCMass
32.755 ――
σKevlarYield
1.5
⎛⎝ ⋅2.413 103 ⎞⎠
ForceFromSC
σKevlarYieldSafety
3.15 2
ForceFromSC
58.853
≔VolumeKevlarReel =⋅LengthKevlarReel CrossSectionalAreaKevlarReel 192.504 3
⎛⎝ ⋅2.772 105 ⎞⎠
≔FiringVelocityCannonTransfer 1 ―― ≔ρCannonMass 2.0 ――3

Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions Full Presentation and Report with Appendices

Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions Full Presentation and Report with Appendices

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions Full Presentation and Report with Appendices

Similar to Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions Full Presentation and Report with Appendices (20)

Recently uploaded

Recently uploaded (20)

Kinetic Energy Transfer of Near-Earth Objects for Interplanetary Manned Missions Full Presentation and Report with Appendices