Mission Opportunies to Trans Neptunian Objects 3

1
MISSION OPPORTUNITIES TO TRANS-NEPTUNIAN OBJECTS –
PART III, ORBITAL CAPTURE, LOW-THRUST TRAJECTORIES
AND VEHICLE RADIATION ENVIRONMENT DURING JOVIAN
FLYBY
Jordan Kreitzman*
, Charles W. Stewart*
, Ethan Cansler*
, Jake Brisby*
,
Matthew Green*
, and James Evans Lyne†
Our group has previously described high-thrust mission opportunities to
a number of trans-Neptunian Objects, including Sedna, Eris, Makemake,
Haumea, Huya, Ixion, Varuna, Quaoar and others. In the current study,
we extend that work to examine the possibility of orbital capture, and
compare the merits of high-thrust and low-thrust primary propulsion
systems in terms of the overall mission performance and potential orbital
capture mass. In all cases, the outbound trajectory includes a Jovian
flyby; radiation exposure during the flyby will influence the viability of
candidate mission designs. Therefore the Jovian flyby segments are
examined in some detail, and radiation dose-depth curves for several
trajectories are presented as a means of comparison. For at least four
targets, orbital capture of a small satellite (100-380 kg) was found to be
feasible, using a high-thrust interplanetary trajectory and a launch on an
Atlas V 551 with a Star 48 upper stage. Low thrust trajectories improve
overall performance, either by increasing delivered mass or allowing a
smaller launch vehicle.
INTRODUCTION
To date, only a single mission, New Horizons, has been launched with the exploration of a trans-
Neptunian object (TNO) as its primary objective. Our group has previously reported on potential high-
thrust missions to other bodies in this distant region of the Solar System (References 1 and 2). In the
current study, we extend that work by evaluating the feasibility of orbital capture of a probe about a TNO
and examine the potential benefits of low thrust interplanetary transfers. Potential target bodies were
selected primarily based on size, with diameters ranging from ~600–1200 km. Data regarding the diameter,
mass, and orbital elements were obtained from a list curated by Caltech astronomer M. Brown (Reference
3). Some of the bodies selected are currently unnamed, and are referred to by their alphanumeric
designation. They are as follows: 2002 TC302, 2007 UK126, 2002 AW197, 2003 AZ84, 2002 UX25, 2002
MS4, 1996 TL66 and 2004 GV9. In addition, the following named bodies were considered: Sedna, Eris,
Makemake, Haumea, Huya, Ixion, Varuna, Quaoar, Orcus, Salacia, and Rhadamanthus.
Several factors are critical to the mission design; these include interplanetary transit time, Earth
departure C3, arrival V∞, and Jovian flyby periapse radius. The importance of transit time is self-evident.
Earth departure C3 determines the payload mass that can be placed on a trajectory by any given launch
vehicle; the target arrival V∞ determines the length of time available for observations in the case of a flyby
mission or the mass that can be captured into orbit. Jovian flyby radius strongly influences the radiation
dose to the spacecraft and the need for shielding to prevent damage to internal components.
*
Undergraduate, Department of Mechanical, Aerospace, and Biomedical Engineering
†
Associate Professor and corresponding author. 414 Dougherty Building, The University of Tennessee at Knoxville,
37996. jelyne@utk.edu.

2
METHODOLOGY AND ASSUMPTIONS
Both high- and low-thrust interplanetary trajectories were examined using the Mission Analysis
Environment (MAnE) and Heliocentric Interplanetary Low-Thrust Optimization Program (HILTOP)
software packages developed by Spaceflight Solutions of Hendersonville, NC (References 4 and 5).
Trajectories were evaluated for times of flight (TOF) generally ranging from 10 years to 25 years (in some
cases more for low-thrust trajectories), using a single unpowered Jupiter gravity assist (JGA) maneuver and
launching on dates ranging from the year 2020-2050. Trajectories on the shorter end of this time frame
were considered for flyby opportunities, while the longer duration trajectories were considered for orbital
insertion missions, due to the lower arrival excess speed.
Low-Thrust Trajectories
An analysis of low-thrust trajectories was carried out to determine what advantages might be achieved
compared with traditional high-thrust Earth departures. HILTOP supports three optimization parameters for
designing missions: maximizing net mass at the primary target, minimizing initial launch mass of the
spacecraft from Earth, and minimizing mission duration to the primary target. Maximizing net mass at the
primary target allows launch dates to fluctuate and determine optimal launch criteria for times of flight
(Reference 5).
For low-thrust mission analysis, the entire range of launch vehicles described in Figure 1 was
considered. Furthermore, Figure 1 displays the relationship between the payload capacity and the C3 values
for each vehicle. C3, the characteristic energy, is the amount of excess energy required to escape a body’s
gravitational influence. Four TNOs were studied in detail for low-thrust missions. These objects were
Makemake, Quaoar, Haumea, and Sedna. Each target was analyzed in HILTOP by finding an optimized
departure date and configuring the program to maximize the net mass on arrival at the target. For each
target, the reference power and thruster number of the spacecraft were varied to determine what would be
adequate for a given mission objective. We assumed that the spacecraft would use NEXT thrusters with
solar power as the power source during flight; therefore, the ISP of the propulsion unit was assumed to be
4,000 sec. HILTOP was specifically designed to be able to model the NEXT thrusters accurately, so there
was high confidence in this part of our analysis (Reference 5). The launch vehicles provided a set C3 value
of 36 km²/s² for every low-thrust Earth departure. As with the high-thrust analysis, all low-thrust
trajectories utilized a JGA to gain heliocentric velocity. Several major assumptions regarding the low-thrust
analysis are summarized in Table 1 below.
Figure 1. Launch Vehicle Comparison (Payload vs. C3). This plot represents all of the launch
vehicles that were considered for use during mission planning.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 10 20 30 40 50 60 70 80 90 100110120
Payload(kg)
C3 (km²/s²)
Delta IV HLV
Atlas V 551 w/ Star 48
Atlas V 551
Atlas V 521
Atlas V 401
Atlas V 501

3
Table 1. Low-Thrust Spacecraft Assumptions
Specific Mass of
Power Source
(kg/kW)
Mass of 1
NEXT
PPU/Thruster
Unit (kg)
Low-Thrust
Propellant
Tankage
Fraction
House-
keeping
Power
(kW)
Input Power Limit
of 1 NEXT
Thruster (kW)
Min. Operating
Power of 1 NEXT
Thruster (kW)
12.5 50 0.03 0.25 7.265 0.638
High-Thrust Trajectories
MAnE is designed to find optimized high-thrust trajectories for a variety of objectives; we used the
software in its default configuration that optimized for minimal departure C3. Within our use of MAnE, we
assumed that the only ΔV maneuvers performed were at the time of Earth departure. Therefore, unlike the
trajectories generated by HILTOP, those generated by MAnE were independent of the spacecraft
configuration. Since high-thrust trajectories rely solely on an initial departure ΔV burn and are unpowered
thereafter, the only requirement imposed by the high-thrust trajectories was that the selected launch vehicle
have the capacity to place the vehicle mass at the required departure C3.
For the high-thrust mission analysis, two Earth launch vehicles were considered: the Delta IV Heavy
Launch Vehicle and the Atlas V 551 with a Star 48B upper stage. These vehicles were selected because
they were the only currently available American vehicles with sufficient launch performance to deliver
substantial mass to such distant objects. Performance data for these vehicles regarding Earth departure C3
vs. potential payload mass was taken from References 6 and 7. While the output trajectories from MAnE
specified values for departure C3, those could not be directly used, as they applied only to a single launch
date and do not allow for launch schedule slippage. Rather than use this minimum C3 to determine payload
capabilities, a 30-day launch window was considered, centered about the optimum departure date. Thus, the
required C3 stated for a given launch opportunity accounted for the C3 penalties imposed by launching on a
non-optimum date.
Orbital Insertion
Only high thrust systems were considered for orbital insertion maneuvers. Methods of inserting
payloads into orbit were considered, and it was quickly determined that, for the arrival speeds encountered
for trajectories to TNOs with reasonable mission durations, a single-stage insertion engine would be
impractical. This is because beyond an arrival speed of ~10 km/s, the chemical potential energy of the
available propellants would be insufficient to overcome the kinetic energy of the incoming mass. Even for
arrival speeds of less than 8 km/s, the insertable mass was typically well under 100 kg. It was therefore
concluded that any orbital insertion would have to be accomplished using a two-stage insertion rocket.
Reliability is a significant concern for long-duration missions, and therefore the minimization of
complexity is desirable. From that perspective, a two-stage rocket is not ideal, but it is still possible to
mitigate some of the added complexity. While a liquid-fueled rocket engine is necessary for the second
stage of the insertion (so that fine control may be exerted by the spacecraft’s computer over the final orbit)
it is possible to use a solid-propellant rocket engine as the first stage. While the ISP realized with a solid
rocket is less than that of a liquid, solid rockets tend to benefit from comparatively lower tankage fractions
owing to their relative simplicity; this ISP-to-tankage fraction tradeoff often results in little or no net benefit
for solid or liquid over the other in terms of performance. The simplicity of a solid-fuelled first stage
promotes mission reliability by offering fewer variables in the insertion portion of the mission.
It was therefore concluded to use as the first stage an off-the-shelf solid rocket booster such as those
manufactured by ATK; their capabilities and other pertinent information are freely available in the
literature. ISP’s of ~286 sec and tankage fractions of ~0.04–0.06 are typical for such boosters (Reference 8).
The second stage would be liquid-fuelled and modeled on the Cassini insertion engine (Reference 9), using
mono-methyl hydrazine (MMH) and nitrogen tetroxide as fuel (N2O4), which are advantageous for

4
missions such as these because they are hypergolic and are therefore very reliable. The Cassini-type liquid
propulsion system would have a tankage fraction of ~0.113. The second stage would make use of the
upgraded version of the Aerojet R-4D engine used on the Cassini engine, now called the HiPAT and
capable of providing an ISP of 323 sec.
While this approach was simple in principle, it was realized that generating an insertion system engine
combination for each calculated trajectory could be prohibitively time-consuming. Therefore, a spreadsheet
was constructed to automate the task to a degree. Parameters from a given trajectory and target were input,
along with the characteristics of a solid rocket booster. This, combined with the Cassini-derived liquid
tankage fraction, yielded a value of insertable mass into orbit. To aid in the selection of an appropriately-
sized solid stage, the spreadsheet also output the payload ratios of the first and second stage; for a
multistage rocket to be optimized, the two ratios should be as close to identical as possible.
JGA Radiation Environment Analysis
Both high- and low-thrust missions made use of a Jovian gravity assist. In view of the potentially
extreme radiation environment during this maneuver, an effort was made to determine the radiation
exposure to a spacecraft for the various trajectories. To date, this analysis has been completed only for
selected high-thrust missions. Constructing dose-depth curves aids in our ability to choose a trajectory that
will require the least shielding or receive the lowest dose of ionizing radiation. To construct these dose-
depth curves, several tools were used. The first step was to take the Keplerian elements produced by
MAnE and use them as inputs for a simulation of the Jovian proximity trajectory calculated using the
Program to Optimize Simulated Trajectories (POST, Reference 10). POST then evaluated the latitude,
longitude, and planetocentric radius of the spacecraft as a function of time. A MATLAB script was then
developed to construct an input file, in the Orbit Ephemeris Message format, that was put into the Space
Environment Information System (SPENVIS, Ref. 11). This is a European Space Agency-sponsored,
online tool for the analysis of space environmental effects. SPENVIS then takes the input file and plots the
desired trajectory and allows an estimation of radiation dosage to be calculated. SPENVIS is able to
estimate the radiation by using a program called GIRE which calculates the trapped proton and electron
flux around Jupiter for a given trajectory and Julian date. The ESA tool then takes the fluxes and runs a
dose model that uses inputs for shielding depths, shielding configuration, and a target material. Due to time
constraints the shielding depth was left at default values and the shielding configuration was set to center of
aluminum spheres. Using silicon as the target material, a dose-depth curve was obtained which shows the
dose in rads as a function of aluminum shield thickness in mils. We found that HILTOP did not output
parameters suitable for use in this analysis regime; as a result, no low-thrust trajectories could be modeled
for radiation exposure.
LOW-THRUST RESULTS
The low-thrust analysis includes a sampled mapped trajectory, Jupiter swing-by distances, arrival
velocities, initial launch masses, and final arrival masses for all four targets while simultaneously varying
reference power, thruster number, and mission duration. Figure 2 is provided as a representation of a low-
thrust trajectory to Makemake. Each target has its own sub-section of results. The first figure for each
section represents initial mass of the spacecraft vs. mission duration for each target while varying thruster
number and reference power. The initial mass is the payload of the launch vehicle that leaves Earth, or the
mass that leaves Earth’s sphere of influence. Horizontal lines were drawn on the figures to represent the
maximum mass that a particular launch vehicle could place on a departure trajectory with a C3 value of 36
km²/s². All launch vehicles considered for these missions and their capabilities are shown in Figure 1 above
(References 2 and 12).
The second figure for each target plots the final arrival mass at the target vs. mission duration while
varying thruster number and reference power. These arrival masses do not account for a capture maneuver,
but are the masses delivered to the target’s sphere of influence before any capture maneuvers. The third
figure for each target plots the arrival velocities at the target vs. mission duration. These graphs are good

5
indicators for showing what mission objectives are best for certain mission durations. The fourth figure for
each target represents the Jupiter swing-by distances that the spacecraft will encounter during the fly-by.
These plots are great visual tools for getting a general understanding of what kind of radiation the
spacecraft will experience for different mission durations, thruster numbers, and reference powers.
Figure 2. Makemake Trajectory Map. This figure represents all of the different trajectories to
Makemake. These trajectories are different because of varied mission durations. The shortest
mission duration corresponds to the straightest trajectory. The opposite is true for the longest
mission duration. The trajectories range from 16 to 36 year mission durations in increments of 2
years. This is for a departure date of roughly June 17, 2023. Also, the unit distance is 5 AU.

6
Makemake
Figure 3. Initial Mass to Makemake versus Mission Duration. This plot represents the mass that will
escape Earth’s sphere of influence to Makemake for a departure date of roughly June 17, 2023. Also,
power input and thruster number was varied to see the effect.
Figure 4. Arrival Mass at Makemake versus Mission Duration. This plot represents the
optimized arrival mass at Makemake for a departure date of roughly June 17, 2023. Also, power
input and thruster number was varied to see the effect.
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
2750
3000
3250
3500
16 18 20 22 24 26 28 30 32 34 36
InitialMass(kg)
Mission Duration (years)
One Thruster (15 kW Ref
Power)
Two Thrusters (30 kW
Ref Power)
Three Thrusters (45 kW
Ref Power)
Atlas V 401
Atlas V 501
Atlas V 551
Atlas V 521
0
250
500
750
1000
1250
1500
1750
2000
2250
16 18 20 22 24 26 28 30 32 34 36
ArrivalMass(kg)
Power)
Two Thrusters (30 kW Ref
Power)
Ref Power)

7
Figure 5. Makemake Arrival Velocity versus Mission Duration. This plot represents the arrival
velocity with which the arrival mass approaches the target for a departure date of roughly June 17,
2023.
Figure 6. Makemake Jupiter Swing-by Distance versus Mission Duration. This plot represents the
Jupiter swing-by distances for a departure date of roughly June 17, 2023.
0
2
4
6
8
10
12
14
16
18
16 18 20 22 24 26 28 30 32 34 36
ArrivalVelocity(km/s)
0
2
4
6
8
10
12
16 18 20 22 24 26 28 30 32 34 36
Swing-byDistance(JovianRadii)
Power)
Ref Power)
Ref Power)

8
Quaoar
Figure 7. Initial Mass to Quaoar versus Mission Duration. This plot represents the mass that will
escape Earth’s sphere of influence to Quaoar for a departure date of roughly September 23, 2026.
Also, power input and thruster number was varied to see the effect.
Figure 8. Arrival Mass at Quaoar versus Mission Duration. This plot represents the optimized
arrival mass at Quaoar for a departure date of roughly September 23, 2026. Also, power input and
thruster number was varied to see the effect.
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
2750
3000
3250
3500
3750
4000
14 16 18 20 22 24 26 28 30
InitialMass(kg)
Power)
Ref Power)
Ref Power)
Atlas V 551
Atlas V 521
Atlas V 401
Atlas V 501
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
14 16 18 20 22 24 26 28 30
ArrivalMass(kg)
Power)
Power)
Ref Power)

9
Figure 9. Quaoar Arrival Velocity versus Mission Duration. This plot represents the arrival velocity
with which the arrival mass approaches the target for a departure date of September 23, 2026.
Figure 10. Quaoar Jupiter Swing-by Distance versus Mission Duration. This plot represents the
Jupiter swing-by distances for a departure date of September 23, 2026.
0
2
4
6
8
10
12
14
16
18
14 16 18 20 22 24 26 28 30
0
2
4
6
8
10
12
14
16
14 16 18 20 22 24 26 28 30
Power)
Ref Power)
Ref Power)

10
Haumea
Figure 11. Initial Mass to Haumea versus Mission Duration. This plot represents the mass that will
escape Earth’s sphere of influence to Haumea for a departure date of roughly July 26, 2036. Also,
Figure 12. Arrival Mass at Haumea versus Mission Duration. This plot represents the optimized
arrival mass at Haumea for a departure date of roughly July 26, 2036. Also, power input and
thruster number was varied to see the effect.
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
2750
3000
3250
3500
14 16 18 20 22 24 26 28 30 32 34
InitialMass(kg)
Power)
Ref Power)
Ref Power)
Atlas V 551
Atlas V 521
Atlas V 401
Atlas V 501
0
200
400
600
800
1000
1200
1400
1600
1800
2000
14 16 18 20 22 24 26 28 30 32 34
ArrivalMass(kg)
Power)
Power)
Ref Power)

11
Figure 13. Haumea Arrival Velocity versus Mission Duration. This plot represents the arrival
velocity with which the arrival mass approaches the target for a departure date of July 26, 2036.
Figure 14. Haumea Jupiter Swing-by Distance versus Mission Duration. This plot represents the
Jupiter swing-by distances for a departure date of July 26, 2036.
0
2
4
6
8
10
12
14
16
18
20
14 16 18 20 22 24 26 28 30 32 34
0
2
4
6
8
10
12
14
16
14 16 18 20 22 24 26 28 30 32 34
Power)
Power)
Three Thrusters (45 kW Ref
Power)

12
Sedna
Figure 15. Initial Mass to Sedna versus Mission Duration. This plot represents the mass that will
escape Earth’s sphere of influence to Sedna for a departure date of roughly January 29, 2031. Also,
Figure 16. Arrival Mass at Sedna versus Mission Duration. This plot represents the optimized arrival
mass at Sedna for a departure date of roughly January 29, 2031. Also, power input and thruster
number was varied to see the effect.
0
250
500
750
1000
1250
1500
1750
2000
2250
2500
2750
3000
3250
3500
3750
4000
25 30 35 40 45 50 55 60
InitialMass(kg)
Power)
Ref Power)
Ref Power)
Atlas V 551
Atlas V 521
Atlas V 401
Atlas V 501
0
500
1000
1500
2000
2500
3000
25 30 35 40 45 50 55 60
ArrivalMass(kg)
Power)
Power)
Ref Power)

13
Figure 17. Sedna Arrival Velocity versus Mission Duration. This plot represents the arrival velocity
with which the arrival mass approaches the target for a departure date of January 29, 2031.
Figure 18. Sedna Jupiter Swing-by Distance versus Mission Duration. This plot represents the
Jupiter swing-by distances for a departure date of January 29, 2031.
0
2
4
6
8
10
12
14
16
18
25 30 35 40 45 50 55 60
0
1
2
3
4
5
6
7
8
9
25 30 35 40 45 50 55 60
Power)
Ref Power)
Ref Power)

14
HIGH-THRUST RESULTS
The table below represents a selection of the best trajectories and opportunities for each target body
listed. These were chosen based on three criteria, the first being that the launch dates have the lowest-
possible Earth departure C3 values, the second being that the mission durations for trajectories with low
target arrival V∞ fall within a 20-25 year TOF, and due to Jupiter’s synodic period the launch opportunities
occur every 12 years. However, it is still feasible to launch within the year preceding or following the 12
year synodic period giving a 3 year launch window. The size of the target body was also taken into
consideration when doing the initial selection of target bodies for which trajectories were calculated.
Table 2 – High Thrust Mission Opportunities
From Table 2, mission parameters were taken and plotted in order to illustrate how varying mission
duration can influence other mission variables. Figures 19-21 contain these plots of various mission
parameters such as payload mass, Earth departure C3, Jovian flyby radii, mission duration, and arrival V∞.
From the figures below, it can be seen how mission duration affects each parameter, with longer mission
durations leading to more favorable C3 conditions and thus more launch-able payload. Avoiding close
TNO
Name
Launch
Date
TOF
(years)
Earth
Dep. C3
(km2
/s2
)
Arrival
V∞ (km/s)
Jovian
Flyby
Radius
Insertable
Mass
(kg)
TNO
Name
Launch
Date
TOF
(years)
Earth
Dep. C3
(km2
/s2
)
Arrival
V∞ (km/s)
Jovian
Flyby
Radius
Insertable
Mass
(kg)
29-Mar-20 10 134.4 22.31 1.82 N/A 20-Jul-23 10 141.57 21.31 4.89 N/A
24-Mar-20 15 99.95 13.47 6.42 N/A 16-Jul-23 15 109.27 12.9 13.96 N/A
24-Mar-20 20 96.41 9.15 10.19 32.3 15-Jul-23 20 102.77 8.77 21.91 28
24-Mar-20 25 98.3 6.74 11.25 105.2 15-Jul-15 25 100.41 6.38 26.81 108.4
11-May-33 10 144.48 19.98 3.69 N/A 24-Jul-35 10 132.08 20.82 3.73 N/A
7-May-33 15 114.46 11.97 8.64 N/A 19-Jul-35 15 102.12 12.5 12.01 N/A
6-May-33 20 108.76 8.09 11.81 36.5 18-Jul-35 20 96.58 8.41 19.59 46.2
6-May-33 25 107.35 5.9 12.98 101.6 18-Jul-35 25 94.65 6.07 24.21 148.4
16-May-45 10 148.09 19.64 2.09 N/A 27-Jul-47 10 125.3 20.33 2.45 N/A
13-May-45 15 113.01 11.74 5.52 N/A 23-Jul-47 15 94.93 12.07 9.66 N/A
12-May-45 20 106.19 7.9 8.18 41 23-Jul-47 20 90 8.02 16.96 72.2
11-May-45 25 104.49 5.74 9.4 127.4 22-Jul-47 25 88.39 5.72 21.33 208.4
21-Jul-23 10 156.86 22.82 1.32 N/A 24-Nov-27 12 110.65 17.6 3.29 N/A
15-Jul-23 15 105.6 13.9 5.21 N/A 22-Nov-27 16 95.43 12.18 8.26 N/A
14-Jul-23 20 97.59 9.48 9.84 23.1 21-Nov-27 20 91.82 8.97 13.29 46.3
14-Jul-23 25 96.26 6.93 12.69 94.5 22-Nov-27 24 90.61 6.9 17.03 132.7
29-Aug-36 10 153.52 21.26 3.32 N/A 4-Apr-44 20 109.28 19.19 1.42 N/A
24-Aug-36 15 114.15 12.9 9.35 N/A 2-Apr-44 25 92.29 14.8 3.27 N/A
23-Aug-36 20 105.77 8.78 14.87 23.8 1-Apr-44 30 87 11.86 5.6 N/A
23-Aug-36 25 102.79 6.41 18.33 94.7 26-Aug-24 12 159.88 22.01 1.54 N/A
4-Sep-48 10 152.61 21.22 2.05 N/A 22-Aug-24 16 124.49 16.96 3.21 N/A
29-Aug-48 15 109.75 12.84 6.72 N/A 18-Aug-24 20 105.02 11.91 7.28 N/A
28-Aug-48 20 100.97 8.71 11.83 32.4 17-Aug-24 24 99.7 9.41 10.72 26.8
27-Aug-48 25 97.94 6.33 15.43 116.1 1-Oct-37 12 140.43 20.05 2.24 N/A
3-May-21 10 117.89 20.57 2.71 N/A 27-Sep-37 16 111.03 14.11 5.58 N/A
29-Apr-21 15 91.94 12.25 9.66 N/A 25-Sep-37 20 102.25 10.55 9.68 11.3
30-Apr-21 20 87.87 8.24 15.97 64.7 25-Sep-37 24 98.87 8.21 13.41 52.4
30-Apr-21 25 86.46 6.05 19.39 202.6 22-Nov-27 20 91.75 6.95 18.14 114.8
15-Jun-34 10 118.73 18.35 6.56 N/A 22-Nov-27 24 91.51 5.23 20.28 232.8
12-Jun-34 15 98.65 10.9 16.73 N/A 25-Nov-39 20 89.27 6.35 12.39 197.9
12-Jun-34 20 94.31 7.41 23.53 83.7 25-Nov-39 24 89.57 4.76 13.73 305.6
12-Jun-34 25 92.45 5.54 26.34 205.4 26-Nov-27 19 91.97 5.44 17.75 215.5
19-Jun-46 10 114.86 18.74 3.21 N/A 26-Nov-27 24 90.82 3.99 20.01 384.3
16-Jun-46 15 92.97 11.14 10.25 N/A 29-Nov-39 20 87.8 6.55 7.1 152.2
16-Jun-46 20 89.53 7.54 16.68 94.4 29-Nov-39 24 87.24 5 6.8 287.9
16-Jun-46 25 88.7 5.59 18.19 227.5
2002TC302
2003AZ84
2002AW197
QuaoarSednaMakemakeHaumea
2007UK126
IxionHuya

15
encounters with Jupiter and its intense radiation belts or executing orbital capture since the arrival
velocities are much lower would be advantageous for longer mission durations and would allow for a larger
payload to be inserted into orbit.
Figure 19. C3, Jupiter Flyby Radius and Arrival V∞ vs. Mission Duration for a launch to 2002 TC302
in March 2020
It was also necessary to determine appropriate launch window dates and, consequently, the possible
payload mass. For the purpose of this mission, it was decided that a 30-day launch window would be
sufficient in order to account for unfavorable launch conditions on certain days. The obviously ideal date
to launch a spacecraft is when the lowest launch energy occurs, since this allows for the maximum payload
to be launched.
Figure 20. Earth Departure C3 as a Function of Launch Date for a 15-Year Mission to 2002 TC302
Once launch windows were found, launch payload mass could be calculated for the rockets being
considered for launching the spacecraft. In this study, an Atlas V 551 with a Star-48B upper stage is
considered, as well as, a Delta IV HLV. The plots display the superiority of the Atlas V since it has the
largest payload capacity. It is especially good for higher launch energies, whereas the Delta IV is better
suited to missions with lower launch energy requirements.
0
20
40
60
80
100
120
140
160
0
3
6
9
12
15
18
21
24
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
C3(km2/s2)
V∞(km/s)
FlybyRadius(JovianRadii)
Varrival
Flyby
Radius
Launch
C3
90
95
100
105
110
115
120
LaunchC3(km2/s2)
Days Past 9-March-2020

16
Figure 21. Earth Departure Payload Mass as a Function of Launch Date for a 15 Year Mission to
2002 TC302
The data that was collected suggest that the TOF for missions is likely to be in the 20-25 year range
because they allow for smaller required C3 values and a greater radius of periapse for the JGA. These
factors are extremely important when considering how much mass can be captured into orbit and when
ionizing radiation poses a threat.
ORBITAL CAPTURE
The possibility of inserting a payload into orbit around one of the target bodies was analyzed. Insertable
mass was calculated using the launch vehicle throw mass for the Earth departure C3 requirements at the
edge of the 30-day launch window. A minimum mass of ~100 kg was assumed to be feasible for a
spacecraft for orbital insertion.
When all of these factors are considered, it becomes clear that a mission involving orbital capture
becomes impractical for transit times much less than 25 years. Table 2 also contains the estimated capture
mass that is allowed for each trajectory and vehicle configuration. There was no mission in the 10-15 year
TOF range that would allow for any significant mass to be placed in orbit around any target TNO. The 25
year missions are the most promising, with some allowing 200-300 kg, or more, of insertable mass.
In order to illustrate the effect that the launch date has on the capture mass, plots are presented in
Figures 22 and 23 to show the range of capture mass possibilities based on the launch window. It can be
seen that this can have a significant effect on capture mass at the target and is enough to lead to a reduction
in the scientific payload which could be carried on an orbital mission.
0
200
400
600
800
1000
1200
1400
1600
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
PayloadMass(kg)
Days Past 9-March-2020
Atlas V
551 w/
Star 48

17
Figure 22. Capture Mass as a function of launch date for 2007 UK126 in June 2046
Figure 23. Capture Mass as a function of launch date for 2002 UX25 in May 2045
HIGH- AND LOW-THRUST COMPARISON
Table 3 compares high and low-thrust missions with regard to flyby mass for selected targets. For this
analysis, the high thrust missions are launched on an Atlas V 551 with a Star 48 upper stage. Due to the
much lower departure C3, the low-thrust missions use a variety of potential launch vehicles. Note that
departure dates for low-thrust trajectories are nearly all one year and two months earlier than for the
corresponding high-thrust case. This is due to low-thrust trajectories requiring a longer Earth-Jupiter transit
time. The advantage of low thrust missions can be seen with comparable masses being delivered to a given
target using a smaller launch vehicle or larger payloads achieved for a given launch vehicle. For example,
an Atlas V 551 with a Star 48 upper stage could launch 1546 kg on a 20-year, high-thrust trajectory to
Quaoar; the same launch vehicle without the Star 48 upper stage could deliver 2000 kg if a low thrust
interplanetary transfer were employed using three thrusters. Likewise, for a 30 year transfer to Sedna, a low
thrust system can deliver about 400 kg more than a high-thrust system launched on the same vehicle, while
not requiring the use of the Star 48 upper stage.
0
50
100
150
200
250
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
CaptureMass(kg)
Days Past 2-June-2046
Atlas V
551 w/
Star 48
Delta IV
HLV
0
50
100
150
200
250
300
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
CaptureMass(kg)
Days Past 10-May-2045
Atlas V
551 w/ Star
48

18
Table 3. Total SOI Arrival Mass Comparison for Varying Targets and Mission Durations
JOVIAN FLYBY RADIATION ANALYSIS
When considering the high-thrust missions’ JGA maneuvers, there are many factors that affect how
much radiation the spacecraft will be exposed to. The inclination, V∞, Jovian periapse radius, and the
longitude of the ascending node are all determining factors in the received dose of radiation for the flyby.
The magnetotail of Jupiter will always be streaming directly away from the sun because of the solar
radiation pressure emitted from the sun. This means that the magnetotail will always be located in the same
position when using a planetocentric reference frame. Also, the magnetosphere is somewhat squashed in
the North-South direction making it more like a tear-drop shaped belt that stretches several Jovian radii.
This is why higher-inclination flybys with larger values of V∞ will receive lower doses of ionizing
radiation. When the flyby periapse radius is below 16 Jovian radii then the radiation environment will be
dominated by trapped electrons. In this region, the strength of the trapped electron radiation is orders of
magnitude greater than the trapped protons, GCR, or Bremsstrahlung radiation. Figure 24 shows the
radiation dose-depth curves for the three high-thrust trajectories described in Table 6. These are the only
cases for which such results have been obtained to date.
MakeMake Launch Date TOF (Years)
Arrival Mass
(kg) Launch Vehicle Launch Date TOF (Years)
Arrival Mass
(kg) Launch Vehicle Thrusters
17-Aug-24 16 1059 Atlas V551 w/ Star 48 17-Jun-23 19 736 Atlas V401 2
18 1191 Atlas V551 w/ Star 48 34 1156 Atlas V521 2
Quaoar
22-Nov-27 16 1468 Atlas V551 w/ Star 48 23-Sep-26 14 844 Atlas V401 2
25 1773 Atlas V551 w/ Star 48 26 2148
Atlas V551 w/
Star 48 3
Haumea
25-Sep-37 16 1174 Atlas V551 w/ Star 48 26-Jul-36 18 786 Atlas V401 2
25 1407 Atlas V551 w/ Star 48
Sedna
28-Mar-32 30 1629 Atlas V551 w/ Star 48 29-Jan-31 34 651 Atlas V401 1
28 1181 Atlas V521 2
29 1958 Atlas V551 3
34 2278
Atlas V551 w/
Star 48 3
Low ThrustHigh Thrust

19
Table 6. Mission Details for Jovian Flyby Radiation Analysis Cases
Sedna
Earth Dep. Date
Transit to Jupiter
(days)
Pass Dist., (Jovian
radii)
V∞ (km/s)
20 Year 2/4/2044 482.8 1.42 13.09
25 Year 2/4/2044 569.3 3.30 10.14
30 Year 2/4/2044 621.0 5.60 8.85
Quaoar
12 Year 24/11/2027 539.0 3.29 12.33
20 Year 1/8/2029 679.6 13.29 8.60
24 Year 22/11/2027 698.7 17.01 8.24
Makemake
12 Year 29/9/2025 397.4 4.67 17.87
16 Year 25/9/2025 461.0 9.37 14.53
20 Year 23/9/2025 495.8 14.37 13.07
Figure 24. Radiation Dose-Depth curves for several potential missions. The “radiation
cutoff” is at a level commonly used as an allowable upper limit.
1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
1.00E+07
1.00E+08
1.0 10.0 100.0 1000.0
IonizingDoseinSilicon,rads
Shielding Thickness, mils
Sedna 20
Year
Sedna 25
Year
Sedna 30
Year
Quaoar 12
Year
Quaoar 20
Year
Quaoar 24
Year
Makemake
12 Year
Makemake
16 Year
Makemake
20 Year
Radiation
Cutoff

20
CONCLUSIONS
Orbital capture of a small satellite (100-380 kg) has been found to be feasible for missions to several
trans-Neptunian objects, using a traditional, high-thrust interplanetary transfer and a Jupiter gravity assist.
Launch would be accomplished using an Atlas V 551 with a Star 48 B upper stage. The most favorable
results were obtained for missions to Huya, Ixion, 2003 AZ84, and 2007 UK126, with transit times of
approximately 25 years necessary to achieve substantial capture mass. The use of a low-thrust propulsion
system has the potential to increase the mass delivered to the target and/or decrease the size of the launch
vehicle as compared to that required for a conventional, high-thrust mission.
ACKNOWLEDGEMENTS
The group would like to thank Jerry Horsewood of Spaceflight Solutions for the use of his trajectory
codes, without which the project could not have been carried out. Dr. Henry Garrett of the Jet Propulsion
Laboratory was also very helpful with regard to Jovian flyby radiation analysis.
REFERENCES
1) McGranaghan, R., Sagan, B., Dove, G., Tullos, A., Lyne, J.E., Emery, J.P., “A Survey of Mission
Opportunities to trans-Neptunian Objects,” Advances in the Astronautical Sciences Series, CP11-615,
Vol.142, Univelt, San Diego, CA, 2012.
2) A Survey of Mission Opportunities to trans-Neptunian Objects - Part II, Orbital Capture; Ashley
Gleaves, Randall Allen, Adam Tupis, John Quigley, Adam Moon and James Evans Lyne; AIAA Paper
2012-5066, presented at the 2012 Astrodynamics Specialists Conference.
3) Brown, M., "How many dwarf planets are there in the outer solar system? (updates daily),"
http://www.gps.caltech.edu/~mbrown/dps.html.
4) Mission Analysis Environment (MAnE), Version 3.5, developed by Space Flight Solutions,
Hendersonville, NC.
5) Heliocentric Interplanetary Low-thrust Trajectory Optimization Program (HILTOP), developed by
Space Flight Solutions, Hendersonville, NC.
6) "Launching Science: Science Opportunities Provided by NASA's Constellation System," National
Research Council, Washington, DC, 2009.
7) "Falcon 9 Launch Vehicle Payload User's Guide," SpaceX, 2009.
8) “ATK Space Propulsion Products Catalog,” 14 May, 2008.
9) “Development of the Cassini Spacecraft Propulsion Subsystem,” Leeds, Michael, Eberhardt, Ralph
and Robert Berry, AIAA Paper 96-2864.
10) “Capabilities and Applications of the Program to Optimize Simulated Trajectories (POST),”
Brauer, G.L, Cornick, D.E., and Stevenson, R., NASA CR-2770, Feb. 1977.
11) http://space-env.esa.int/R_and_D/spenvis.html. Accessed April 12, 2013.
12) Kroening, K., Sollitt, L., “Small Body Mission Concepts: Presentation to the Small Bodies
Assessment Group, January 13th
, 2009,” Civil Space Business Development, Northrop Grumman.
http://www.lpi.usra.edu/sbag/meetings/jan2009/presentations/sollittKroening.pdf. Accessed April 17, 2013.

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