Manuscript7

69th
International Astronautical Congress (IAC), Bremen, Germany, 1-5 October 2018.
Copyright ©2018 by the International Astronautical Federation (IAF). All rights reserved.
IAC-18-C4.6.8 Page 1 of 14
IAC-18,D2,8-A5.4,5,x44792
ANALYSIS OF NUCLEAR THERMAL PROPULSION (NTP) ENABLED HELIOPAUSE TRAJECTORIES,
USING SOLAR-OBERTH MANEUVERS
Mr. Dennis L. Scotta,b
The Ohio State University, United States, scott.776@osu.edu
Co-Authors
Mr. Michael J. Boazzoa,b
The Ohio State University, United States, boazzo.2@osu.edu
Dr. John M. Horacka,b
The Ohio State University College of Engineering, United States, horack.1@osu.edu
Dr. Elizabeth Newtonb
The Ohio State University, United States, newton.387@osu.edu
a
The Ohio State University, College of Engineering, Columbus OH 43210, United States
b
Battelle Center for Science, Engineering, and Public Policy at The Ohio State University, John
Glenn College of Public Affairs, Columbus OH 43210, United States
Abstract
This paper focuses on the application of nuclear thermal propulsion to reach the heliopause and exit the solar system
on significantly shorter timescales than possible with chemical propulsion. We employ calculations based on the well-
known Oberth Method. Advances in nuclear thermal propulsion are being pursued by NASA and private companies,
such as BWXT. These advances will allow for multiple large ΔV to be executed within a single mission and at high
ISP.
Acronyms/Abbreviations
a = semi-major axis
au = astronomical units
μ = gravitational constant
M = mass of the central body
ISP = specific impulse
𝛥𝑣 = change in velocity
rp = radius of periapsis
ra = radius of apoapsis
gc = Earth gravitational constant
ε = specific orbital energy
c3 = characteristic energy
MR = mass ratio
SR = radius of the sun
SOI = sphere of influence
I. Introduction
The concept of nuclear thermal propulsion (NTP) has
been in development for over 60 years. Project Rover
was a joint program lead by the Atomic Energy
Commission and NASA that operated between 1955
and 1972.1
In this program, flight hardware
components for NTP were built and tested, acquired 17
hours of burn time for various types of reactor designs.
The most famous design created from the program was
the NERVA rocket engine, which was able to achieve
a specific impulse (ISP) of 850 seconds in a vacuum.2
This value is nearly double that of the RS-25 (Space
Shuttle Main Engine), which achieved an ISP of 452
seconds within a vacuum.
NTP technology was considered for integration into
flight hardware of the Apollo Applications program,
which sought to expand human exploration to Mars.
However, as public interest waned, the program was
cancelled, and the development of NTP was scrapped.
Later, in the 1970’s, various unmanned missions were
launched to explore the outer planets of the solar
system. Voyager 1 was launched in September 1978.
On August 25, 2012, nearly 35 years after launch, it
reached the termination shock, one of the outer limits
of the solar system. This distance is 124 astronomical
units (au)3
from the Sun. The New Horizons probe
launched aboard an Atlas V in January 2006 and is
predicted to reach the heliopause in 2040, 36 years
after launch.4
Designing missions to the outer planets and deep solar
system is difficult primarily due to constraints of fuel
and time. To save on these, spacecraft typically utilize
planetary flybys to help achieve their change in

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velocity (Δv) requirements. Often, months or years of
mission time are needed to rendezvous with a planet
for a change in velocity that is not even part of the
primary scientific mission. The direct approach option
is also not desirable due to the prohibitive amount of
fuel required to reach the destination and then to slow
down to reach a parking orbit.
NTP offers a greater amount of ISP than that of
conventional chemical boosters while also providing
high thrust. Because of the increased capabilities, the
spacecraft can devote more Δv into achieving
trajectories that will arrive at a destination more
quickly. In this paper, the benefits of NTP and the
Oberth Maneuver are applied in conjunction with
existing launch vehicles to investigate the fastest
possible trajectories across the solar system. These are
compared to Hohmann-type burns and more
commonly used trajectories.
II. Rockets and Orbital Mechanics Background
i. The Rocket Equation
Two of the primary limiting factors in a mission are
energy available from the launch vehicle and the Δv
available for post-launch maneuvers. The relation
between Δv and ISP is demonstrated through the use of
the well-known Konstantin Tsiolkovsky or “rocket
equation”:
∆𝑣 = 𝐼𝑠𝑝 ∗ 𝑔𝑐 ∗ ln (
𝑀𝑖
𝑀 𝑓
) [1]
Δv is a function of both ISP and the ratio of the initial
mass of the rocket (Mi) to the final mass (Mf) after all
the fuel is spent. By holding ISP constant and varying
the mass ratio (MR), the importance of the ISP is shown
below.
Figure 1: This figure illustrates the Tsiolkovsky
rocket equation of Δv versus a variable mass ratio
with various levels of ISP held constant. The higher
the value of ISP, the more Δv is available for a
given mass ratio.
ii. The Oberth Maneuver
Oberth briefly described a “powered flyby” in his
paper “Ways to Spaceflight”5
. The idea is that to
change the maximum specific orbital kinetic energy,
the largest increase or decrease is achieved by
changing velocity when the potential energy is
lowest. The topic was expanded upon by Adams and
Richardson in “Using the Two-Burn Escape
Maneuver for Fast Transfers in the Solar System and
Beyond”6
.
Figure 2: This figure illustrates an elliptic orbit of
a spacecraft around a central body.
Referring to figure 2 above, the Oberth maneuver
illustrates that it is most advantageous to add additional
Δv when the spacecraft is traveling at its fastest point
in its orbit, rp. This is derived from the use of the
specific orbital energy equation and noting the specific
energy is a constant for a defined orbit.
𝑣2
2
−
𝜇
𝑟
= 𝜀 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 [2]
𝑣 𝑝
2
2
−
𝜇
𝑟𝑝
= 𝜀1 = 𝜀2 =
𝑣 𝑎
2
2
−
𝜇
𝑟𝑎
Applying a fixed Δv at both rp and rp, it is shown below
through manipulation that
𝜀1 ≠ 𝜀2
𝜀1 =
(𝑣 𝑝 + ∆𝑣)2
2
−
𝜇
𝑟𝑝
𝜀2 =
(𝑣 𝑎 + ∆𝑣)2
2
−
𝜇
𝑟𝑎
∆𝜀 = 𝜀1 − 𝜀2

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∆𝜀 =
(𝑣 𝑝 + ∆𝑣)2
2
−
𝜇
𝑟𝑝
−
(𝑣 𝑎 + ∆𝑣)2
2
−
𝜇
𝑟𝑎
∆𝜀 =
𝑣 𝑝
2
+ 2𝑣 𝑝∆𝑣 + ∆𝑣2
2
−
𝜇
𝑟𝑝
−
𝑣 𝑎
2
+ 2𝑣 𝑎∆𝑣 + ∆𝑣2
2
−
𝜇
𝑟𝑎
∆𝜀 = (
𝑣 𝑝
2
2
−
𝜇
𝑟𝑝
) − (
𝑣 𝑎
2
2
−
𝜇
𝑟𝑎
) +
(𝑣 𝑝∆𝑣 − 𝑣 𝑎∆𝑣)
∆𝜀 = (𝜀 𝑝 − 𝜀 𝑎) + (𝑣 𝑝∆𝑣 − 𝑣 𝑎∆𝑣)
∆𝜀 = (𝑣 𝑝∆𝑣 − 𝑣 𝑎∆𝑣)
At this point note that:
𝑣 𝑝 > 0, 𝑣 𝑎 > 0 , ∆𝑣 > 0
Therefore, executing a burn maneuver when potential
energy is low and kinetic energy is high maximizes
energy gained if Δv is held as a constant.
The following trajectories have been analyzed. First,
an Earth departure trajectory is required to place the
spacecraft on a heliocentric orbit with perihelion near
the sun. After a large Δv is applied at or near perihelion,
the spacecraft then will executes a heliocentric
hyperbolic trajectory to the outer solar system. With
ra = rEarth set, the final solar system exit velocity of
the spacecraft becomes a function of target perihelion
(rp) and the Δv applied at perihelion. Utilizing the
commonly known orbital equations for Keplerian
orbits, found in common text7
, the final solar system
exit velocity equation can be calculated to be:
vfinal =
μSun
√2μSun √
rarp
r1 + r2
√(
[
rp
(
√2μSun√
rarp
ra + rp
r2
+ ∆v
)]
2
rpμSun
− 1
)
2
− 1
Figure 3: This figure illustrates the Oberth
maneuver where the the NTP spacecraft follows
an inbound elliptical trajectory to get close to the
Sun, and then follows a hyperbolic trajectory after
firing at the Perihelion. The orbital angular
momentum is in to the page.
Figure 4: The graph displays the heliocentric solar
system exit velocity as a function of Δv for different
Perihelia (𝒓 𝒑) . For a given Δv value, if the perihelia
is decreased, the final velocity increased.
III. Methodology
i. Limitations and Specifications
There is a limitation placed on the closest periapsis
radius, as it is clear that the craft may not travel
arbitrarily close to the sun and survive. As of this
writing, the closest man-made object to approach the
sun will be the Solar Parker Probe, which launched on
August 12, 2018. This probe will reach 9.8 solar radii

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perihelion.9
Consequently, in our analysis, a limitation
of 10 perihelion is used.
ii. Launch Vehicle Selection
For this analysis, we have examined six different
launch vehicles. They are: the Space Launch System
Family Block 1 through 2B, SpaceX’s Falcon Heavy,
ULA’s Atlas V, and ULA’s Delta IV Heavy. This is a
simplified case-study; therefore, a more detailed
analysis, including booster configurations, will be
necessary to move beyond preliminary mission
calculations. The vehicles in this analysis were chosen
for their c3 output for various payloads.
Figure 5: The graph illustrates the relevant launch
energy (c3) curves for five (5) launch vehicles.9,10,11
The c3 value is defined as the square of the residual
velocity the payload will have upon exiting the Earth’s
Sphere of influence (SOI).
iii. Computation Methodology
The algorithm for computing the Oberth maneuver
trajectories incorporates three factors: The Launch
vehicle that will carry the spacecraft outside of the
Earth’s SOI, and two free parameters, the target solar
perihelia and the mass of the NTP spacecraft.
Possible mass ratios of the NTP spacecraft are stored
as a vector ranging from 1 to 100. We recognize these
values extend well beyond current state of the art
technology, but are included to better understand the
physics of the situation.
For each launch vehicle, the published c3 values
achieve a set of earth departure velocities for a given
set of mass ratios. When propelled opposite the
direction of Earth travel, this places creates multiple
spacecraft inbound heliocentric orbits with varying
values of perihelia. In some cases, we can achieve
small perihelia using the launch vehicle alone while in
other cases Δv must also be extracted from the NTP
system. As the analysis shows, this has important
consequences from the ultimate solar system residual
velocity.
The final output of this analysis for a given launch
vehicle produces a set of final solar system exit
velocities as a function of target solar perihelion for
differently assumed mass ratios. These results are
shown and described in the following figures.
IV. Trajectory Analyses
The curves for ULA Atlas V and ULA Delta IV Heavy
show two distinct regimes, and a notable "breakpoint",
where the solar system exit velocity is maximized for
the given configuration. This point describes the solar
system exit velocity where the launch vehicle provides
the maximum Δv possible, with the NTP spacecraft
providing the all the Δv possible for the Oberth burn.
To achieve a smaller perihelion, where one might
expect an additional impact from the Oberth maneuver,
additional Δv from the NTP system is required, and
therefore that energy is no longer available, resulting
in a decreasing solar system exit velocity. To the right
of the breakpoint, use of Δv is available, but at
increased perihelion, the spacecraft is moving more
slowly. Thus, the Oberth effect is less pronounced, and
thus solar system exit velocities are correspondingly
reduced.
Figure 6: The curvatures represent a fixed mass
ratio and demonstrates the effect of the selected
target perihilion. The breakpoint for each curve
shows the perihilion distance where NTP is
required to further reduce the perihelian. Notice
for mass ratio 12 the spacecraft preforms more
poorly compared to a mass ratio of 10 for closer
select perihion. This is due to the rapid decline in c3
the Atlas V offers for higher mass ratios, forcing too
much input from the NTP. This causes a new MR
“breakpoint” to exist as MR increases.

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Figure 7: For a launch vehicle with a greater
launch energy, such as the ULA Delta IV Heavy,
there is no similar cross over point for higher mass
ratios.
Figure 8: By holding the mass ratio constant, the
effectiveness of the launch vehicles c3 energy is
shown. MR = 10 results in only the SLS Block 2B
having enough residual energy in the NTP to begin
to see a return at decreased target solar perihelion.
Resulting solar system exit velocities provided by the
SLS family above show a notable advantage over the
Delta IV Heavy, Atlas V, and Falcon Heavy. The SLS
family is able to deliver a much larger payload to a
given target perihelion, resulting a much larger
available Δv from the NTP spacecraft for the Oberth
burn.
To explore this further, we show solar system exit
velocities in a 3D plot, as a function of both perihelion
values and mass ratios.
Figure 9: A 3D representation for maximum solar
system exit velocity as a function of both mass ratio
and target perihelion. Note the ridgeline indicating
the smallest target perihelion reached before the
launch vehicle c3 is insufficient and additional NTP
power is needed. This leads to a decrease in the
maximum solar exit velocity as both mass ratio
increases and target perihelion decreases.
Figure 10: Similar to figure 9, a 3D representation
for maximum solar system exit velocity as a
function of both mass ratio and target perihelion.
Unlike figure 9, note the ridgeline is followed by a
flat region before a sharp increase in maximum
solar exit velocity as target perihelion decreases and
mass ratio increases.
By examining the maximum solar system exit velocity
at each target perihelion, one can determine the
relationship between this maximum velocity and the
mass ratio for each vehicle. These are shown in the
figure below.

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Figure 11: Maximum solar system exit velocity as a
function of mass ratio alone
The additional capabilities possessed by the SLS
family is again visible across typical current mass
ratios, as well as for more ambitious values.
At this point the Oberth maneuver trajectories may be
compared to that of the direct burn maneuver. The
direct burn maximum solar system exit velocity is a
function of mass ratio alone and corresponds directly
to the mass of the spacecraft and the c3 characteristics
of the launch vehicle.
Figure 12: The direct burn maneuver expands and
adds together both launch vehicle Δv and NTP
spacecraft Δv from a heliocentric Earth orbit,
where perihelion is 1 au. The resulting solar system
exit velocity is a function of mass ratio alone.
V. Results
Analysis of the results provides sufficient data for
determining preliminary maximum heliocentric
velocity, the time to exit the solar system, as well as a
comparison to a direct burn method.
i. Velocity
A comparison of the Oberth maneuver to direct burn
for the ULA Atlas V and SLS Block1 are shown below:
Figure 13: The ULA Atlas V Oberth and direct
burn maneuver maximum solar system exit
velocity. Note that the Oberth maneuver velocity
never exceeds that of the direct burn.
Figure 14: The NASA SLS Block 1 maximum solar
system exit velocity. The Oberth maneuver
surpasses the direct burn method at MR = 8,
corresponding to a combined launch vehicle and
NTP spacecraft Δv= 26.82 km/s
For each launch vehicle, except the ULA Atlas V, the
heliocentric exit velocity achieved by the Oberth
maneuver is greater than that of the direct burn
maneuver. For each of these cases, spacecraft powered
through the Oberth method catch and surpass the
output of the direct method at a particular MR.
Computationally calculated, this MR point provides a
combined Δv budget from the launch vehicle and the
NTP system of ~26.58 km/s. Graphically this is shown
below in figure 15. A corresponding table is located in
the appendix [B.1]

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Figure 15: The intersection of the Oberth and direct
burn maneuver for each launch vehicle occurs
when the total Δv budget ~26.58 km/s. Except for
the ULA Atlas V, which cannot produce a launch
vehicle Δv plus spacecraft NTP Δv combination that
can exceeds this threshold.
It can inferred that a total mission Δv budget ~26.58
km/s is a potential threshold point for an Oberth
maneuver to exceed that of the direct burn for any
vehicle configuration in terms of maximum solar exit
velocity when launch mass is the free variable.
It is beneficial to compare the maximum solar system
exit velocity from an Oberth maneuver to that of a
direct burn. The mass ratio of each is the free variable.
For each launch vehicle the mass ratio of the direct
burn that resulted in the maximum solar exit velocity
was identical to the mass ratio of the Oberth maneuver
that resulted in maximum velocity. The velocity results
are graphically shown below and tabulated in the
appendix. [B.2]
Figure 16:Comparison of the maximum solar
system exit velocity for the Oberth and direct burn
maneuvers. Note that the ULA Atlas V, SpaceX
Falcon Heavy, and ULA DeltaIV Heavy have nearly
identical comparison outputs.
Below, we shall employ payload mass ratios that far
exceed that of a current technology but are included for
a more complete look at the situation. As previously
stated, the maximum exit velocity of ULA Atlas direct
burn is greater than that of the Oberth maneuver
performed with this launcher. The maximum solar
system exit velocity achieved by the DeltaIV Heavy
and Falcon Heavy by the direct burn and Oberth
maneuver are virtually identical. This comes from the
fact that the maximum Δv budget that can be obtained
by the launch vehicle and NTP spacecraft combination
is only ~1 km/s above the aforementioned “threshold”.
The SLS family has a greater amount of Δv budget
available, and this greatly increases the effects of the
Oberth maneuver.
ii. Time
Voyager 1 encountered the heliopause ~124 au from
the Sun and serves as a distance useful to employ as
the edge of the solar system. Below, the maximum
solar system exit velocity is used for each of the six
launch vehicles to calculate how long it would take
each to reach the heliopause.
Figure 17: The figure shows the time it takes to
reach the heliopause utilizing the maximum solar
system exit velocity from an Oberth maneuver.
As with the maximum velocity, it is beneficial to
compare the heliopause mission times from the direct
burn to that of the Oberth maneuver and is shown
graphically below with a corresponding table in the
appendix [B.3]

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Figure 18: Comparison of the time it takes to reach
the heliopause for the Oberth and direct burn
maneuvers.
It is not surprising that the ULA Atlas V direct burn
maneuver is reaches the heliopause in less time than
the Oberth maneuver, because the maximum solar
system exit velocity is higher. It is also useful to note
the comparison values for the ULA Delta IV Heavy
and SpaceX Falcon Heavy. Although the maximum
velocity of the Oberth maneuver is greater than that of
the direct burn, the difference is not great enough to
overcome the time spent traveling to a closer
perihelion for the maneuver. The move does eventually
overtake the direct burn, but well beyond the
heliopause as discussed in the section [V.iii] below.
For the SLS family, the difference is more pronounced
and follow the expected results from the heliocentric
solar system exit velocities.
iii. Oberth Maneuver Direct Burn Rendezvous
For the SLS family, in addition to an increased velocity
to reach the heliopause, the solar Oberth maneuver can
be used to explore the outer solar system on time scales
less than that of the direct burn. For example, to reach
the orbit of Pluto, an SLS Block 1B with parameters
from table B.2 delivers a time of 2.56 years. This can
be compared to the direct burn time of 3.41 years.
To illustrate the region where the Oberth maneuver is
more effective than the direct burn the rendezvous
distance and time are calculated by setting the launch
time for both equal to zero. Below in figure 19 and
figure 20 the locations and time period elapsed are
provided. The SLS block 1 direct burn reaches a
distance of 11.92 au before the Oberth Maneuver,
requiring 1.13 years. Beyond this distance, Oberth
trajectories are faster in elapsed time. For the Falcon
Heavy the two maneuvers provide equal distances and
elapsed times well beyond the heliopause, at 205.07 au
and 24.66 years.
Figure 19: Rendezvous distance and time for the
NASA SLS Block 1. The radius of equal mission
duration is 11.91 au, just beyond Saturn. Inside this
region, a direct burn is more effective. Outside this
rendezvous distance, for planets such as Uranus,
Neptune and Pluto, the Oberth maneuver provides
greatly reduced mission times.
Figure 20: Oberth vs direct burn rendezvous
distance and time for the SpaceX Falcon Heavy.
Although the maximum solar system exit velocity is
higher for the Oberth maneuver the rendezvous
distance is well outside of the heliopause, after more
than 24 years of flight.
6. Conclusions and Recommendations
For the launch vehicles investigated, independent of
configuration, the addition of an NTP spacecraft
results in maximum solar system exit velocities at least
twice that of Voyager 1, with corresponding
heliopause mission times that are cut in half.
For these set of launch vehicles and NTP spacecraft
configurations, the threshold for the Oberth maneuver
to be produce a greater maximum solar system exit
velocity than the direct burn method required the total
mission Δv budget to be higher than 25.58 km/s. This
threshold was computational calculated. To take the

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analysis further, it is recommended to include a greater
range of launch vehicles and as well as vary the NTP
ISP values to explore the total Δv budget threshold
value.
The complete SLS family is able to take full advantage
of the Oberth maneuver for increased maximum solar
system exit velocities, as well as decreased the overall
mission time for heliopause trajectories. The SLS
Block 1 is able to take the maximum advantage of the
Oberth maneuver with a NTP spacecraft mass ratio of
41 and a solar perihelion at 10 solar radii. For example,
comparing the SLS block 1 to the Falcon Heavy, an
increase in total Δv budget of 6.17km/s (from 27.89
km/s to 34.06 km/s) results in an increase in solar
system exit velocity from 39.74 km/s to 59.81 km/s.
This increase of ~20km/s that exceeds even the current
velocity of Voyager 1.
This mass ratio is clearly larger than state of the art
technology available, but even with current values, the
entire SLS family sees significant gains in both time
savings and solar system exit velocity by performing
an Oberth maneuver vs direct burn. Spacecrafts with a
mass ratio ~10, launched onboard an SLS Block 1B,
diving to a perihelion of 10 solar radii and executing a
Δv burn of ~9.2 km/s can exit the solar system with
velocities approaching 43 km/s, nearly 3 times that of
Voyager.
The SpaceX Falcon Heavy and similarly powered
launch vehicles are able to use the Oberth manuever,
but with little gain for exploring the heliopause. The
maneuver could be used however to explore distances
greater than 2 times that of the heliopause with
shortened mission times. These launch vehicles may be
able to take greater advantage of the Oberth maneuver
if an inner planetary gravity assists from Venus takes
the craft to a closer perihelion distance to enhance the
energy gained from an NTP burn at that perihelion.
The thermal nuclear propulsion enabled Oberth
maneuver is ideal for a number of near future NASA
missions and challenges, such as the 100 - Year
Starship and the interstellar precursor missions.
Launched aboard a NASA SLS Block 1B, an NTP
spacecraft could reach a distance of 500 au in just 32
years, allowing scientist to perform experiments and
collect information in a single lifetime.
References
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Conference; 25-28 Jul. 2010; Nashville, TN
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[12] Chreech, Stepehn NASA’s Space Launch
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Appendix A (Figures)
Figure 21: ULA Atlas V final solar system exit velocity
Figure 22: ULA DeltaIV Heavy final solar system exit velocity

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Figure 23: SpaceX Falcon Heavy final solar system exit velocity
Figure 24: NASA SLS Block 1 final solar system exit velocity

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Figure 25: NASA SLS Block 1B final solar system exit velocity
Figure 26: NASA SLS Block 2B final solar system exit velocity

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Appendix B (Tables)
Launch Vehicle Launch Vehicle Δv NTP Δv Total Δv
ULA Atlas V 3.6257 19.3652 22.9909
ULA Delta IV Heavy 5.7298 20.7895 26.5193
SpaceX Falcon Heavy 5.1880 21.1602 26.3482
NASA SLS Block 1 8.7365 18.0866 26.8231
NASA SLS Block 1B 10.4890 16.2259 26.7150
NASA SLS Block 2B 11.8303 14.8004 26.6307
Table 1: Total Δv Budget when the Oberth maneuver v∞ exceeds that of the Direct Burn. The total Δv budget
for the crossing point is 26.577 km/s with a “range” of .475 km/s. The final 5 launch vehicles are very close in
proximity.
ULA
Atlas V
ULA
DeltaIV Heavy
SpaceX
Falcon Heavy
NASA
SLS Block 1
NASA
SLS Block 1B
NASA
SLS Block 2B
OBERTH
𝑣∞,𝑚𝑎𝑥 (km/s) 31.72 39.19 39.74 59.81 73.09 81.72
𝛥𝑣𝑡𝑜𝑡𝑎𝑙 (km/s) 22.98 27.54 27.89 34.06 38.48 41.62
MR 11 19 21 41 63 95
SR 146 146 155 10 10 10
DIRECT
𝑣∞,𝑚𝑎𝑥 (km/s) 31.78 38.88 39.38 41.96 53.61 57.65
𝛥𝑣𝑡𝑜𝑡𝑎𝑙 (km/s) 22.98 27.54 27.89 34.06 38.41 41.63
MR 11 18 21 41 64 94
Table 2: Maximum solar system exit velocity comparison of the Oberth and Direct Burn Maneuver
ULA
Atlas V
ULA
Delta IV Heavy
SpaceX
Falcon Heavy
NASA
SLS Block 1
NASA
SLS Block 1B
NASA
SLS Block 2B
OBERTH
𝑡 𝑚𝑖𝑛 (years) 17.8 14.6 14.43 9.595 7.912 7.107
𝛥𝑣𝑡𝑜𝑡𝑎𝑙 (km/s) 22.98 27.54 27.8770 34.06 38.4071 41.6295
MR 11 18 20 41 64 94
SR 146 138 142 10 10 10
DIRECT
𝑡 𝑚𝑖𝑛 (years) 17.405 14.35 14.174 11.708 10.502 9.77
𝛥𝑣𝑡𝑜𝑡𝑎𝑙 (km/s) 22.98 27.54 27.89 34.06 38.4071 41.6295
MR 11 18 21 42 64 94
Table 3: Heliopause mission time comparison of Oberth and Direct Burn Maneuver

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