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AAS 18-416
PRELIMINARY INTERPLANETARY MISSION DESIGN AND
NAVIGATION FOR THE DRAGONFLY NEW FRONTIERS MISSION
CONCEPT
Christopher J. Scott∗
, Martin T. Ozimek∗
, Douglas S. Adams†
, Ralph D. Lorenz‡
,
Shyam Bhaskaran§
, Rodica Ionasescu¶
, Mark Jesick¶
, and Frank E. Laipert¶
Dragonfly is one of two mission concepts selected in December 2017 to advance into Phase A
of NASA’s New Frontiers competition. Dragonfly would address the Ocean Worlds mission
theme by investigating Titan’s habitability and prebiotic chemistry and searching for evi-
dence of chemical biosignatures of past (or extant) life. A rotorcraft lander, Dragonfly would
capitalize on Titan’s dense atmosphere to enable mobility and sample materials from a vari-
ety of geologic settings. This paper describes Dragonfly’s baseline mission design giving a
complete picture of the inherent tradespace and outlines the design process from launch to
atmospheric entry.
INTRODUCTION
Hosting the moons Titan and Enceladus, the Saturnian system contains at least two unique destinations that
have been classified as ocean worlds. Titan, the second largest moon in the solar system behind Ganymede
and the only planetary satellite with a significant atmosphere, is larger than the planet Mercury at 5,150 km
(3,200 miles) in diameter. Its atmosphere, approximately 10 times the column mass of Earth’s, is composed
of 95% nitrogen, 5% methane, 0.1% hydrogen along with trace amounts of organics.1Titan’s atmosphere
may resemble that of the Earth before biological processes began modifying its composition. Similar to the
hydrological cycle on Earth, Titan’s methane evaporates into clouds, rains, and flows over the surface to
fill lakes and seas, and subsequently evaporates back into the atmosphere. Beneath its surface, Titan likely
contains a briney, global ocean under a layer of ice.2Interestingly, on Titan, water plays the role of magma
on Earth and methane plays the role of water. Because of its similarities with an early Earth, complex and
active organic chemistry, internal water ocean as well as liquid water on the surface in the past, and a possible
model for a future Earth, Titan is a compelling destination of high astrobiological value.3
Titan has been considered many times in the past as a potential destination for robotic exploration. As
technology and our knowledge of Titan has advanced over the last few decades a plethora of mission concepts
have been explored including entry probes, penetrators, sounding rockets, balloons, dirigibles, landers, and
even submarines.4More recently, the Johns Hopkins Applied Physics Laboratory (APL) was a central partner
in the team that developed the Titan Mare Explorer (TiME) concept (a floating, lake lander),5led a 2007
NASA Titan Flagship Mission Study,6and was a contributing institution for the Planetary Decadal Survey
Titan Saturn System Mission Concept Study.7Although rotorcraft have previously been identified as an
enabler on Titan,4advances in multi-rotor drones have led to simpler mechanical implementations, compact
∗Mission Design Engineer, Space Exploration Sector, Johns Hopkins Applied Physics Laboratory, 11101 Johns Hopkins Road, Laurel,
Maryland 20723.
†Systems Engineer, Space Exploration Sector, Johns Hopkins Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, Maryland
20723.
‡Project Scientist, Space Exploration Sector, Johns Hopkins Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, Maryland
20723.
§Supervisor, Outer Planets Navigation Group, California Institute of Technology, 4800 Oak Grove Drive, Pasadena CA, 91109.
¶Navigation Engineer, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena CA, 91109.
1
sensors, and reliable autonomy that can be applied to drone-like, planetary landers. The 2007 flagship study
called for a multi-vehicle solution which included an orbiter, a hot-air balloon, and a lander. Dragonfly would
achieve most of the science objectives of at least two of the three principle elements (lander and hot-air
balloon) on a New Frontiers budget by the paradigm-shifting utilization of modern rotorcraft technology.
(See Figure 1.)
Figure 1. Dragonfly mission arriving on Saturn’s moon Titan and flying in its atmosphere.
The goal of the Dragonfly interplanetary mission design and navigation is to deliver the entry vehicle to the
Titan atmospheric interface condition. This condition must target the selected landing site while judiciously
balancing the use of system resources and risk. Due to the low gravity, the density of Titan’s atmosphere
decreases slowly with altitude compared to those of Venus, Earth, or Mars. This characteristic stretches the
typical time and distance scales associated with atmospheric entry and eliminates the need for a shallow
approach into the atmosphere. Dragonfly enters Titan’s atmosphere directly from interplanetary space before
landing. Eliminating the need for large maneuvers, flybys of Titan, or aerocapture, direct entry dramatically
simplifies the mission design and operations prior to landing.
An overarching theme of the trajectory design is simplicity in terms of both the trajectory and opera-
tions. As described in the following sections, the low deterministic post-launch ∆v interplanetary trajectory
possesses nearly constant arrival conditions throughout both the primary and backup launch periods. For a
given arrival asymptote with respect to Saturn, the locus of all possible Titan entry conditions is determined
semi-analytically which ultimately bounds accessible areas on the surface. Acceptable designs must reach
the target landing site and allow sufficient time between landing and Earthset (for communication) while
satisfying the aerothermal heating, and acceleration requirements of the entry system.
This paper outlines the major mission design trades and relevant theory from launch to atmospheric entry.
First, the interplanetary trade space is introduced in the context of the design parameters which constrain the
space of all feasible designs. The performance of a variety of launch vehicles is tabulated including launch
capability and delivered mass into the Saturnian system. Arrival conditions upon entry into the Saturnian
system and thus Titan entry conditions are coupled to the interplanetary trajectory type, time-of-flight, and
launch energy. The next section mathematically describes the relationships between the Saturnian system
entry condition and the space of all Titan arrival conditions including entry speed, entry flight-path-angle
(EFPA), target latitude and longitude, arrival time, and time to Earthset. These conditions are mapped to
parameters which directly influence the Thermal Protection System (TPS) design such as heat flux, heat
load, and stagnation pressure, in addition to the peak acceleration experienced by the entry system. Lastly,
a description of the navigation strategy is introduced with a high-level introduction of the pragmatic design
flow among mission design, navigation, and atmospheric descent modeling. A detailed analysis of the entry
and descent strategy and modeling will be provided in a future publication.
2
The full end-to-end baseline trajectory is developed by a multi-institutional mission design and naviga-
tion team. (See Figure 2.) A team at APL derives an optimized high-fidelity interplanetary trajectory to the
Saturn-Titan system based on a set of mission constraints. The Saturn incoming hyperbolic excess veloc-
ity (v∞) analytically maps to site selection accessibility. A navigation team at the Jet Propulsion Laboratory
(JPL) analyzes the orbit determination uncertainties of the selected trajectory subject to a ground-based radio-
metric observation campaign and associated spacecraft hardware uncertainties such as maneuver execution
errors. This analysis influences a set of atmospheric entry simulations led by a team at NASA’s Langley
Research Center (LaRC) using the Program to Optimize Simulated Trajectories (POST-II) software, creating
a landing ellipse on the surface. This analysis can inform entry vehicle hardware adjustments by NASA
Ames and LaRC. The entire process iterates until a nominal interplanetary trajectory is selected that guides
the Dragonfly entry vehicle to a feasible landing footprint across an entire launch period.
EV
Hardware Adjustments
IP Arrival
Conditions
Time
Saturn Incoming v∞ vec.
EDL Inputs
Entry State Covariance
Accessible
Entry Space
Accessible Area at
Interface Altitude
Site Selection
Science Targets
Surface Lat./Long
End-to-End
Optimization Navigation Analysis
Entry Calculations
Entry Constraints
Min. Time to Earthset
Max. Entry Velocity
Angle of Attack Range
IP Transfer Constraints
Flyby Sequence
Minimum Altitudes
Max Time of Flight
Max C3, DV
Interplanetary Transfer
Calculation
Update Nominal
Trajectory as Needed
Final Design
EDL Analysis
APL
JPL
LaRC
Ames
Figure 2. Trajectory design process. Here “IP” stands for interplanetary.
INTERPLANETARY TRANSFER
Broad Search for Enabling Interplanetary Trajectories
The interplanetary trajectory is subject to the constraints listed in Table 1. The launch, cruise, and gravity
assist constraints drive the interplanetary search space independent of Titan entry, while the subsequent entry
constraints functionally depend on the arrival v∞into the Saturnian system. This section covers the first
three blocks in Figure 2. A patched conics broad search was performed over the entire baseline launch period
over the 2025 calendar year in addition to the backup 2026 calendar year. The goal of the broad search
was to obtain a mass-optimal baseline and backup pair such that the worst-case mass of the pair is highest
with respect to all alternative solution pairs. Gravity assists of Earth, Venus, and Mars were included with
a patched conics assumption. Jupiter was immediately discarded as it is out of phase during the desired
time period. Possible trajectory arcs between gravity assist bodies included non-resonant ballistic transfers,
v∞-leveraging arcs,8and even-πresonant returns.9The results of the interplanetary trajectory broad search
appear in Figure 3, assuming a monopropellant main engine specific impulse of 230 seconds, and launch
performance consistent with the NASA NLS-II launch vehicle contract. The Atlas V-411 was selected as a
representative launch vehicle as it lies within the intermediate performance launch vehicle class as specified
in the announcement of opportunity (AO) which incurs no cost penalty. On the basis of selecting an optimal
pair of primary and backup trajectories that satisfy all mission constraints, a 2025 EVEE is paired with a
2026 VEE. The 2025 EVEE is equivalent to the 2026 VEE with a prepended 1:1 Earth resonance. Since
both trajectories are geometrically equivalent from the 2026 Earth encounter or launch for the baseline and
backup respectively, it is possible to maintain the exact same terminal phases for Titan encounter, vastly
simplifying navigational and operational planning. Adding the option for the equivalent mission a year later
3
Table 1. Dragonfly trajectory constraint drivers.
Affected Phase Reason for Constraint Constraint Name Condition Converged Value*
Launch Schedule/AO Requirement Baseline Departure date 1/1/2025 −12/31/2025 4/12/2025 −5/2/2025
Launch * Schedule Backup launch date 6-18 months after baseline date
Launch Launch vehicle provider, injected mass Launch declination (DLA) −28.5◦≤DLA ≤28.5◦21.8◦
Launch Cost Launch vehicle Atlas V-411 or equivalent
Cruise Cost Time-of-Flight ≤11 years 9.7 years
Gravity Assists Thermal Venus Closest Approach Altitude ≥300 km 4000 km
Gravity Assists Probability of Impact Earth Closest Approach Altitude ≥1000 km {1134,1409,1002}km
Entry TPS Design Deceleration <12 Earth g’s211.9Earth g’s
Entry TPS Design Nominal Heat Flux <300 W/cm2(goal) 146 W/cm2
Entry TPS Design Nominal Heat Load <10,000 J/cm29,460 J/cm2
Entry Communications Time to First Earthset >61 hours Satisfied
*Driving parameters across 20-day launch period and entry dispersions.
provides significant advantages including schedule flexibility, a shorter time-of-flight, and less multi-mission
radioisotope thermoelectric generator (MMRTG) degradation after launch. In fact, this pairing of trajectories
repeats again in 2027 and 2028 with qualitatively similar arrival conditions at Titan, launch costs, and ∆v
requirements. For the EVEE sequence, the acronyms EGA0, EGA1, and EGA2 are used to denote the first,
second, and third Earth gravity assists respectively, and VGA1 denotes the Venus gravity assist. This naming
convention remains the same for the 2026 VEE trajectory with the exception of EGA0 which is eliminated
from the sequence, instead becoming equivalent to the Earth launch.
01/25 03/25 05/25 07/25 09/25 11/25 12/25 03/26 05/26 07/26 09/26 11/26
0
500
1000
1500
2000
2500
3000 VEE
VVE
VVEE
VEVVE
VE3
VEVE
VMVE
EVEE
7
8
9
10
11
12
Time-of-Flight (Years)
Figure 3. Broad search delivered mass capability on an Atlas V-411 launch vehicle.
Solutions with time-of-flight ≤12 years are displayed.
With the 2025 EVEE and 2026 VEE pair selected as the optimal configuration, the total time-of-flight is
minimized given the mission constraints. The most effective portion of the trajectory to minimize time-of-
flight is on the transfer leg from the final Earth gravity assist (EGA2) to arrival in the Saturn-Titan system.
This time reduction equates to piercing the Saturn-Titan system at lower heliocentric true anomalies, and
therefore at higher arrival v∞to minimize the arrival date. Assuming that the entry vehicle can compensate
for the increased v∞, then the arrival date is fundamentally limited by the constraint on minimum Earth
gravity assist altitude (Table 1), as shown in Figure 4. Note that a direct launch with a time of flight of 3.3
years, equivalent to the last segment of the EVEE, requires a C3 of about 135 km2/s2.
4
15.7 15.8 15.9 16 16.1 16.2
Nov 2034
Jan 2035
Mar 2035
May 2035
Jul 2035
Figure 4. Arrival date versus C3 for the EVEE baseline interplanetary transfer.
Optimized High-Fidelity Solutions and Launch Period
Within the “End-to-End Optimization” block of Figure 2, all baseline and backup trajectories are con-
verted from patched conics into a high-fidelity, numerically integrated force model in accordance with the
specifications in Table 2. The entire trajectory is converged as part of one multiple shooting direct ∆v
Table 2. High-fidelity force modeling settings for Dragonfly.
Phase Central Forces
Body
Launch Earth 21x21 Earth Gravity Model (WGS84 EGM96)
and Earth Gravity Assists Point-Mass Perturbations: Sun, Moon
Venus Gravity Assist Venus 21x21 Venus Gravity Model (MGNP180U)
Point-Mass Perturbations: Sun,Earth-Moon System, Mercury
Interplanetary Sun Solar Point-Mass Gravity
Point-Mass Perturbations: Mercury, Venus, Earth-Moon System,
Mars, Jupiter System, Saturn System, Uranus System
Titan Arrival Saturn 4x0 Titan Gravity Model (Zonals - J4)
Point-Mass Perturbations: Sun, Jupiter System, Saturn
minimization problem solved with nonlinear programming (NLP). The optimization problem is established
under the well-known formulation paradigm of control points at ephemeris bodies (e.g. launch, flyby, arrival)
and breakpoints satisfying state continuity in heliocentric space.10, 11, 12 The breakpoints exist between neigh-
boring control points in time and are evaluated by forwards and backwards propagation emanating from the
control points. The selected times for the breakpoints are fixed epochs that are approximately at the midpoint
in time between neighboring control points. Additional control points also exist as heliocentric states on the
EGA2 to Saturn-Titan system transfer to minimize sensitivity. Fully assembled, the trajectory optimization
problem contains seven legs consisting of eight control points, two maneuvers to be optimized (launch in-
jection and Titan targeting), and seven breakpoint constraints. Using this framework, the entire trajectory
has been converged from a patched conics initial guess in Analytical Graphics’ Systems Tool Kit R
Astroga-
tor module and in JPL’s Monte toolset using the Computer Optimization System for Multiple Independent
Courses (COSMIC) application. The preceding process is repeated at daily fixed launch epochs correspond-
ing to daily launch opportunities. The arrival state at Titan entry interface is held inertially fixed and locked
in time. Near the beginning of the launch period, the Titan targeting maneuver (i.e. Mvr. 2 in Figure 5)
optimally reduces to zero through EGA2. However, on later days of the launch period, the effectiveness of
the Earth gravity assist saturates due to the minimum altitude constraints being reached, and the magnitude of
the Titan targeting maneuver reaches nonzero values to preserve the fixed entry interface state (see Figure 6).
Figure 7 shows the trajectory corresponding to the open of the launch period.
5
Figure 5. High-fidelity control point (CP), breakpoint (BP), and maneuver (Mvr.) transcription.
1 3 5 7 9 11 13 15 17 19 21
15
16
17
18
19
20
0
4
8
12
16
20
Figure 6. Dragonfly launch period performance over launch day. Due to the 1:1 Earth
resonance, the baseline and backup launch periods have near-identical performance,
varying only in declination of launch asymptote (DLA).
Figure 7. Interplanetary trajectory for the primary 2025 EVEE pathway to Titan
corresponding to the open of the launch period. The numbers indicate each sequential
encounter body or maneuver in the sequence.
6
Table 3. Dragonfly trajectory constraint drivers.
Parameter Baseline Backup
Max. DLA (◦)21.8 6.8
Max. C3 (km2/s2)19.9 19.9
Max. Post-Launch ∆v(m/s)*20.7 20.7
EGA0 Min. Flyby Alt. (km) 1134 N/A
VGA1 Min. Flyby Alt. (km) 4000 4000
EGA1 Min. Flyby Alt. (km) 1409 1409
EGA2 Min. Flyby Alt. (km) 1002 1002
*Deterministic value only considers Titan targeting
and excludes Earth bias maneuvers that are the
subject of future work.
SYSTEM ENTRY
Covering the “Entry Calculations,” “Entry Constraints,” and “Accessible Entry Space” blocks in Figure 2,
this section describes the theory used to map the trade space of atmospheric entry conditions. The process
used for landing site selection is beyond the scope of this paper. The analysis begins with an approach similar
to that used to calculate dual satellite-aided capture solutions in the Jovian system.13 Each interplanetary
trajectory maps to a Saturn arrival time, to, and an incoming v∞vector. These in turn, map to a space of
atmospheric entry conditions upon arrival to Titan.
Saturnian System Entry
Defining a reference frame where the x-yplane lies in the orbital plane of Titan, the incoming v∞vector
with respect to Saturn can be expressed as
v∞=v∞cos αcos δsin αcos δsin δT(1)
where αand δare the right ascension and declination. The range of possible inclinations of the incoming
hyperbola with respect to this plane is constrained to δ≤i≤π−δ. To encounter Titan, the incoming
hyperbola must have a node crossing radius equal to the orbital radius of Titan at the time of entry. Using
this constraint, the orbital elements of the incoming hyperbola can be calculated analytically for Titan entry
before and after periapse, and for prograde and retrograde approach geometries with respect to Saturn. Also,
the existence of Saturn-centered ascending and/or descending node encounter geometries can be calculated
(see Appendix). Using the orbital elements, the velocity of the spacecraft with respect to Saturn at the node
crossing, vN, can be calculated analytically. If at the instant of the node crossing Titan’s velocity with respect
to Saturn is vT, the v∞vector with respect to Titan is expressed as
vT∞=vN−vT(2)
To this point, the analysis has omitted phasing. Mathematically a position in Titan’s orbit must be mapped
to a time and to a set of spacecraft orbital elements. To first order we assume that the Titan arrival time, te
can be modified to within plus or minus a half orbital period of Titan, PT, with only trivial changes in the
corresponding interplanetary trajectory. The time of Titan entry is then bounded by,
to−1
2PT< te< to+1
2PT(3)
where tois the nominal arrival time (measured as the time of Saturn periapse passage without Titan entry).
The orbit of Titan is discretized into nsegments in time which can be mapped to a phasing angle, β, measured
from the incoming asymptote direction projected into Titan’s orbital plane, ˆv∞xy. Considering an arbitrary
entry time tethe necessary value of node radius, rN, and phase angle, β, can be found from Titan’s ephemeris.
Then considering one of either pre- or post-Saturn periapsis encounters and either a prograde or retrograde
solution about Saturn, the six classical orbital elements can be fully determined for a given rp. Each feasible
7
value of rpwill map to a specific value of β. Thus, a simple 1-dimensional root solve can be performed to
find the value of rpnecessary for a Titan entry at time te.
β(rp)−β(te)=0 (4)
The space of all Titan intercepting trajectories corresponding to the chosen interplanetary trajectory is plotted
in Figure 8. The entry velocity is independent of latitude and longitude for each trajectory and is shown
in Figure 9 along with the Earth sub-latitude and longitude. Considering only prograde Saturnian orbits,
each reachable point on Titan’s surface will have entry conditions characterized by a corresponding EFPA
for a given entry time. Since Titan is tidally locked, the point where the incoming Saturn-centered hyperbola
intercepts its trajectory directly maps to the region of its surface available for landing.
Figure 8. Trajectories entering the Saturnian system for the nominal interplanetary trajectory.
Dec 20, 2034 Dec 23, 2034 Dec 26, 2034 Dec 29, 2034 Jan 01, 2035 Jan 04, 2035 Jan 07, 2035 Jan 10, 2035
7
8
9
10
11
12
13
14
15
16
17
-200
-150
-100
-50
0
50
100
150
200
Earth sub-latitude/longitude (deg.)
Figure 9. Titan entry velocity at an atmospheric interface altitude of 1,270 km and
sub-Earth latitude and longitude versus time.
Target Latitude and Longitude
We define two altitudes which will be important to the following developments. The first is the entry
interface altitude, 1,270 km, above which the effects of the atmosphere are negligible and where the entry
velocity and EFPA constraints are set. The second is the landing site target altitude, 100 km, which serves as a
convenient heuristic to map the arrival geometry to the landing site. If this altitude can be reached ballistically
8
while satisfying all constraints, then the landing site is assumed to be reachable by the entry system. More
detailed analyses are used to refine the targeting. Note that a Titan radius of 2,575 km is assumed for all
calculations.
A local coordinate system whose x-axis points in the direction of the target location on the surface is conve-
nient for the following developments. Letting Sb=hˆ
ibˆ
jbˆ
kbiT
be composed of the unit vectors of the
Titan-fixed body frame, the transformation to the local coordinate system defined by Sl=hˆ
ilˆ
jlˆ
kliT
becomes,
Sl=Cl/bSb(5)
where
Cl/b =
cos λcos λsin φsin λ
−sin φcos φ0
−sin λcos φ−sin λsin φcos λ
(6)
and a Titan body-fixed frame described in the report of the IAU/IAG working group is used.14 If the direction-
cosine matrix from an inertial frame to the Titan-fixed frame is Cb/I, then the v∞of the spacecraft with
respect to this local frame is
vT∞l=Cl/bCb/I vT∞(7)
The goal is to find orbital elements consistent with this asymptote which reach the atmospheric interface
altitude above the target latitude and longitude. A process similar to the Saturnian system entry is followed
where the node crossing radius in the local frame is set to the atmospheric entry radius. Following the
equations in the Appendix there is one degree of freedom available, rp, to control the latitude and longitude
of the interface condition. By construction, if the y-component of the state vector in the local frame, yloc, is
zero for a given rp, then the spacecraft reaches the target altitude above the target latitude and longitude if a
solution exists. Thus, the problem reduces to a 1-dimensional root solve,
yloc (rp)=0 (8)
Constraints Based on Orbital Geometry
An altitude, spacecraft sub-latitude, λ, and sub-longitude, φ, are the spherical coordinates that are typically
used to specify the position vector at atmospheric interface. The locus of all reachable points in terms of
latitude and longitude for a specific altitude depends on both the direction and magnitude of vT∞. Expressing
this vector in the Titan-fixed frame
vT∞b=Cb/I vT∞(9)
It is instructive to identify the sub-latitude and longitude of vT∞on both the near and far side of Titan’s
globe. If the longitude is measured positively counter-clockwise from the x-axis in the body-fixed frame,
λf= arcsin vT∞bz
vT∞
φf= arctan (vT∞by, vT∞bx )
λn=−λf
φn=φf+π
(10)
where the appropriate quadrant check is performed for the longitude and the subscripts ‘n’ and ‘f’ denote
the near and far side, respectively.
The degenerate case occurs when every point on Titan’s globe is reachable. In this case a parabolic orbit
reaches periapsis at the required altitude at a sub-latitude and longitude of λfand φf. All other locations
at the same altitude are reached prior to periapsis. All realistic cases will have geometrically inaccessible
portions of Titan’s globe centered about φfand λf. The area of this region varies inversely with the bend
angle, ∆T, of the incoming hyperbola about Titan,
sin ∆T
2=1
eT
(11)
9
where the eccentricity about Titan can be expressed as
eT= 1 + rpT v2
T∞
µ(12)
and rpT is the radius of periapsis set by the target altitude. Using the formula for the surface area of a spherical
cap and Eq. 11, the fraction of Titan’s surface which is accessible can be expressed as
1
21 + 1
eT(13)
Constraints Derived from the Entry System
The peak deceleration, heat flux, and heat load for the entry vehicle are functions of both the velocity and
EFPA at the entry interface altitude. In general for a given entry interface velocity, the peak deceleration and
heat flux increases as the magnitude of the EFPA is increased. Thus, a maximum EFPA magnitude, |γ|max,
can be identified consistent with the constraints outlined in Table 1. There is also a minimum bound on the
EFPA magnitude, |γ|min, which corresponds to a trajectory that does not have adequate time to dissipate its
energy within the atmosphere to reach the surface. Figure 10 shows the inaccessible regions on a cross-section
of Titan’s globe. The fraction of Titan’s surface which is accessible is then,
1
2(cos κ1−cos κ2)(14)
where
κ1,2=1
2(π−∆1,2)−θ1,2(15)
Here θ1,2are the absolute values of true anomaly at the target altitude set by the lower and upper bounds of
the EFPA at the interface altitude. ∆1,2are the bend angles of the hyperbola corresponding to these bounding
orbits. κ1,2can be calculated using the following well-known relationships
h1,2=rIvIcos |γ|min,max
e1,2=q1−h1,2
µa
cos θ1,2=h2
1,2
µrTe1,2−1
e1,2
(16)
where rIand vIare the position and velocity vector magnitudes at the entry interface and rTis the position
vector magnitude at the target altitude.
Time to Earthset
The previous sections have identified points on the surface that are both geometrically accessible by an
incoming trajectory and physically reachable by a flight system with bounds on the entry interface velocity
and EFPA. An additional Earth-access constraint is placed on the mission that ensures ample time for system
check-out and initial science operations after landing. The analysis found in the Appendix,shows that for a
finite Earth declination relative to Titan’s equatorial plane at least one continuous region of latitude values
centered about the north or south poles never has Earth access. If a declination constraint on antenna pointing
relative to the local horizon is introduced (corresponding to values of Θmax <90◦) then two bands of
latitudes without Earth access centered about the north and south poles can exist depending on the Earth
declination. The longitude band which satisfies the Earth-access constraint depends on the time of entry in
addition to the Earth declination and pointing constraint. Figure 10 shows the general geometry relevant to
Dragonfly. The scientific choice of landing site within the accessible region will be discussed elsewhere.
10
Figure 10. Cross-section of Titan’s globe with the accessible regions shown in white.
The regions shown in light and dark gray correspond to inaccessible regions due to
EFPA and geometric constraints of the incoming hyperbola, respectively. The hatched
region shows areas in terms of latitude which can not meet the minimum time to
Earthset requirement.
DESIGN SPACE AND SAMPLE ENTRY
For all entry times, a maximum deceleration value of 12 g’s is used as an upperbound for the design of the
entry system. This value sets the maximum absolute value of the EFPA, |γ|max, as shown in Figure 11. The
lower absolute bound on EFPA, |γ|min, is conservatively set to the value which renders ballistically reaching
the target altitude impossible. This value is approximately 45◦for the range of entry interface velocities
highlighted in Figure 11.
The nominal interplanetary trajectory design corresponds to a Titan entry time with a low entry velocity,
relative to the rest of the design space. In a high-fidelity model the spacecraft arrives at Titan on December 30,
2034 15:13:13 UTC with v∞T= [−0.910,5.081,4.710]Tkm/s. This vector translates into a velocity of 7.3
km/s at the entry interface altitude. The maximum deceleration and thermal conditions at this velocity upon
entry can be found in Figure 11. A maximum deceleration value of 12 g’s corresponds to a maximum absolute
value of the EFPA of approximately 51◦with the minimum bound at approximately 45◦. Figure 12 shows the
build up of the inaccessible region based on the geometry of the hyperbolic orbit, EFPA constraints, and time
to Earthset constraint in that order. Table 5 shows the reduction in accessible surface area with the addition
of each constraint.
Using the developments in Appendix and imposing no Earth declination constraints (Θmax =π/2) for
the time period of interest, the latitude range which yields no Earth access is approximately 72◦to 90◦
Conversely, latitudes from -90◦to -72◦yield continuous access. Of particular interest is the latitude range for
which the minimum time to Earthset can be satisfied. This range is −90◦to 67◦, using Eq. 45. These results
are summarized in Table 4.
As the nominal entry time is moved backwards or forwards the entry velocity increases which decreases
the accessible region on the surface before the Earthset constraint is considered. The accessible region also
shifts relative to the surface as Titan rotates ( 22.6◦/day) and the direction of vT∞changes inertially. These
changes over a period of 1.5 Earth days are shown in Figure 13.
As an illustrative example, we show the entry sequence corresponding to the second arrival point in Fig-
ure 13 starting with the Saturnian system arrival. In this case, a target latitude and longitude of 22◦and 100◦
specify a point that lies on the edge of the design space with an interface velocity of 7.5 km/s, corresponding
to maximum deceleration 12 g’s and EFPA of −50◦. Note that the interface point is reached prior to crossing
the equatorial plane of Titan, as seen in Figure 14.
11
Figure 11. Entry acceleration and representative heat load/flux conditions. The
shaded area corresponds to the design space encompassed by the nominal interplan-
etary trajectory and falls comfortably within the bounds listed in Table 1. Graphic
courtesy of Aaron Brandis and Gary Allen at NASAs Ames Research Center.
Table 4. Summary of Earth access regions in terms of latitude for the nominal interplanetary trajec-
tory.
Access Type Latitude Bounds Calculation
No Access 72◦to 90◦Equation 41
Continuous Access −90◦to −72◦Equation 40
Constraint Satisfaction Possible −90◦to 67◦Equation 44
Table 5. Percent of accessible surface with constraint additions for the nominal case.
Constraints Accessible Surface Fraction Calculation
Hyperbolic Geometry 53% Equation 13
Hyperbolic Geometry+EFPA Constraints 22% Equation 14
Hyperbolic Geometry+EFPA Constraints
+Earthset Constraint 7% Numerical Integration
12
(a) (b)
(c) (d)
(e) (f)
Figure 12. Build-up of inaccessible regions for the nominal entry time. The Earth’s
sub-longitude, sub-latitude (φE,λE) and the near and far projections of the v∞vec-
tor (φn,f ,λn,f ) are shown. The brightest region on each map is accessible with view
point looking down approximately at the trailing edge for the globes and the sub-
Saturn point for the 2-D maps. (a) Geometrically accessible latitude and longitude
of incoming hyperbola; (b) Geometrically accessible latitude and longitude; (c) Ac-
cessible region with EFPA constraints; (d) Accessible region with EFPA constraints;
(e) Accessible region with Earthset constraint. The green and red lines correspond to
Earthrise and Earthset, respectively. The magenta line corresponds to Earthset line
shifted by the 61 hr. constraint.; (f) Accessible region with Earthset constraint on
globe.
13
Figure 13. Change in accessible surface area versus time and as a function of entry
interface velocity. The filled and open circles represent Titan entry before the space-
craft has passed periapsis with respect to Saturn and after it has passed periapsis,
respectively. The viewpoint is stationary above the trailing edge of Titan. Proceed-
ing in order with time, the fraction of the accessible surface is 4%, 6%, 7%, and 5%
considering all constraints.
Figure 14. A typical entry geometry corresponding to the second arrival point in Figure 13.
14
NAVIGATION
The maneuvers are predominantly driven by statistical factors with the mission ∆vbudget for the prelimi-
nary design appearing in Table 6. With the exception of the deep space maneuver (DSM) to maintain a fixed
Titan entry state vector, all other maneuvers are either purely statistical or deterministically driven by statis-
tical factors. Since the baseline mission concept is powered by an MMRTG, each Earth gravity assist must
include a biased aimpoint such that the impact probability is sufficiently low. The biasing analysis will be
documented in a future publication. This section presents the preliminary ∆v99 results which are currently
being refined in conjunction with Earth-biasing.
The required ∆v budget is estimated via a statistical process that accounts for errors in determining the
orbit of the spacecraft as well as errors in executing trajectory correction maneuvers (TCMs) needed to
maintain a reference trajectory.15 For a trajectory with planetary gravity assists, it is especially important to
maintain close adherence to the reference trajectory at the time of each flyby since offsets from the nominal
flyby condition will be amplified on the following leg. To manage these navigation errors, we devised a series
of TCMs consisting of three maneuvers approaching each flyby and one cleanup maneuver following each
flyby. The approach maneuvers (with some exceptions) are scheduled for 90, 30, and 10 days prior to each
flyby, and the cleanup maneuver is placed 20 days following each flyby. In addition, there is a launch cleanup
maneuver 15 days after launch, and the EGA1 to EGA2 transfer has an extra maneuver 800 days prior to the
EGA2 flyby to prevent errors from building over this longer transfer. The EGA2 to Titan leg has a post-EGA2
cleanup 60 days after the flyby. TCMs targeting the Titan arrival are scheduled for 548, 45, 15, 5, and 2 days
prior to landing.
The process used to obtain an estimate of the uncertainty in the orbit is a standard covariance analysis.16
Simulated tracking data is used in a least squares filter which provides the covariance of the orbit estimate
at the time of each TCM data cutoff (5 days before each TCM). The simulated tracking data includes range
and range rate measurements, and the estimated parameters in the filter include the position and velocity of
the spacecraft, as well as parameters related to the dynamical model of the trajectory and error sources. A
Monte Carlo technique is applied which samples a trajectory, first from the dispersions due to the delivery
to the injection state from the launch vehicle, and subsequently from errors in determining the orbit of the
spacecraft. For each sample, a TCM is designed using the linearized state transition matrix to compute the
∆vrequired to remove the error at the time of the next flyby. Maneuver execution errors are also added to
each TCM. The process is repeated ntimes to obtain statistics on the mean, standard deviation, and 99th
percentile of the size of the maneuvers needed. The results of this analysis are shown in Table 7. For these
results, 5000 samples were used in the Monte Carlo simulation, and 99% of these samples required not more
than 95 m/s of ∆vto adhere to the reference trajectory. Note that this estimate of the statistical maneuvers is
30 m/s greater than the initial estimate listed in Table 6. Further refinements to the process will be made in
conjunction with the biasing analysis moving forward.
Table 6. Dragonfly interplanetary ∆vbudget for the preliminary design. Statistical maneuvers are
estimated.
Maneuver Total ∆vDeterministic ∆vStatistical ∆vComment
(m/s) (m/s) (m/s)
1. Launch Cleanup 20.0 0.0 20.0 Typical value, pending Phase A analysis
2. EGA0 50.0 40.0 10.0 Estimate pending further analysis
(Bias and Targeting)
3. VGA1 10.0 0.0 10.0 Estimate pending further analysis
(Bias and Targeting)
4. EGA1 50.0 40.0 10.0 Estimate pending further analysis
(Bias and Targeting)
5. EGA2 50.0 40.0 10.0 Estimate pending further analysis
(Bias and Targeting)
6. DSM for fixed
20.7 17 3.7 Worst case over launch period
Titan state
(at EGA2+90 days)
7. Titan Targeting 10.0 0.0 10.0
Subtotals 210.7 137 73.7
Contingency 7.0 0.0 7.0 Unforeseen scenarios, 5% of deterministic
Grand Total 217.7 Deterministic +statistical +contingency
15
Table 7. Updated Statistical Maneuver ∆vBudget
Maneuver
Relative
Epoch (day)
Mean
∆v(m/s)
Standard
Deviation (m/s) 99%tile (m/s)
TCM-0 Launch + 15 2.915 2.132 9.242
TCM-1 EGA0 −90 0.671 0.725 3.533
TCM-2 EGA0 −30 0.093 0.076 0.394
TCM-3 EGA0 −10 0.040 0.017 0.087
TCM-4 EGA0 + 20 4.605 3.545 16.414
TCM-5 VGA1 −90 0.508 0.537 2.664
TCM-6 VGA1 −30 0.086 0.068 0.344
TCM-7 VGA1 −10 0.044 0.019 0.095
TCM-8 VGA1 + 20 5.774 4.211 19.934
TCM-9 EGA1 −90 1.905 2.149 9.928
TCM-10 EGA1 −30 0.189 0.216 1.086
TCM-11 EGA1 −10 0.048 0.023 0.125
TCM-12 EGA1 + 20 7.000 5.640 27.724
TCM-13 EGA2 −800 0.436 0.473 2.452
TCM-14 EGA2 −90 0.977 0.754 3.380
TCM-15 EGA2 −30 0.113 0.091 0.439
TCM-16 EGA2 −10 0.040 0.017 0.087
TCM-17 EGA2 + 60 3.644 3.031 15.385
TCM-18 Entry −548 0.326 0.305 1.557
TCM-19 Entry −45 0.529 0.232 1.151
TCM-20 Entry −15 0.065 0.032 0.162
TCM-21 Entry −5 0.027 0.012 0.059
TCM-22 Entry −2 0.007 0.003 0.015
Total 30.043 18.487 95.169
CONCLUSIONS
Dragonfly has a simple interplanetary design consisting of at most one deterministic maneuver (excluding
biasing maneuvers), and sometimes none would be required throughout the launch period. This single ma-
neuver allows the spacecraft to enter Titan’s atmosphere at the exact time and state through both the primary
and backup launch periods, greatly simplifying operational planning. Upon entry into the Saturnian sys-
tem Dragonfly would have access to a wide region of Titan’s northern hemisphere and areas of the southern
hemisphere with small adjustments in the entry time. Overall, these attributes constitute a mission concept
design that is both flexible to surface targets and robust to launch delays. Future publications will address the
navigation of the spacecraft which includes the ongoing ∆v99 analysis and the Earth biasing study, which is
necessary for a spacecraft with a nuclear payload.
ACKNOWLEDGMENTS
The authors wish to thank the Dragonfly Principal Investigator, Elizabeth Turtle, for her contributions
to the development of the baseline mission design. The authors would like to express our appreciation to
Aaron Bandis and Gary Allen of NASA Ames for the production of Figure 11 and Robert Maddock, Joseph
White, and Richard Winski of LaRC for their support throughout the project. The authors would also like to
thank Sumita Nandi and Zahi Tarzi of JPL for the initial navigation studies of the Step 1 proposal, and Jim
McAdams for his mission design work in the earlier stages of the project. Part of the research described in
this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract
with the National Aeronautics and Space Administration. The information presented about the Dragonfly
mission concept is pre-decisional, and is provided for planning and discussion purposes only.
16
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Techniques, Madrid, Spain, May 3-6,2010.
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17
APPENDIX
Titan Excess Velocity
Using the orbit equation, the true anomaly of the spacecraft at a node is
θN=
arccos p
erN−1
e(Titan entry after Saturn periapsis)
−arccos p
erN−1
e(Titan entry before Saturn periapsis)
(17)
where rNis the radius of the node, pis the semi-parameter, and eis the eccentricity about Saturn. Here eand
pare known as v∞is set by the interplanetary trajectory and rpis chosen a priori. The argument of periapsis
is
ω=−θN(Titan entry at ascending node)
π−θN(Titan entry at descending node) (18)
and the radius at the node is
rN=(p
1+ecos(−ω)(Titan entry at ascending node)
p
1+ecos(π−ω)(Titan entry at descending node) )(19)
Because rN>0, the existence of the nodes is given as follows:
cos ω > −1
e: Titan entry possible at ascending node
cos ω < 1
e: Titan entry possible at descending node
−1
e<cos ω < 1
e: Entry possible at both ascending and descending nodes
(20)
The incoming asymptote is connected to the orbital elements of the hyperbola using the standard perifocal
frame, ˆ
p-ˆ
q-ˆ
w, as
vpqw
∞=P(Ω, ω, i)v∞(21)
where Pis given by the standard conversion.17 Here, Ωand iare the right ascension of the ascending node
and inclination with respect to the Saturn, respectively. The velocity vpqw
∞is obtained via the true anomaly at
negative infinity.
It follows from Eqs. 1 and 21
sin i=v∞sin δ
vpqw
∞ycos(ω) + vpqw
∞xsin(ω)=sin δ
cos ω+ arctan −vpqw
∞x
vpqw
∞y (22)
where the quadrant is chosen in accordance with a prograde or retrograde solution. Similarly
Ω = α−arcsin tan(δ)
tan(i)=α+ arccos vpqw
∞xcos(ω)−vpqw
∞ysin(ω)
v∞cos(δ)(23)
A quadrant check is performed by comparing the two expressions in equation 23.
The radius and velocity vectors at the node are now computed as
rN=PTrpqw
N
vN=PTvpqw
N
(24)
where
rpqw
N=rNcos θNsin θN0T
vpqw−
N=qµ
psin θNe+ cos θN0T(25)
Thus, the full state at the node is defined analytically.
18
The incoming v∞vector relative to Titan is defined provided that the state of Titan at the first node is
known. A fully analytical expression can be found if Titan’s orbit is assumed to be circular. However, for the
purpose of this study JPL Spice ephemerides are used for increased accuracy. The incoming excess velocity
relative to the Titan is
vT∞=vN−vT(26)
where vTis the velocity of Titan relative to Saturn.
Time to Earthset
Expressing the inertial Earth direction from Titan ˆnEin the Titan body frame,
ˆnE=CI/bˆnEb (27)
where the superscript “I” indicates the time derivative in an inertial frame. Therefore the velocity of the unit
vector as seen from the Titan-fixed frame is,
˙
ˆ
nEb =˙
ˆ
nI
Eb −Cb/I ˙
Cb/I ˆnEb (28)
This expression is convenient for operating on the DCM directly. If it is also assumed that the Titan body
frame rotates with an angular velocity with respect to the inertial frame, ω
ω
ω=ωxωyωz, then by the
kinematic transport theorem, the definition of cross product
˙
ˆ
nEb =˙
ˆ
nI
Eb −ω
ω
ωb׈
nEb =˙
ˆ
nI
Eb −Ωbˆ
nEb (29)
If it is assumed that the Titan rotation axis is inertially fixed within plus or minus a half orbital period and
that the z-axis of the inertial frame is aligned with axis of rotation then Cb/I takes the form of the standard
right-handed, direction-cosine-matrix. Also assuming that rotation rate and inertial Earth direction is constant
over plus or minus a half orbital period and defining
ˆ
nEb =nEbx nEby nEbz T(30)
then ˙
ˆ
nEb =ωbnEby −ωbnEbx 0T(31)
where
θ(t) = ωb(t−te)(32)
Defining the direction of a potential target site in the Titan-body frame,
ˆ
rT Sb =cos φT S cos λT S sin φT S cos λT S sin λTS T(33)
and letting the inertial Earth direction be
ˆ
nE=cos αEcos δEsin αEcos δEsin δET(34)
Using the previous relationships it can be shown that cos Θ = ˆ
rT Sb ·ˆ
nEb becomes,
cos Θ = cos λT S cos δEcos (θ+φT S −αE) + sin δEsin λT S
˙
Θ = 1
sin Θ (ωbcos λT S cos δEsin (θ+φT S −αE)) (35)
This relationship can also be derived using spherical trigonometry. The declination of the Earth with respect
to the target site is
δE/T S =π/2−Θ(36)
For Earth communication the declination must remain above some minimum value, δE/T Smin, which corre-
sponds to a maximum value of Θ. It can be shown via Eq. 35 or geometrically that for communication to be
possible,
Θmax >|δE−λT S |(37)
19
For a given target latitude at the entry time the longitude coordinates corresponding to a given value of Θis
φT S =αE±arccos cos Θ
cos λT S cos δE
−tan λT S tan δE(38)
The time available at a given latitude below Θmax becomes,
∆t=2
ωbarccos cos Θmax
cos λT S cos δE
−tan λT S tan δE(39)
There are two cases of particular interest corresponding to latitudes that mark no access and those that mark
continuous access barring other obstructions, corresponding to ∆t= 0 and ∆t= 2π/ωb. By geometrical
inspection if there is a solution where ∆t= 2π/ωbthen there is one solution where ∆t= 0. Alternatively,
if there are no solutions where ∆t= 2π/ωbthen there are two solutions where ∆t= 0. Thus, if there is a
solution to the following equation where |λT S (∆t= 2π/ωb)|< π/2,
λT S (∆t= 2π/ωb) = −δE+ sign (δE) (π−Θmax )(40)
then
λT S (∆t= 0) = δE−sign (δE) Θmax (41)
or alternatively
λT S (∆t= 0) = δE±Θmax (42)
with the maximum possible time, ∆tmax, occurring at
λ∆tmax = arcsin sin δE
cos Θmax (43)
Upon landing the mission requires minimum duration for Earth contact, ∆tmin. If there is a solution such
that ∆t= 2π/ωbthen there is at least one latitude where the time to Earthset equals ∆tmin . Using Eq. 38
and simplifying,
λtmin =−sign (δE) arccos cos Θmax
A−∆(44)
Alternatively, if there are two latitudes such that ∆t= 0 and if ∆tmin <∆tmax then there are two
latitudes where time to Earthset equals ∆tmin.
λtmin =±arccos cos Θmax
A−∆(45)
where
A2= cos2ωb∆tmin
2cos2(δE) + sin2(δE)(46)
and
∆ = arctan −sin (δE)
cos ωb∆tmin
2cos (δE)!(47)
20
