2023 VEMEGA to Jupiter
Kevin Dinkel
ASEN 6008 – Interplanetary Mission Design
University of Colorado at Boulder
4/23/2012
I. Introduction
D
esigning a trajectory to an outer planet in our solar system such as Jupiter is a difficult astrodynamics problem,
subject to the nature of planetary alignment and resting heavily on the constraints of modern rocket technology.
Fortunately, it lends itself well to creativity. Using the inner planets as gravity assist agents can greatly decrease the
total cost of the mission while providing interesting scientific prospects. One of the most affordable opportunities to
Jupiter is a Venus-Earth-Mars-Earth-Gravity-Assist (VEMEGA) to Jupiter launching in the year 2023. A plot of this
trajectory simulated in Satellite Toolkit (STK) is shown in Figure 1.
Figure 1: 2023 VEMEGA Trajectory to Jupiter
This report outlines the methods used for finding this optimal VEMEGA trajectory, provides supporting analysis on
its characteristics, and offers insights into possible scientific missions that could be conducted.
II. Finding an Optimal Trajectory
Designing an “optimal” trajectory is subjective to what criteria are deemed most important to a certain mission.
The main objective of this trajectory design is affordability. This goal was met by looking for VEMEGA trajectories
that met the following constraints:
| must be less than 50 cm/s. This ensures that all flybys are realistic and decreases the total
1) Flyby |
delta-V used for trajectory correction maneuvers (TCMs) between the different legs of the journey.
2) Flyby altitudes must be greater than 1000 km above the planet. This ensures that the spacecraft will not hit
the flyby planet even with small TCM errors during flight.
3) The C3 of the trajectory must be as low as possible assuming that constraints 1and 2 are met. This will give
the scientists and spacecraft designers the most flexibility with regards to the spacecraft mass budget and in
selecting a launch vehicle.
Following these guidelines, preliminary analysis of the trajectory was performed in MATLAB. Using a polynomial
expansion for the planet ephemerides and a lambert solver, trajectories were constructed between planets.
1
A powerful tool in interplanetary mission design is the Pork Chop Plot. This plot relates
,
, and time
of flight (TOF) for a set of departure dates from the first planet to a set of arrival dates at the second planet. The
VEMEGA trajectory can be modeled using 5 Pork Chop Plots for the different legs of the mission: 1) Launch-VGA
2) VGA-EGA1 3) EGA1-MGA 4) MGA-EGA2 and 5) EGA2-JOI.
Using these 5 plots as well as the optimal trajectory constraints, a filter was constructed in MATLAB to begin
searching for valid VEMEGA trajectories beginning in 2023. The basic design of this filter is shown in Figure 2.
Figure 2: Planetary Flyby Trajectory Filter
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Baseline Trajectory
0 Valid Departure Region
24 Valid Arrival Region
Valid Trajectories
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Arrival at Mars: Days Past 2460669.2 (12/24/2024)
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A set of departure and arrival dates for each Pork Chop Plot are given to the filter. The filter looks for planetary
flybys that have matching |
| and |
| to within some definable tolerance, |
|, and that fly above the
planet’s surface by an altitude of at least
. After running this filter, a set of valid trajectories can be shown on
each Pork Chop Plot, Figure 3.
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14
18
0
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30
40
50
60
70
Departure from Earth: Days Past 2460502.4 (7/10/2024)
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Figure 3: Pork Chop Plot with Valid Trajectory Regions
The magenta contours represent a region of valid trajectories that have a flyby of Earth (EGA1) that have
|
|
and an
. The cyan contours represent the region of valid trajectories for a flyby of
Mars (MGA) for the same constraints. The region of valid trajectories from Earth to Mars (EGA1-MGA) can be
found where these two regions overlap, denoted in green.
This procedure was run on each leg of the VEMEGA trajectory to find reasonable regions. These regions were
further refined by constricting the values of |
| and
, finding new smaller valid regions, revising the
input departure and arrival dates, and repeating. This method was run in an iterative fashion until it converged on a
set of optimal dates, meeting all the optimal criteria. From this set of dates, the most affordable trajectory, the one
with the lowest C3 value, was selected as the optimal trajectory.
2
III. Baseline Mission Trajectory in MATLAB
The dates and TOF for each leg of the optimal trajectory are listed in Table 1. The arrival at Jupiter for this
mission occurs in February of 2030, 6.75 years after launch in May of 2023.
Table 1: Critical Events VEMEGA Trajectory
Calendar Date
Julian Date
TOF to Next Event
[Days]
05/25/2023
2460089.91600
148.69
10/21/2023
2460238.61000
313.77
08/29/2024
2460552.38000
166.81
02/12/2025
2460719.19000
648.25
11/22/2026
2461367.44500
1187.35
02/22/2030
2462554.80000
Total: 2464.88
Event
Launch
Venus Flyby (VGA)
Earth Flyby (EGA1)
Mars Flyby (MGA)
Earth Flyby (EGA2)
Jupiter Arrival (JOI)
TOF to Next Event
[Years]
0.41
0.86
0.46
1.78
3.25
Total: 6.75
The Pork Chop Plot for the Launch-VGA leg is shown in Figure 4 below. The chosen trajectory is a type II
transfer.
0
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Time of Flight (days)
Baseline8 Trajectory
4.3 Valid Trajectories
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Arrival at Venus: Days Past 2460234.6 (10/17/2023)
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Departure from Earth: Days Past 2460074.9 (5/10/2023)
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Figure 4: Launch-VGA Pork Chop Plot
Regions of valid trajectories are found very near the asymptote of the plot. This means that this trajectory is very
close to the 180 degree solution, making it highly inclined leaving Earth’s gravity. The valid region is highly
dynamic in terms of the varying C3 levels within it, as can be seen by the tightly grouped contours. The chosen
trajectory provides the launch parameters shown in Table 2.
C3
RLA
DLA
Table 2: Launch Parameters
10.098437 km2/s2
138.816155° (w/rt Earth ecliptic)
35.810823° (w/rt Earth ecliptic)
3
The small C3 of this launch provides flexibility in the choice of payload mass and launch vehicle. This
will be discussed more in Section VI.
After leaving Earth, the next step is to target a location around Venus such that a gravity assist will propel the
spacecraft back to Earth. This point is defined in the VGA B-Plane. The B-Plane parameters for the VGA and the
associated s are shown in Tables 3 and 4.
Table 3: VGA B-Plane Parameters
20683.298507 km
13864.692430 km
46.348062°
16426.867944 km
10375.067944 km
|
|
|
|
|
|
|
Table 4: VGA Velocities
5.520645 km/s
5.520685 km/s
0.000039 km/s
2.071392 km/s
|
The spacecraft safely passes over Venus with a 10375 km margin, nearly matching s, and a ~2 km/s boost in
velocity with respect to the sun.
The Pork Chop Plot for the VGA-EGA1 leg is shown in Figure 5 below. The chosen trajectory is a Type II
transfer.
100
V @ Arrival (km/s)
Arrival at Earth: Days Past 2460502.4 (7/10/2024)
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35
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Baseline Trajectory
Valid Departure Region
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Valid Arrival Region
Valid Trajectories
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Departure from Venus: Days Past 2460234.6 (10/17/2023)
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Figure 5: VGA-EGA1 Pork Chop Plot
The selected date has the B-Plane parameters and velocities for the EGA shown in Tables 5 and 6.
Table 5: EGA1 B-Plane Parameters
-11804.510322 km
5146.755794 km
44.701534°
8628.893831 km
2255.757531 km
|
|
|
|
4
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|
|
Table 6: EGA1 Velocities
8.677073 km/s
8.677123 km/s
0.000049 km/s
5.266652 km/s
|
4
V @ Departure (km/s)
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V @ Arrival (km/s)
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Time of Flight (days)
Baseline Trajectory
0
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Valid Arrival Region
Valid Trajectories21 0
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The Pork Chop Plot for the EGA1-MGA leg is shown in Figure 6 below. The chosen trajectory is a Type I
transfer.
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Departure from Earth: Days Past 2460502.4 (7/10/2024)
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Figure 6: EGA1-MGA Pork Chop Plot
The valid trajectories in this region fell within a window of approximately 25 days departure from Earth. The chosen
trajectory is near the middle of this region. I produced the B-Plane parameters and velocities for the MGA shown in
Tables 7 and 8.
Table 7: MGA B-Plane Parameters
-2258.836185 km
4828.546100 km
9.773320°
4894.466976 km
1498.276976 km
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Table 8: MGA Velocities
9.693889 km/s
9.693899 km/s
0.000011 km/s
-0.655282 km/s
|
The spacecraft actually loses energy with respect to the sun during this flyby, as it passes in front of Mars. The
purpose of this flyby is to turn the spacecraft’s trajectory back to Earth for a second EGA. Using the MGA, the
spacecraft can flyby Earth when it is is a better position to target Jupiter.
5
The Pork Chop Plot for the MGA-EGA2 leg is shown in Figure 7 below. The chosen trajectory is a type II
transfer.
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V @ Departure (km/s)
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V @ Arrival (km/s) 1
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Figure 7: MGA-EGA2 Pork Chop Plot
Coming back to Earth for the final boost to Jupiter, the final flyby of Earth increases the spacecraft’s velocity by
3.7 km/s with respect to the sun. The B-Plane parameters and velocities for the EGA2 flyby are shown in Tables 9
and 10.
Table 9: EGA2 B-Plane Parameters
10854.454072 km
3780.803233 km
33.898878°
8513.015379 km
2139.879079 km
|
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6
Table 10: EGA2 Velocities
10.667945 km/s
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10.667943 km/s
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0.000002 km/s
3.704252 km/s
|
The final Pork Chop Plot shows the trajectory from EGA2-JOI. The chosen trajectory is a Type I transfer.
400
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Arrival at Jupiter: Days Past 2462254.8 (4/28/2029)
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Time of Flight (days)
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Baseline Trajectory
Valid Trajectories
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Departure from Earth: Days Past 2461317.4 (10/3/2026)
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Figure 8: EGA2-JOI Pork Chop Plot
The value
selected at Jupiter is vital to mission performance, as it determines the size of the
needs to enter into an orbit about Jupiter. The value selected is shown in Table 11 below.
Table 11: Arrival Parameters (Jupiter Inertial)
5.699752 km/s
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7
the spacecraft
IV. Trajectory Analysis
From the baseline dates discussed in the previous section, analysis was conducted to see how the chosen trajectory
performed against many important factors. First, a 3D model of the trajectory was constructed by integrating the
spacecraft’s trajectory during each leg of the mission. This was done by integrating the 2-body equations of motion
(spacecraft and sun) using the Dopri54 variable step integrator. The resulting trajectory is shown in Figure 9.
5
Sun
Earth @ Launch
Venus @ VGA
Earth @ EGA1
Mars @ MGA
Earth @ EGA2
Jupiter @ JOI
VEMEGA Trajectory
4
3
2
Y [AU]
1
0
-1
-2
-3
-4
-5
-6
-4
-2
0
X [AU]
2
4
6
Figure 9: MATLAB 2-Body Propagated VEMEGA Trajectory
One of the most interesting parameters to look at during the course of the flight is how the spacecraft energy
changes. This trend is shown in Figure 10.
-100
-150
-200
Energy [km2/s 2]
-250
-300
-350
-400
-450
S/C Energy
VGA
EGA1
MGA
EGA2
-500
-550
0
1
2
3
4
5
TOF [years]
Figure 10: Spacecraft Energy vs. Time of Flight
8
6
7
During each transfer from planet to planet, the energy of the spacecraft remains constant with respect to the sun.
This is expected because no maneuvers are simulated during each trajectory. When the spacecraft encounters each
planet its energy changes with respect to the sun. The spacecraft accelerates its velocity using Venus gravity and
Earth gravity twice to gain enough energy to get to Jupiter. These assists are essentially “free”
s due to the large
mass difference between the planet and the spacecraft, giving the satellite a big boost in energy without using any
fuel. Although the spacecraft flies behind Venus and Earth to gain energy, it flies in front Mars, loosing energy with
respect to the sun. While this seems undesirable, the purpose of this gravity assist is to better align the spacecraft
with Earth for the its second Earth gravity assist (EGA2). The Mars assist changes the spacecraft’s angle
(9.773320°) and energy just enough to shift the timing of EGA2 into a more ideal position for the transfer to
Jupiter.
The spacecraft’s energy with respect to the sun is composed of both its position relative to the sun as well as its
velocity relative to the sun. A plot of the spacecraft’s position magnitude from the sun is shown in Figure 11.
7
6
S/C Distance From Sun [AU]
5
4
3
2
S/C Distance From Sun
VGA
EGA1
MGA
EGA2
1
0
0
1
2
3
4
5
6
7
TOF [years]
Figure 11: Distance from Sun vs. Time of Flight
The spacecraft begins at 1 AU, the distance from the sun to the Earth. It then flies inwards towards the sun to gain a
gravity assist off of the closer orbiting Venus. The spacecraft again passes through the 1 AU boundary as it flies by
Earth for the first time before flying outwards away from the sun towards Mars orbit. As seen in Figure 9, the
spacecraft flies outside of Mars orbit before swinging back to Earth a final time to perform EGA2. This final gravity
assist from Earth hurtles the spacecraft away from the sun towards Jupiter.
9
The velocity of the spacecraft with respect to the sun is shown in Figure 12.
45
S/C Velocity Magnitude
VGA
EGA1
MGA
EGA2
40
S/C Velocity Magnitude [km/s]
35
30
25
20
15
10
5
0
0
1
2
3
4
5
6
7
TOF [years]
Figure 12: Velocity Magnitude vs. Time of Flight
The spacecraft’s velocity rapidly increases with each gravity assist. This is what causes the abrupt changes in
energy seen in Figure 10. Also, the spacecraft’s velocity increases as it flies inwards, towards the sun, and decreases
as it flies outwards, away from the sun. Its velocity is slowest at it reaches Jupiter’s orbit.
One of the most important factors for communicating with the spacecraft is its distance away from the ground
stations on Earth. A plot of the spacecraft’s distance from Earth during the course of the flight is shown in Figure 13.
7
6
S/C Distance From Earth [AU]
5
4
3
2
S/C Distance From Earth
VGA
EGA1
MGA
EGA2
1
0
0
1
2
3
4
5
TOF [years]
Figure 13: Distance from Earth vs. Time of Flight
10
6
7
This plot is useful for mission operators who must know how the signals to and from the spacecraft are
atttenuated over different range distances to the spacecraft. Comminucating with the spacecraft will be hardest when
the distance between the ground station and the spacecraft is furthest, which occures when the spacecraft is on its
way to Jupiter.
Another important factor for communication with a spacecraft is the angle between the Earth-spacecraft vector
and the Earth-sun vector. If these vectors become to close (ie. below 5°) the satelite will enter into the solarexclusion-zone. Within this zone, the satellites downlink will have to contend with solar radio waves. This will
greatly redice the telemetry link margin during the transit. It is important for operators to know when they will not
be able to communicate with the spacecraft. If periods of latency are unnacceptable, the trajectory may have to be
altered to meet communication requirements. The Earth-spacecraft-sun angle for the entire VEMEGA trajectory is
shown in Figure 14 below.
180
Earth-S/C-Sun Angle
SEZ
VGA
EGA1
MGA
EGA2
160
Earth-S/C-Sun Angle [deg]
140
120
100
80
60
40
20
0
0
1
2
3
4
5
6
7
TOF [years]
Figure 14: Earth-Spacecraft-Sun Angle vs. Time of Flight
During the flight, the Earth-spacecraft-sun angle dips into the solar-exclusion-zone on 4 ocassions: once on the
way from MGA to EGA2 and 3 times on the way from EGA2 to JOI. These times of no communication must be
thought out critically by mission operators before the spacecraft leaves the ground.
11
V. Implementing Trajectory in STK
Satellite Toolkit (STK) is a great tool for simulating an interplanetary trajectory. It offers the complete
ephemeris, with more accurate planetary positions than the MATLAB polynomial model. It has many useful tools
for propagating satellites, targeting B-Plane parameters for flybys, and doing analysis on launch and arrival
conditions. Finding an optimal trajectory was not done in STK because MATLAB offers a simpler interface for
comparing the performance of thousands of trajectories against each other. However, when modeling a single
trajectory, STK offers better accuracy, integrating the trajectory against the full ephemeris.
To construct the trajectory, STK’s Astrogator was used. Building the launch sequence consisted of targeting a
desired C3, RLA, and DLA, while varying the launch parking orbit duration and
for departure. To construct each
other leg, a single trajectory correction maneuver (TCM) was used to target B-Plane parameters and arrival times for
each planetary flyby. These parameters were positioned and timed such that when the spacecraft flies through them,
the planet’s gravity changes the spacecraft’s trajectory setting it up for the next planetary flyby. After executing all
flybys through EGA2, a final TCM was constructed to target a periapsis arrival altitude and arrival time for JOI.
Finally, to insert successfully into Jupiter’s gravity, an insertion burn was targeted along the X-axis of the
spacecraft. This burn was varied to achieve a target orbital period of 350 days.
The resulting inner trajectory of the VEMEGA is shown in Figure 15.
Figure 15: STK Simulated Inner VEMEGA Trajectory
The inner trajectory illustrates each flyby clearly. The satellite leaves Earth and in an almost 180 degree Type II
transfer towards Venus. With the extra energy gained from the VGA, the satellite swings outside Earth’s orbit. In an
almost 360 degree Type II trajectory from Venus, the satellite flies by Earth followed by Mars in quick succession.
With the extra energy, the satellite swings outside Mars’ orbit before coming back into the inner solar system to fly
by Earth for the final time. After EGA2 the satellite has enough energy to reach Jupiter.
12
The outer trajectory is shown in Figure 16 below.
Figure 16: STK Simulated Outer VEMEGA Trajectory
After departing from EGA2 the spacecraft progresses in a long, almost 180 degree, Type I transfer to Jupiter.
The trajectory shown in 3 dimensions is shown in Figure 17.
Figure 17: VEMEGA Trajectory in 3 Dimensions
Rotating the trajectory onto the solar system ecliptic shows the dynamics of the spacecraft in the Z dimension.
Because many of the trajectories in this VEMEGA solution are near 180 degree solutions, they send the spacecraft
soaring above and below the solar system plane.
Figure 18: VEMEGA Trajectory Viewed from the Solar System Ecliptic
13
VI. Launch
One of the most complicated parts of a mission is the actual launch of the spacecraft. Looking at the Pork Chop
Plot for the Launch-VGA trajectory again, Figure 19, it can be seen that there is only a 3 day launch window in
which the spacecraft can still hit VGA near the same time as the optimal trajectory. This small window is a result of
the highly dynamic behavior that the trajectories have near the 180 degree solutions. The C3 in this region changes
rapidly as a function of departure and arrival date. A larger launch window could be constructed if the designer was
willing to sacrifice a low C3.
Figure 19: Launch-VGA Pork Chop Plot Showing VEMEGA Launch Window
Recall the target C3 for the optimal trajectory is 10.098437 km2/s2. This number is very low compared to most
interplanetary missions to Jupiter. Having a low C3 offers the mission many advantages. Because the energy to get
the vehicle out of Earth gravity is low, a smaller rocket can be used, saving on expenses, or a heavier spacecraft can
be constructed, providing more space for scientific instruments. This trade space must be evaluated when
considering the proposed mission to Jupiter.
14
Table 12 shows many commonly used rockets and their available C3 for three different sized satellites: 1000 kg,
3000 kg, and 6000 kg. Entries marked in green can support the discussed optimal transfer from Earth to VGA.
Entries marked in red do not supply enough energy to support the VEMEGA mission. With such a low C3, any
Atlas V or Delta IV rocket can easily carry a 1000 or 3000 kg payload to Jupiter.
Table 12: Launch Vehicle C3 Performance1,2,5
Launch Vehicle
Delta II 742X
Delta II 732X
Delta II 792X
Delta II 792XH
Atlas V 401
Atlas V 501
Proton M
Atlas V 411
Atlas V 421
Atlas V 431
Atlas V 511
Atlas V 521
Atlas V 531
Atlas V 541
Atlas V 551
Delta IV M
Delta IV H
C3 with 1000 kg
Payload (km2/s2)
C3 with 3000 kg
Payload (km2/s2)
C3 with 6000 kg
Payload (km2/s2)
17
21
56
67
50
66
73
77
85
88
>100
>100
>100
>100
>100
6
0
30
19
26
33
15
25
35
44
45
68
>100
10
-20
-13
-5
0
5
33
74
The optimal trajectory launch sequence was constructed in STK. The resulting parameters are shown in Table
13. Kennedy Space Center was chosen as the launch site. To avoid impacting Earth a high parking orbit of 600 km
was chosen. From this parking orbit, the RLA, DLA, and C3 of the interplanetary trajectory to Venus were targeted.
The
of this maneuver was 3.59213 km/s. To ensure that this value was of the correct magnitude, a patched
conics trajectory of the Launch-VGA trajectory was computed. The
at Earth from the calculation was of similar
magnitude: 3.43159 km/s.
Table 13: STK Launch Parameters
Epoch
2460089.72194 JD
Location
Kennedy Space Center
Latitude
28.615°
Longitude
-80.694°
Altitude
0 km
C3
10.098437 km2/s2
RLA
138.816155° (w/rt Earth ecliptic)
DLA
35.810823° (w/rt Earth ecliptic)
600 km
3.59213 km/s
3.43159 km/s
15
A ground track of the spacecraft’s first week in flight is shown in Figure 20. Launching from Kennedy Space
Center, the satellite enters its parking orbit. It remains there for slightly longer than one revolution before
performing an in plane maneuver to enter into its Launch-VGA trajectory. During the first week of flight, the Deep
Space Network (DSN) facilities in Goldstone, CA and Madrid, Spain have communication access to the spacecraft.
Figure 20: Earth Ground Track for First Week of Mission
VII. Planetary Flybys
STK provides a decent interface for visualizing the simulated trajectory. This section shows what the flybys of
each planet look like. The left picture in each figure set is the view of the flyby from a view point outside the
planet’s orbit looking inwards towards the sun. The right picture in each set is the view of the flyby as seen from the
Earth. This view is important because it can be determined if the satellite’s line of sight to Earth is obstructed by the
planet. If this is the case, communication with the satellite during this crucial maneuver could be lost. Figures 21 and
22 show the Venus flyby.
Figure 21: Gravity Swingby of Venus
Figure 22: Gravity swingby of Venus as Observed from
Earth
During the flyby of Venus, the satellite passes behind the planet, accelerating with respect to the sun. It should
be noted that the satellite passes in Venus’ shadow during this time. Earth has line of sight visibility to the satellite
during this entire flyby. There should be no communication problems during the VGA.
16
The satellite has three trajectories passing by Earth during the VEMEGA: the launch, EGA1 between VGA and
MGA, and EGA2 between MGA and JOI. All three of these trajectories are shown in Figure 23.
Figure 23: Launch, EGA1, and EGA2 as Observed From Earth
Because this image is captured at the time when the satellite begins its Launch-VGA transit it is difficult to tell that
the satellite passes behind Earth during EGA1 and EGA2 to increase its energy with respect to the sun. Both EGA1
and EGA2 pass at an altitude above 2000 km. This means that there should not be much risk of the spacecraft
colliding with any LEO satellites or impacting the Earth on accident.
The Mars flyby is shown in Figure 24 below.
Figure 24: Gravity Swingby of Mars
Figure 25: Gravity Swingby of Mars as Observed from
Earth
Since the spacecraft actually decreases its energy at Mars it must fly in front of the planet. This slows the planet
down with respect to the sun. From the view of the Earth, the satellite flies between Mars and Earth. There should be
no line of sight obstructions during this flyby.
17
The spacecraft arrives at Jupiter in a highly inclined fashion. This insertion orbit is discussed further is Section
IX. Fortunately, the entirety of the Jupiter insertion orbit can be seen from Earth. This means that all planetary
flybys during this VEMEGA trajectory have no communication disruptions due to planetary interference.
Figure 26: Arrival at Jupiter
Figure 27: Arrival at Jupiter as Observed from Earth
VIII. Trajectory Correction Maneuvers
Trajectory correction maneuvers (TCMs) are necessary on interplanetary missions in order to correct attitude and
orbit determination errors during flight. The maneuvers are used to redirect the satellite back onto the designed
trajectory and to target B-plane parameters for flyby accurately. However, to implement TCMs on a trajectory you
must carry more fuel. Thus, keeping TCMs to a minimum is very important.
|s for flybys is as close to zero as possible. Despite
One way to minimize TCMs is to ensure that the |
keeping these values below 50 cm/s for the optimal trajectory, the differences in ephemeris between MATLAB and
STK still requires the usage of TCMs of appreciable magnitude. A single TCM was implemented for each trajectory
for simplicity in STK modeling. In a real operation, several TCMs would be used during each segment to correct for
real world errors, ensuring that the spacecraft is always on the correct trajectory. The TCM components and
magnitudes for each transit are shown in Tables 14 through 19 below.
Table 14: Launch-VGA TCM (VNC Venus Frame)
Date
2460124.916 (Launch +35 days)
-80.1459 m/s
95.7908 m/s
17.9614 m/s
| |
126.1818 m/s
Table 15: VGA-EGA1 TCM (VNC Earth Frame)
Date
2460263.61 (VGA +25 days)
150.01 m/s
35.8562 m/s
-255.619 m/s
| |
298.5460 m/s
Table 16: EGA1-MGA TCM (VNC Mars Frame)
Date
2460562.38 (EGA1 +10 days)
134.391 m/s
30.4172 m/s
-114.588 m/s
| |
179.2109 m/s
Table 17: MGA-EGA2 TCM (VNC Earth Frame)
Date
2461244.19 (MGA +525 days)
-49.5307 m/s
48.2045 m/s
142.538 m/s
| |
158.4110 m/s
Table 18: EGA2-JOI TCM (VNC Jupiter Frame)
Date
2461392.445 (EGA2 +25 days)
-34.4137 m/s
15.5962 m/s
123.56 m/s
| |
129.2076 m/s
Total TCMs
| |
| |
18
Table 19: Total TCMs
5
178.3115 m/s
891.5575 m/s
Each TCM is implemented within the first 35 days of passing the flyby planet in order to save fuel, with the
exception of the TCM implemented on the MGA-EGA2 trajectory. This one is implemented near the end of flight
for ease of convergence in STK. The largest TCM is the VGA-EGA trajectory at a total
| | of 298.5460 m/s. The average | | for all 5 TCMs is 178.3115 m/s. Totaling up all the TCMs for the entire
mission we have a total TCM | | of 891.5575 m/s. To refine this number, further analysis should conducted in the
full ephemeris to better match the
and
of each flyby.
IX. Jupiter Arrival
Arrival at Jupiter is a very critical point in the mission. The satellite must perform a maneuver within a very
small time window, very far from Earth. The selected Jupiter insertion orbit was chosen to be a highly elliptical orbit
with a period of 350 days. This orbit is ideal for keeping the
of the insertion maneuver reasonably low. A figure
of this insertion orbit is shown in Figure 28 below.
Figure 28: Elliptical Jupiter Insertion Orbit
From a different view, it can be seen that this orbit is nearly a 90° inclination polar orbit around Jupiter.
Figure 29: Nearly Polar Jupiter Insertion Orbit
19
The parameters associated with Jupiter arrival are shown in Table 20 below.
Table 20: Arrival Parameters (Jupiter Inertial)
5.699752 km/s
|
|
0.9779 km/s
| =|
|
|
|
|
0.6898 km/s
P
a
e
i
RAAN
w
285951.85 km (4 Jupiter Radii)
28,347,569.49 km
350 days
14,316,760.67 km
0.9800
90.1088°
123.8624°
333.7919°
The radius of closest approach was chosen to be 3 Jupiter Radii away from Jupiter’s surface to avoid planetary
impact. The 350 days insertion orbit keeps the insertion maneuver below 1 km/s. This value was checked against a
patched conics solution. The patched conics solution is much lower because the |
| at Jupiter for the MATLAB
ephemeris was slightly different than the resulting |
| at Jupiter from the STK simulation, due to implementation
in the full ephemeris with TCMs.
During this important maneuver it is important to investigate what the satellite trajectory looks like from Earth.
Communication with DSN facilities during this point in flight will be critical to exectuing the manuever properly.
Figure 30 shows the location of the satellite and its 15° line of site envelope during the beginning of the insertion
maneuver. Since the satellite is off the east coast of South America, it can be accessed by the Madrid DSN facility.
Figure 30: Earth Ground Track Before Jupiter Insertion Burn
20
If a specific ground station needs to execute the insertion burn command, the trajectory can be tweaked slightly
to allow this to happen. Figure 31, shows an example of an altered EGA2-JOI trajectory that allows for line of site
with the Goldstone DSN facility in CA. To achieve this, the arrival time at Jupiter was delayed only 3.5 hours using
a small adjustment to the EGA2-JOI TCM.
Figure 21: Altered Jupiter Insertion Time to Allow for JOI Operation out of Goldstone, CA
X. Potential Science Missions
There are many unanswered questions about Jupiter which may improve our understanding on the formation of
our solar system and its early evolution. Currently en route to Jupiter is the Juno mission, which is carrying an array
of instruments to better understand the gas giant. These
instruments will give insight into the atmospheric structure,
magnetic field, and the gravity field around the planet.3 Similar to
the intended Juno insertion, the VEMEGA mission naturally
inserts into Jupiter gravity using an elliptical polar orbit. A
similar mission could be conducted in the year 2023 to help
answer other questions raised by the Juno mission.
The most intriguing part of Jupiter is below its surface. Many
scientists believe that the hot gases at the surface condense
inwards to form a liquid and possibly even a solid at the center.
To investigate Jupiter’s atmosphere directly a device would have
to be deorbited similar to the probe dropped by Galileo in 1995.
This mission would be capable of dropping many probes at any
place on Jupiter’s surface due to its polar insertion orbit. Another
interesting idea would to have the spacecraft drop a nuclear
powered ramjet into Jupiter’s atmosphere. This jet could fly
around for months collecting vast amounts of valuable science
Figure 32: Jupiter's Red Spot4
data.
21
XI. Conclusion
There is still much to discover within our own solar system. Interplanetary mission design can provide scientists
affordable methods of reaching these far out destinations. The 2023 VEMEGA trajectory to Jupiter boasts in terms
of affordability because of its very low C3. It is compared to the Galileo mission and a simple Hohmann transfer
below.
C3
|
TOF
| |
| |
| |
|
Table 21: Trajectory Comparison
VEMEGA 2023
Galileo VEEGA Baseline
10.098437 km2/s2
18.079243 km2/s2
5.6998 km/s
5.8346 km/s
6.75 years
6.45 years
3.5921 km/s
3.9943 km/s
0.9779 km/s
0.9998 km/s
4.5700 km/s
4.9941 km/s
Hohmann Transfer
79.9053 km2/s2
5.6542 km/s
2.90 years
6.37611 km/s
0.68125 km/s
7.05736 km/s
The VEMEGA 2023 has a much lower C3 than the Galileo mission and the direct Hohmann transfer. It also has a
lower |
| at Jupiter than Galileo, approaching the performance of the Hohmann Transfer. However, it does take
longer to get to Jupiter than any of the other trajectories; a few months longer TOF than Galileo. Where the
VEMEGA shines in terms of affordability is the | |
, which is lower than both the Galileo mission and the
Hohmann transfer. Because this mission will need to be launched in 2023 there is still time to construct a spacecraft
tailored to it. With times as tight as they are today, this opportunity may be too good to pass up.
References
1
Atlas Launch System Mission Planner’s Guide, Lockheed Martin Co., 2004, Revision 10a, January 2007.
2
Delta II Payload Planners Guide, United Launch Alliance, December 2006.
3
“Juno,” <http://science.nasa.gov/missions/juno/>.
4
“On Planet Jupiter,” <http://g8ors.blogspot.com/2012/02/on-planet-jupiter_09.html>.
5
Proton Launch System Mission Planner’s Guide, International Launch Services, September 2009.
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