Mission Development:
Putting It All Together
ASEN 6008
Interplanetary Mission Design
The Story So Far…
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Lambert’s Problem
Pork Chop Plots
Gravity Flybys
Resonant Orbits
B-Plane Parameters
Example
• Apply techniques to Galileo
– Venus-Earth-Earth-Gravity Assist (VEEGA)
Necessary Conditions
• What conditions are necessary for
interplanetary mission, particularly missions
that include flybys?
Necessary Conditions
• What conditions are necessary for
interplanetary mission, particularly missions
that include flybys?
– Fuel perspective
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Low C3
Low arrival V
Reasonable TCM Budget
Deep Space Maneuvers?
Necessary Conditions
• What conditions are necessary for
interplanetary mission, particularly missions
that include flybys?
– Flybys
• V, in = V, out
– If V, in ≠ V, out, need powered flyby.
• Flyby radius > planetary radius + tolerance
• Dates: JD of V, in = JD of V, out
– Resonant Orbits
• Spacecraft must re-encounter the planet after n number of
complete planet revs where n is an integer.
• Spacecraft can re-encounter a planet at a different location
in its orbit
– Cassini did this. It needed a sizeable DSM.
Cassini Trajectory
• Launch from Earth to 1st Venus Flyby
• Deep Space Maneuver: 450 m/s
• 2nd Venus Flyby, Earth flyby, Jupiter flyby
Necessary Conditions
• What conditions are necessary for
interplanetary mission, particularly missions
that include flybys?
– Other considerations
• Time of flight
– Hardware considerations?
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Radiation
Eclipse
Communication
etc
PCPs and Flybys
• Pork Chop Plots (PCPs) can be useful for
graphically narrowing down regions where
valid trajectories may exist.
• NOT good for final (or even intermediate)
mission design
PCPs and Flybys
• Current PCPs: Show outgoing C3 at launch and
incoming |V| at the target planet
– Works great for Launch at Earth to Venus
• Gravity flyby requires |Vin| = |Vout|
• Alter PCPs to illustrate |Vin| and |Vout|
– Venus to Earth leg
• Given Vin and Vout, we can determine Bplane
parameters and |RP|
– Check for planetary impacts!
• Match PCPs to determine possible flybys
Example: VGA
• |Vin| = |Vout| = 6.2 km/s
• Rp = 18928 km
|V|, not C3
Launch to Venus Leg
Venus to Earth Leg
Example: VGA
• |Vin| = |Vout| = 6.2 km/s
• Rp = 18928 km
|V|, not C3
Arrival/Departure Dates are the same
How do we do it?
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Develop code to determine possible gravity
flybys
1. Search PCP data
2. Arrival date matches departure date at flyby
planet
3. Difference between |Vin| and |Vout| less than
some tolerance
4. |RP| > radius of planet plus margin (ex: 300 km)
Is a resonant orbit necessary?
• What if we skip the resonant orbit and go from Earth to Jupiter?
• No outgoing trajectories with |V,out| < 9 km/s
• Can’t backtrack to match with a launch and valid Venus flyby (C3
constraints)
Venus to Earth Leg
Earth to Jupiter Leg
Resonant Orbits
• If arrival at Earth will not produce flight to
Jupiter  Add Resonance Orbit
– Try multiple combinations (2:1, 3:1, 5:2, etc.)
– Ex: Satellite would make it to Jupiter X-years later
• Verify that |Vin| = |Vout| between orbit flybys
• Verify resonant orbit does not impact planet
Resonant Orbit PCPs
• Trajectory available 2 Earth years later
Venus to Earth Leg
Earth to Jupiter Leg
B-Plane Parameters
• Given all of the gravity flybys and velocities,
we can easily solve for all B-Plane parameters.
• Intermediate TCMs can be used to guarantee
correct flyby
– Apply TCMs early in trajectory to minimize V
– However, must wait until accurate OD solution
• TCMs can also be used to target orbital
parameters for flyby/orbit insertion
– Example: Current Trajectory at Earth will arrive at
Jupiter near its Equator. Use TCM to target into
polar orbit
TCMs
• TCM costs can be improved by adjusting
critical events dates
– Dates only accurate to 1 day
• TCM may be 100s of m/s
– Dates accurate to hours or minutes
• TCMs down to few m/s
• Don’t want too many TCMs (critical events)
– Each critical event is a risk to the mission
(execution error, possible hardware failure)
Other Considerations
• Planetary Quarantine
• Communication
– Satellite visible to DSN at TCMs and flybys?
– When is satellite obstructed?
– Distance to satellite
• Consider mission when at planetary orbit
insertion
– Orbit insertion burn
– Lunar flybys
– Satellite inclination for study of magnetosphere
The Best Trajectory?
• Given all trajectories that satisfy the criteria,
determine “best” trajectory (Cost Function)
• Best may defined as a minimum variable or
weighted combination of variables
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C3
TOF
V∞ at the final planet
Matching V∞ in and V∞ out
C = [w1*C3 + w2*TOF + w3*V∞ + …]
Designing a good trajectory
• Requires an iterative approach
– Determine regions of possible optimal trajectories
– Narrow search while increasing fidelity
• Initial Search: PCPs show 1 year time frame in 5 JD increments
• Final Search: PCPs show 100 day time frame in 6 hr increments
• Automate using software
– “Brute Force” commonly employed
• Check every single possibility (all combinations of
dates/resonances)
– Store trajectory data if all criteria are met
» Launch C3, V-infinity differences, flyby radii, etc
• For VEEGA: 6 DOF problem
• Computationally intensive
• Practically guaranteed to find the best solution among the given
inputs
Brute Force Approach
(SIMPLIFIED!)
Given Date for Launch,
VGA, EGA1, EGA2 and
JOI and the Resonance
Lambert’s from
Launch to VGA
No
No
( |Vin| - |Vout| ) < tol for
VGA?
C3 < Launch Capability?
Lambert’s from VGA to
EGA1
Rp > Min Radius for VGA?
Yes
Yes
|Vin| < Max Allowable?
( |Vin| - |Vout| ) < tol for
EGA1 and EGA2?
Lambert’s from EGA2 to
JOI
Rp > Min Radius for EGA1
and EGA2?
No
Yes
Good
Trajectory!
Store for
Analysis
Optimizing Algorithms
• Hill Climbing
– Genetic Algorithms, Simulated Annealing, Steepest Descent,
Random Start Hill Climbing, etc
– Reduce computation time
– Not guaranteed to find the globally optimal solution
• Basic Algorithm
– Initial guess: Evaluate the cost
– Perturb the trajectory: Evaluate the cost
– New Trajectory Better? Store it and move to next
• No? Start with new initial guess (different perturbation?)
– Algorithm continues until best local solution is found