Mission Development: Putting It All Together ASEN 6008 Interplanetary Mission Design.
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Transcript of Mission Development: Putting It All Together ASEN 6008 Interplanetary Mission Design.
![Page 1: Mission Development: Putting It All Together ASEN 6008 Interplanetary Mission Design.](https://reader036.fdocuments.net/reader036/viewer/2022062413/5a4d1b487f8b9ab0599a4701/html5/thumbnails/1.jpg)
Mission Development:Putting It All Together
ASEN 6008Interplanetary Mission Design
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The Story So Far…• Lambert’s Problem• Pork Chop Plots• Gravity Flybys• Resonant Orbits• B-Plane Parameters
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Example• Apply techniques to Galileo
– Venus-Earth-Earth-Gravity Assist (VEEGA)
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Necessary Conditions• What conditions are necessary for
interplanetary mission, particularly missions that include flybys?
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Necessary Conditions• What conditions are necessary for
interplanetary mission, particularly missions that include flybys?– Fuel perspective
• Low C3• Low arrival V
• Reasonable TCM Budget• Deep Space Maneuvers?
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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.
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Cassini Trajectory• Launch from Earth to 1st Venus Flyby• Deep Space Maneuver: 450 m/s • 2nd Venus Flyby, Earth flyby, Jupiter flyby
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Necessary Conditions• What conditions are necessary for
interplanetary mission, particularly missions that include flybys?– Other considerations
• Time of flight– Hardware considerations?
• Radiation• Eclipse• Communication• etc
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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
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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 |Vin| = |Vout|• Alter PCPs to illustrate |Vin| and |Vout|
– Venus to Earth leg• Given Vin and Vout, we can determine
Bplane parameters and |RP|– Check for planetary impacts!
• Match PCPs to determine possible flybys
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• |Vin| = |Vout| = 6.2 km/s• Rp = 18928 km
Example: VGA
|V|, not C3
Launch to Venus Leg Venus to Earth Leg
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• |Vin| = |Vout| = 6.2 km/s• Rp = 18928 km
Example: VGA
|V|, not C3
Arrival/Departure Dates are the same
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How do we do it?• Develop code to determine possible gravity
flybys1. Search PCP data2. Arrival date matches departure date at flyby
planet3. Difference between |Vin| and |Vout| less than
some tolerance4. |RP| > radius of planet plus margin (ex: 300
km)
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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)
Earth to Jupiter LegVenus to Earth Leg
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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 |Vin| = |Vout| between orbit flybys
• Verify resonant orbit does not impact planet
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Resonant Orbit PCPs• Trajectory available 2 Earth years later
Earth to Jupiter LegVenus to Earth Leg
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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
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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)
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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
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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– C3 – TOF– V∞ at the final planet– Matching V∞ in and V∞ out
– C = [w1*C3 + w2*TOF + w3*V∞ + …]
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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
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Lambert’s from VGA to EGA1
Brute Force Approach (SIMPLIFIED!)
Given Date for Launch, VGA, EGA1, EGA2 and JOI and the Resonance
Lambert’s from Launch to VGA
C3 < Launch Capability?
( |Vin| - |Vout| ) < tol for VGA?
Rp > Min Radius for VGA?
Lambert’s from EGA2 to JOI
|Vin| < Max Allowable?( |Vin| - |Vout| ) < tol for
EGA1 and EGA2?Rp > Min Radius for EGA1
and EGA2?
Yes
No
Yes
No
Good Trajectory!
Store for Analysis
Yes
No
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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