Mission Development:Putting It All Together

ASEN 6008Interplanetary Mission Design

The Story So Far…• 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

• 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?

• 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 |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

• |Vin| = |Vout| = 6.2 km/s• Rp = 18928 km

Example: VGA

|V|, not C3

Launch to Venus Leg Venus to Earth Leg

• |Vin| = |Vout| = 6.2 km/s• Rp = 18928 km

Example: VGA

|V|, not C3

Arrival/Departure Dates are the same

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)

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

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

Resonant Orbit PCPs• Trajectory available 2 Earth years later

Earth to Jupiter LegVenus to Earth 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– 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

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

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