multiple nea rendezvous mission: solar sailing options · 2017-01-17 · multiple nea rendezvous...

17th Jan 20174th International Symposium on Solar Sailing,

Kyoto, Japan

Multiple NEA Rendezvous Mission:Solar Sailing Options

Alessandro PeloniBernd DachwaldMatteo Ceriotti

Near-Earth Asteroids (NEAs)

17th Jan 2017 2Alessandro Peloni, Bernd Dachwald, Matteo Ceriotti

NEA scientific relevance:Asteroid Itokawa studied by “HAYABUSA”

Image credits: “HAYABUSA” mission overview, ISAS – JAXA website

15 Feb 2013Chelyabinsk impact

Image credits: ESA website

Objective:Multiple asteroid rendezvous mission

17th Jan 2017 Alessandro Peloni, Bernd Dachwald, Matteo Ceriotti

Mixed combinatorial/continuous optimisation problem

Develop a method to find multiple NEA rendezvous

sequences with a solar sail

3

Tree-Search Algorithm


…

Solar-sail trajectory optimization

N objects

…… … K*(N-1) objects

… … … W*(K-1)*(N-1) objects

NEA & PHA


You are here

Body sizes not to scale!

NEA Databases

*NHATS = NEO Human Spaceflight Accessible Target Study: NEAs for which a low-thrust return mission can be found within a set of design parameters (http://neo.jpl.nasa.gov/nhats/):

𝑡𝑡𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜 ∆𝑣𝑣 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ≤ 8 ⁄km s𝑡𝑡𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜 𝑚𝑚𝑟𝑟𝑚𝑚𝑚𝑚𝑟𝑟𝑜𝑜𝑚𝑚 𝑟𝑟𝑟𝑟𝑟𝑟𝑜𝑜𝑡𝑡𝑟𝑟𝑜𝑜𝑚𝑚 ≤ 450 days𝑚𝑚𝑡𝑡𝑜𝑜𝑠𝑠 𝑡𝑡𝑟𝑟𝑚𝑚𝑟𝑟 𝑜𝑜𝑡𝑡 𝑡𝑡𝑡𝑟𝑟 𝑜𝑜𝑜𝑜𝑜𝑜𝑟𝑟𝑜𝑜𝑡𝑡 ≥ 8 days

𝑜𝑜𝑜𝑜𝑟𝑟𝑚𝑚𝑜𝑜𝑡: 2015 − 2040𝐻𝐻 ≤ 26 mag

**LCDB = Lightcurve database: NEAs with light curve quality code 𝑈𝑈 ≤ 2 − (i.e. objects for which the given value of the rotation rate is not reliable for statistical analysis)


NEAs

PHAs 1607

NHATS* 204

LCDB** 271

Total 12,840

PHA-NHATS PHA-LCDB

1607 1607

204 8

72 271

1801 1813

2 DATABASES CONSIDERED

http://neo.jpl.nasa.gov/nhats/

Multiple NEA Rendezvous Mission:Mission Requirements

Dachwald, B. et al., “Gossamer Roadmap Technology Reference Study for a Multiple NEO Rendezvous Mission”, Advances in Solar Sailing, edited by M. Macdonald, Springer Praxis Books, Springer-Verlag, Berlin, 2014, pp. 211-226.


Missionrequirement

Mission duration < 10 yearsNumber of rendezvous At least 3

Stay time [days] At least few days

Rendezvous with PHA At least 1

Rendezvous with NHATS asteroids At least 1

Characteristic acceleration [ mm/s2 ]≤ 0.3

( 𝐴𝐴𝑚𝑚≤ 33 m2

kg)

Solar Sail: ideal model


22 ˆcos

2

c

c

rarAa PM

α⊕ =

=

a N

Sunjammer. Image credits:www.sunjammermission.com

IKAROS. Image credits:JAXA website

8

http://www.sunjammermission.com/

Method


Preliminary sequences found via heuristic rules and semi-analytical approximated

trajectory model

Optimal control problem performed on best sequences found, in order to obtain feasible

trajectories for solar sails

Optimal control problem performed on best sequences found, in order to obtain feasible

trajectories for solar sails

2D shape-based approach


3rµ= +

ra r

( ) ( )( ) ( )( ) ( )

0 1 0 1 1

0 1 0 2 0 2

0 1 0 2 0 2

exp sin

sincos

p p p L L L

f f f L L L Lg g g L L L L

λ ϕ

λ ϕλ ϕ

= − + + = + − + − +

= + − − − +

Peloni, A., Ceriotti, M., and Dachwald, B., “Solar-Sail Trajectory Design for a Multiple Near-Earth-Asteroid Rendezvous Mission”, Journal of Guidance, Control, and Dynamics, 39 (2016), pp. 2712-2724.

( )( )( )

21

cossin

p a e

f eg e

L

ωω

ω ν

= − = +Ω

= +Ω = +Ω +

In-plane ModifiedEquinoctial Elements:

10

Sequence Search


Complete database𝑜𝑜 ∈ 𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚,𝑜𝑜𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟 ∈ 𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚, 𝑟𝑟𝑚𝑚𝑚𝑚𝑚𝑚𝜛𝜛1 − 𝜛𝜛2 ≤ 𝛿𝛿𝜛𝜛𝑚𝑚𝑚𝑚𝑚𝑚

arccos 𝒉𝒉1 𝒉𝒉2 ≤ 𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚

Local pruning on Keplerian elements

Semi-analytical approximated trajectory (coplanar shape-based method) to all available NEAs

Sequence complete

Mission time < 10 years?YES

NO

At least one trajectory satisfies the accelerations requirements?

YES

NO

OptimizationOCP with Pseudospectral Method


Input sequence(departing and arrival objects and times for each leg)

Compute 4 different initial-guess solutions for each leg through coplanar shape-based

approach

Solve the optimization problem for each leg

separately

Solve the optimization problem for each leg

separately

With scaling Without scaling

Feasible or optimal solutions found in all the

legs?

Feasible or optimal solutions found in all the

legs?

Build the whole multi-leg trajectory

Build the whole multi-leg trajectoryNo solutions

YES YES

NONO Both mesh refinements already

used?

NO

YES

Change the mesh refinement method


RESULTS

PHA-NHATS Database:Sequence Search (1/2)


Characteristic acceleration: 𝑜𝑜𝑐𝑐 = 0.2mms2

> 4,800 unique sequences of at least 5 NEAs, of which at least 1 PHA!!!

PHA-NHATS Database:Sequence Search (2/2)


Earth (14 August 2022)

2001 QJ142 2012 BB14

2014 EK24

2011 CG2 2011 CG2 2000 SG344

2000 EA14

2008 TX3

2008 DB

2006 BZ147 2014 UN1142012 WH

2007 UY12012 WH

2014 YN

2013 BS45 2012 EC2014 UN114

2009 UZ872011 UX275 2013 BS45

PHA-NHATS Database:First Optimized Sequence (1/2)


Object Stay time[days] Start End ToF

[days]

Earth // 24/08/2022 18/08/2024 7252012 BB14 126

22/12/2024 03/10/2026 6502011 CG2 123

03/02/2027 21/11/2028 6582006 BZ147 166

07/05/2029 23/06/2030 4122013 BS45 188

28/12/2030 13/04/2032 4732014 YN //

5-NEA Rendezvous Mission – Mission parameters:

𝑜𝑜𝑐𝑐 = 0.2 mms2

Mission duration: 9.6 years

PHA-NHATS Database:First Optimized Sequence (2/2)


PHA-NHATS Database:Sequence Optimization – Summary


Missionrequirement

1st sequence(presented) 2nd sequence 3rd sequence

Mission duration < 10 years 9.6 years 9.6 years 7.8 yearsNumber of rendezvous At least 3 5 5 4

Stay time [days] At least few days > 4 months > 1.7 months > 5 months

Rendezvous with PHA At least 1 1 1 2Rendezvous with NHATS asteroids At least 1 5 4 3

Characteristic acceleration [ mm/s2 ]

≤ 0.3( 𝐴𝐴𝑚𝑚≤ 33 m2

kg) 0.2 ( 𝐴𝐴

𝑚𝑚= 22m2

kg)

PHA-LCDB Database:Sequence Search


Characteristic acceleration: 𝑜𝑜𝑐𝑐 = 0.2mms2

589 unique sequences of 3 NEAs, of which at least 1 PHA

PHA-LCDB Database:Sequence Optimization

All 589 sequences found with at least 3 NEAs have been optimized

Automatic optimization algorithm used without any additional user input

343 fully-optimized sequences 58% of the preliminary sequences found by the sequence-search algorithm are proven to be feasible mission scenarios

Total Δ𝑣𝑣 needed for each whole mission up to 52 km/s


Conclusions

A solar sail with lower AMR has been used in this study, loweringthe technological requirement of this kind of mission

PHA-NHATS database:• More than 4,000 unique sequences have been found over 10 years of

possible launching dates: all the sequences are made of asteroidsinteresting both from a human mission point of view (NHATS) and from aPlanetary Defence point of view (PHA)

• At least 1 month spent in the vicinity of each object for close-upobservations → Better knowledge about NEAs (Orbit estimation, Mass,Composition, Porosity, Shape, Spin) → Possibility to plan more effectivedeflection missions

PHA-LCDB database:• Validation of the proposed approach for more challenging scenarios• Demonstration of the reliability of the sequence-search algorithm:

58% of the sequences found converged upon optimisation• Fully-automatic optimization


Space Glasgow@SpaceGlasgow

www.glasgow.ac.uk/space

Thank you!

[email protected] [email protected]@mtcerio

multiple nea rendezvous mission: solar sailing options · 2017-01-17 · multiple nea rendezvous...

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