1. 28 October 2014 1 st Space Glasgow Research Conference, Glasgow, United Kingdom Solar Sailing: How to Travel on a Light Beam Alessandro Peloni Supervisor: Matteo Ceriotti Image credits: NASA website

2. How to travel on a light beam? Solar Radiation Pressure 28 October 2014Alessandro Peloni2

3. How to travel on a light beam? Solar Sail ideal model 28 October 2014Alessandro Peloni Sunjammer. Image credits: www.sunjammermission.com IKAROS. Image credits: JAXA website 3

4. How to travel on a light beam? Solar Sail vs Low-Thrust spacecraft 28 October 2014Alessandro Peloni4

5. Why NEOs? 28 October 2014Alessandro Peloni NEO scientific relevance: Asteroid Itokawa studied by “HAYABUSA” Image credits: “HAYABUSA” mission overview, ISAS – JAXA website 15/02/2013 Chelyabinsk impact Image credits: ESA website 5

6. Why NEOs? 28 October 2014Alessandro Peloni You are here 6

7. Multiple NEO Rendezvous Mission: Mission Requirements [1] 28 October 2014Alessandro Peloni7

8. Objective 28 October 2014Alessandro Peloni Mixed combinatorial/optimisation problem Develop a method to find as many sequences as possible feasible by a solar sail 8

9. Approach method 28 October 2014Alessandro Peloni Preliminary sequences found via heuristic rules and simplified trajectory models Optimal control problem performed on better sequences found, in order to obtain feasible trajectories for solar sails 9

10. 2D shape-based approach [1] 28 October 2014Alessandro Peloni [1] De Pascale, P. and Vasile M., “Preliminary design of low-thrust multiple gravity-assist trajectories”, Journal of Spacecraft and Rockets, Vol. 43, No. 5, 2006 In-plane Modified Equinoctial Elements: 10

11. Sequence finder 28 October 2014Alessandro Peloni Complete list of NEOs Pre-pruning on Keplerian parameters Local pruning on semi-major axis Shaping function from Earth to all available NEOs Local pruning on Keplerian parameters Local pruning on semi-major axis Shaping functions to all available NEOs Add stay time at the object Sequence complete YES NO Add a new object Mission time > 10 years? 11

12. Optimisation 28 October 2014Alessandro Peloni Trajectories and controls of each leg separately through shape-based method Pseudospectral transcription (GPOPS-II) used in order to find feasible solutions of the 2D problem for each leg separately Pseudospectral transcription (GPOPS-II) used in order to find the global multiphase solution I NITIAL G UESS 12

13. Optimisation 28 October 2014Alessandro Peloni Objective function: Endpoint constraints: Control vector: Derivatives: Automatic differentiation 13

14. Multiple NEO Rendezvous Mission: First Sequence (1/7) Mission parameters for 5 NEO rendezvous: Mission Duration: 10.8 years 28 October 2014Alessandro Peloni StartEndDuration [days] Transfer leg 1: Earth  2006 RH 120 18 Dec 201917 Jul 2021578 Transfer leg 2: 2006 RH 120  2000 SG 344 06 Jan 202223 Nov 2023687 Transfer leg 3: 2000 SG 344  2009 BD 12 May 202431 Aug 2026842 Transfer leg 4: 2009 BD  2006 JY 26 29 Dec 202630 Mar 2028457 Transfer leg 5: 2006 JY 26  2005 QP 87 26 Sep 202814 Oct 2030747 14

15. Multiple NEO Rendezvous Mission: First Sequence (2/7) 28 October 2014Alessandro Peloni15

16. Multiple NEO Rendezvous Mission: First Sequence (3/7) 1 st leg of the 5 NEO rendezvous mission 28 October 2014Alessandro Peloni Departing orbit Arrival orbit Transfer trajectory 16

17. Multiple NEO Rendezvous Mission: First Sequence (4/7) 2 nd leg of the 5 NEO rendezvous mission 28 October 2014Alessandro Peloni Departing orbit Arrival orbit Transfer trajectory 17

18. Multiple NEO Rendezvous Mission: First Sequence (5/7) 3 rd leg of the 5 NEO rendezvous mission 28 October 2014Alessandro Peloni Departing orbit Arrival orbit Transfer trajectory 18

19. Multiple NEO Rendezvous Mission: First Sequence (6/7) 4 th leg of the 5 NEO rendezvous mission 28 October 2014Alessandro Peloni Departing orbit Arrival orbit Transfer trajectory 19

20. Multiple NEO Rendezvous Mission: First Sequence (7/7) 5 th leg of the 5 NEO rendezvous mission 28 October 2014Alessandro Peloni Departing orbit Arrival orbit Transfer trajectory 20

21. Multiple NEO Rendezvous Mission: Second Sequence Mission parameters for 4 NEO rendezvous: Mission Duration: 8.5 years 28 October 2014Alessandro Peloni StartEndDuration [days] Transfer leg 1: Earth  2001 GP 2 18 Dec 201908 Sep 2021631 Transfer leg 2: 2001 GP 2  2007 UN 12 05 Apr 202223 Aug 2023504 Transfer leg 3: 2007 UN 12  2009 YF 17 Jan 202418 Apr 2026822 Transfer leg 4: 2009 YF  (99942) Apophis 03 Sep 202621 Jun 2028657 21

22. Multiple NEO Rendezvous Mission: Summary of results 28 October 2014Alessandro Peloni RequiredSequence 1Sequence 2 Mission duration Number of rendezvousAt least 3 Stay time [days] At least few days Rendezvous with PHOAt least 1 Rendezvous with NHATSAt least 1 Last objectH > 25.5 Characteristic acceleration [ mm/s 2 ] Total  v [ km/s ] // 22

23. Conclusions and Future work 28 October 2014Alessandro Peloni23

24. Space Glasgow @SpaceGlasgow www.glasgow.ac.uk/space Thank you! a.peloni.1@research.gla.ac.uk