1. Advanced method of virtual trajectories for the preliminary design of gravity-assist missions Sergey Trofimov Keldysh Institute of Applied Mathematics Moscow Institute of Physics and Technology Maksim Shirobokov Keldysh Institute of Applied Mathematics Moscow Institute of Physics and Technology

2. Content Motivation Method of virtual trajectories Benefits and flaws Test case: flight to Jupiter Conclusion 2/20

3. Gravity-assist interplanetary missions Two stages of a mission to any planet and its moon system: – takes most of flight time and imposes principal restrictions on the mission timeline – fine adjustment of the moon orbit insertion conditions Gravity assists (swing-bys) are of vital importance for saving fuel and increasing the scientific payload 3/20 Cruise Orbital tour

4. Mission feasibility study When studying the mission feasibility, a designer wants: To quickly estimate the best  V, the transfer time and launch windows for a number of planetary sequences To have an option of varying some mission constraints and imposing new ones (ideally without recalculating the whole optimization procedure) To do all of this without involving skilled specialists in astrodynamics These goals are rather challenging in case of multiple gravity-assist (MGA) trajectory design 4/20

5. Method of virtual trajectories Based on the fact that the orbits of planets are changing very slowly For a given planetary sequence, a database of all “geometrically feasible” trajectories can be constructed once and for all (“for all” means at least for several decades) The second, fast computing step: to screen and refine such a database of virtual trajectories 5/20

6. Classes of trajectories considered Basic class of trajectories: Coast heliocentric conic arcs Powered gravity assists (single impulse at the pericenter) Method of VT was also adapted to the trajectories with non-powered gravity assists deep space maneuvers (DSM) At most one DSM is allowed on each heliocentric arc 6/20

7. Some basic concepts and assumptions 1)The orbits of planets: assumed to be closed curves fixed in space are discretized (i.e., represented as a 1D mesh) 2)Virtual trajectory (VT): consists of heliocentric conic arcs sequentially connecting the mesh points on the orbits of planets included in the planetary sequence chosen 3)A virtual trajectory is referred to as near-feasible if a spacecraft moving along it would fly by the mesh node on the planet’s orbit approximately (within some time tolerance) at the same time with the planet itself 7/20

8. Discretization of planetary orbits and beams of virtual trajectories 8/20

9. Beam of heliocentric arcs with different elevation angles 9/20

10. Patching of incoming and outgoing planetocentric hyperbolic arcs 10/20

11. Screening of VT database 11/20

12. Refinement of near-feasible trajectories 12/20

13. Comparison of computational costs Number of gravity assists CPU time for VT database screening and refinement, min* CPU time for classical Lambert-based approach, min* 10.5-22-3 23-610-15 38-1560-80 420-40>200 13/20 *All values of computational time are relative to a PC with 2.13 GHz CPU and 2Gb RAM

14. Benefits and flaws of the VT method +One and the same set of databases can be used many times for the design of various missions +Easy handles with imposing different additional constraints, without extra computational cost −Sensitive to step sizes during the discretization of planets’ orbits when constructing a database of VT −Requires considerable hard disk space for saving all of VT databases 14/20

15. Sample problem: transfer to Jupiter Objective functional: Constraints: No conjunctions during performing GAs or DSMs To check some standard planetary sequences: EVJ, EVEJ, EEVJ, EVEEJ 15/20

16. EVEEJ: similar to the baseline trajectory of Jupiter Ganymede Orbiter (JGO) mission 16/20

17. EVEEJ: similar to the baseline trajectory of Jupiter Ganymede Orbiter (JGO) mission 17/20 In synodic (Earth co-rotating) frame

18. EVEEJ: similar to the baseline trajectory of proposed Ganymede Lander mission 18/20

19. EVEEJ: similar to the baseline trajectory of proposed Ganymede Lander mission 19/20 In synodic (Earth co-rotating) frame

20. Conclusion Based on a number of beforehand computed databases of virtual trajectories, a mission designer can: quickly estimate the possible mission timeline options (planetary sequence, launch date, transfer time) pick and choose the planetary sequence which is best suited to various constraints and scientific requirements change his mind and impose new constraints without a serious increase in time of mission feasibility analysis 20/20

21. Thank you for attention