Low Energy Interplanetary Transfers Using the Halo Orbit Hopping Method with STK/Astrogator

1. Low Energy Interplanetary Transfers Using the Halo Orbit Hopping Method with STK/Astrogator Tapan R. Kulkarni Daniele Mortari Department of Aerospace Engineering, Texas A&M University College Station, TX 77840 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

2. Outline • Aims and Scope of this research • Circular restricted three-body problem • Halo orbit targeting methods using STK/Astrogator • Results • Discussion • Conclusion 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

3. Aims and Scope • To find low energy interplanetary transfer orbits from Earth to distant planets • To find L2 halo orbit insertion method, • Perform the L2 station-keeping operations, and • To determine halo orbit hopping method between subsequent L2 halo orbits. • To find a method of maintaining seamless radio contact with Earth and simultaneous planetary exploration • To design all the trajectories using STK/Astrogator 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

4. Gravity Assisted Trajectory Method • Most famous method for sending spacecraft to distant planets. E.g., Cassini mission to Saturn (Oct ’97- Jul ’04) • Advantages: higher speeds (short transfer times). • Disadvantages: cost, constraint imposed by the fly-by body, limitations due to impact parameter. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

5. Circular Restricted Three-body Problem • Solution of E.O.M. is not periodic and hence need of a control effort (L2). • This is called Period or Frequency control in literature. • The resulting periodic orbit is called a halo orbit. • When the spacecraft is actively controlled to follow a periodic halo orbit, the orbit, generally does not close due to tracking error. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

6. Targeting Methods Using STK/Astrogator • The whole mission is split in steps and phases. • Steps: Halo orbit insertion at SEL2, Halo orbit hopping sequence. • Phases: Impulsive maneuvers, propagation, stopping conditions. • Targeting method at every step uses the Differential Corrector (SVD) by defining a 3-D target. • Perform a burn in anti-Sun line that takes the S/C in vicinity of Sun-Earth L2 Lagrangian point. • Insertion: Adjust the burn in such a way the S/C crosses Sun-Planet L2 Z-X plane with Sun-Planet L2 Vx=0 Km/s. • Station keeping: After several Sun-Planet Z-X plane crossings, perform station keeping operations. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

7. Performing the Engine burn I • Getting to the vicinity of L2 • Estimating the size of the burn • Setting up the Targeter • Propagating to the Anti-Sun Line • Creating Calculation objects • Setting up the Targeter • Running the Targeter Start 1 2 • Adjusting the Engine burn • Targeting on the 2nd ZX plane crossing • Setting up the Targeter • Creating a Targeting profile • Running the Targeter • Performing the Engine burn II • Creating a Targeting Profile • Running the Targeter • Specifying the constraints • Cross the ZX plane with Vx=0 3 4 5 Completing the First Target sequence to Orbit around L2 • Performing the station keeping Maneuver • Setting up the Targeter • Running the Targeter 6 7 Sequences in halo orbit insertion & station keeping operations Targeting Methods using STK/Astrogator 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

8. Halo Orbit Targeting methods using STK/Astrogator Initial Earth-circular orbit and Halo orbit insertion at Sun-Earth L2 Lagrangian point trajectory ( as seen in VO view) 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

9. Halo Orbit Targeting methods using STK/Astrogator Halo orbit at Sun-Earth L2 Lagrangian point trajectory as seen in Y-Z plane (Map View) Halo orbit at Sun-Earth L2 Lagrangian point trajectory as seen in X-Z plane (Map View) 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

10. Halo Orbit Targeting methods using STK/Astrogator Variation of Delta V and Propagation time for Halo Orbit Hopping Segment from SE L2 to SM L2 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

11. Halo Orbit Targeting methods using STK/Astrogator Halo orbit at Sun-Earth L2 Lagrangian point in Sun-Earth rotating frame of reference as seen in X-Y plane Interplanetary trajectory from Sun-Earth L2 to Sun-Mars L2 in Sun-centered inertial frame of reference as seen in X-Y plane 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

12. Halo Orbit Targeting methods using STK/Astrogator Halo Orbit around Sun-Mars L2 Lagrangian point in Sun-Mars rotating frame of reference as seen in X-Y plane Interplanetary trajectory from Sun-Mars L2 to Sun-Jupiter L2 in Sun-centered inertial frame of reference as seen in X-Y plane 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

13. Halo Orbit Targeting methods using STK/Astrogator Halo orbit insertion at Sun-Jupiter L2 Lagrangian point in Sun-Jupiter rotating frame of reference as seen in X-Y plane Halo orbit around Sun-Jupiter L2 Lagrangian point in Sun-centered inertial frame of reference as seen in X-Y plane 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

14. Halo Orbit Targeting methods using STK/Astrogator Jupiter located here Halo orbit around Sun-Jupiter L2 Lagrangian point in Sun-Jupiter rotating frame of reference as seen in X-Y plane Interplanetary trajectory from Sun-Jupiter L2 to Sun-Saturn L2 in Jupiter-centered inertial frame of reference as seen in Y-Z plane 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

15. Halo Orbit Targeting methods using STK/Astrogator Saturn & Titan located here Halo orbit around Sun-Saturn L2 Lagrangian point in Sun-Saturn rotating frame of reference as seen in X-Y plane 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

16. Results • Earth Departure: 2007/8/1 • Halo Orbit Insertion at Sun Earth L2 Lagrangian point • Duration: 14.5 days (approx.) • ∆V: 3.170804 km/s ( approx.) • Transfer from Sun Earth L2 to Sun Mars L2 Lagrangian point • Duration: 955 days (approx.) • ∆V :1.0318345 km/s • Halo Orbit Insertion at Sun Mars L2 Lagrangian point • Duration: 321 days (approx.) • ∆V: -0.279681 km/s • Station Keeping at Sun Mars L2 Lagrangian point • Duration: 378 days (approx.) • ∆V:0.19742 km/s 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

17. Results • Transfer from Sun Mars L2 to Sun Jupiter L2 Lagrangian point • Duration: 2595 days (approx.) • ∆V: 2.08933911 km/s • 7. Halo Orbit Insertion at Sun Jupiter L2 Lagrangian point • Duration: 411 days (approx.) • ∆V: -0.42396 km/s • 8. Station Keeping at Sun Jupiter L2 Lagrangian point • Duration: 1642.5 days (approx.) • ∆V: 0.40629 km/s • 9. Transfer from Sun Jupiter L2 to Sun Saturn L2 Lagrangian point • Duration: 4881 days (approx.) • ∆V: 1.3077 km/s • 10. Station Keeping at Sun Saturn L2 Lagrangian point • Duration: 2244 days (approx.) • ∆V:0.87984 km/s 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

18. Results • More details about Station-keeping at SE L2, SML2, SJL2 and SSL2 : • Station Keeping at Sun-Earth L2: • DeltaV per year = 0.024827 km/s • Duration = 1.0274 years • No. of Z-X plane crossings = 4 • 2. Station-keeping at Sun-Mars L2: • DeltaV per year = 0.19063 km/s • Duration = 1.0356 years • No. of Z-X plane crossings: 3 • 3. Station-keeping at Sun-Jupiter L2: • DeltaV per year = 0.090286 km/s • Duration = 4.5 years • No. of Z-X plane crossings: 3 • 4. Station-keeping at Sun-Saturn L2: • DeltaV per year = 0.143111 km/s • Duration = 6.148 years • No. of Z-X plane crossings: 3 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

19. Discussion • Planets do not eclipse the spacecraft as seen in Y-Z plane • Halo orbit originating in vicinity of L2 grows larger, but shorter in period as it shifts towards planet • Small ∆V budget for station-keeping operations for halo orbit around Sun-Planet L2 Lagrangian point • Halo orbit hopping method is slower than gravity assisted trajectory method (approximately 5 times slower) • Saving of fuel by over 35% over gravity assisted trajectory method 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

20. Conclusion • Continuous radio contact with Earth • Simultaneous mapping of the planets possible • Potential utility of placing satellites orbiting L2 and L1 Lagrangian points serving as Earth-Moon and Earth-Mars communication relays • Method suitable for spacecrafts only, not for manned missions • Suitability for multi-moon orbiter missions at Jupiter and Saturn 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

21. Questions ? 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado

22. Thank you !! 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado