1. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

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

3. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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 Aims and Scope

4. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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.

5. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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. Circular Restricted Three-body Problem

6. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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.

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

8. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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)

9. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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)

10. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

11. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

12. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

13. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

14. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado Halo Orbit Targeting methods using STK/Astrogator 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 Jupiter located here

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

16. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado Results 1.Earth Departure: 2007/8/1 2.Halo Orbit Insertion at Sun Earth L2 Lagrangian point Duration: 14.5 days (approx.) ∆V: 3.170804 km/s ( approx.) 3.Transfer from Sun Earth L2 to Sun Mars L2 Lagrangian point Duration: 955 days (approx.) ∆V :1.0318345 km/s 4.Halo Orbit Insertion at Sun Mars L2 Lagrangian point Duration: 321 days (approx.) ∆V: -0.279681 km/s 5.Station Keeping at Sun Mars L2 Lagrangian point Duration: 378 days (approx.) ∆V: 0.19742 km/s

17. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado Results 6. 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

18. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado Results More details about Station-keeping at SE L2, SML2, SJL2 and SSL2 : 1. 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

19. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

20. 15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Colorado 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

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

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