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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. Outline. Aims and Scope of this research - PowerPoint PPT Presentation
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15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
Low Energy Interplanetary Transfers Using the Halo Orbit Hopping Method with
STK/Astrogator
Tapan R. KulkarniDaniele Mortari
Department of Aerospace Engineering, Texas A&M University
College Station, TX 77840
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
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, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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.
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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.
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
Targeting Methods using STK/Astrogator
StartPropagating to the Anti-Sun Line•Creating Calculation objectsSetting up the TargeterRunning the Targeter
Performing the Engine burn I•Getting to the vicinity of L2Estimating the size of the burnSetting up the Targeter
Specifying the constraints•Cross the ZX plane with Vx=0
Performing the Engine burn II•Creating a Targeting ProfileRunning the Targeter
Adjusting the Engine burn•Targeting on the 2nd ZX plane crossingSetting up the TargeterCreating a Targeting profileRunning the Targeter
Completing the First Target sequence to Orbit around L2
Performing the station keeping Maneuver•Setting up the TargeterRunning the Targeter
12
3
4
5
6
7
Sequences in halo orbit insertion & station keeping operations
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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)
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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)
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
Results1. Earth Departure: 2007/8/12. 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
Results6. 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, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
ResultsMore 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 = 42. Station-keeping at Sun-Mars L2: DeltaV per year = 0.19063 km/s Duration = 1.0356 years No. of Z-X plane crossings: 33. Station-keeping at Sun-Jupiter L2: DeltaV per year = 0.090286 km/s Duration = 4.5 years No. of Z-X plane crossings: 34. 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, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper 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
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
Questions ?
15th AAS/AIAA Space Flight Mechanics Meeting, C15th AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain, Coloradoopper Mountain, Colorado
Thank you !!
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