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

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

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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

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

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


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


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


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


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


  • 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


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


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


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


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


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


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


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


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


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


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


    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


    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


    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


    Questions ?

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


    Thank you !!

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


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