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

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


Outline Aims and Scope of this research Circular restricted three-body problem Halo orbit targeting methods using

STK/Astrogator Results Discussion Conclusion


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


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.


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


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.


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


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)



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)



Variation of Delta V and Propagation time for Halo Orbit Hopping Segment from SE L2 to SM L2



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



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



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



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



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


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


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


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


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


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


Questions ?


Thank you !!

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

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