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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 â€™97- Jul â€™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.)
- âˆ†V: 3.170804 km/s ( approx.)

- Transfer from Sun Earth L2 to Sun Mars L2 Lagrangian point
- Duration: 955 days (approx.)
- âˆ†V :1.0318345 km/s

- Halo Orbit Insertion at Sun Mars L2 Lagrangian point
- Duration: 321 days (approx.)
- âˆ†V: -0.279681 km/s

- Station Keeping at Sun Mars L2 Lagrangian point
- Duration: 378 days (approx.)
- âˆ†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.)
- âˆ†V: 2.08933911 km/s

- Duration: 411 days (approx.)
- âˆ†V: -0.42396 km/s

- Duration: 1642.5 days (approx.)
- âˆ†V: 0.40629 km/s

- Duration: 4881 days (approx.)
- âˆ†V: 1.3077 km/s

- Duration: 2244 days (approx.)
- âˆ†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 âˆ†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