1. Asteroid Tour Trajectory D. Hyland Nov 21, 2012

2. Voyage Concepts We sketch potential trajectories for our deep space vessel: –Initial voyage from LEO to Sun-Earth L2 –Repetitive grand tour of Near Earth Asteroids (mining operations) Calculations are based on the patched Planar Circular Restricted Three Body Problem (PCR3BP) method. Additional guidance from: –Past missions (e.g. Genesis) –Published mission concepts (Earth-Moon L1 to Sun-Earth L2, Jupiter orbiter – see Koon, Lo, Marsden and Ross) –Astronomical observations (e.g. Jupiter comet Oterma)

3. Planar Circular Restricted Three Body Problem (PCR3BP)

4. The Jacobi Integral: Five Cases of Possible Motions

5. Initial Deployment: Spiral out to E-M L1  Start in 300 km circular orbit about Earth  Spiral out to a coasting trajectory to the E-M L1 “throat”.  Meld into the Lyapunov orbit of L1 Station and refuel

6. From E-M L1 to S-E L2: Start of the First grand Tour Moon L1 Lyapunov Orbit Orbit of the Moon Earth-Moon FrameSun-Earth Frame L2L2 L2L2 L 1 Sun E-L1 to S-L2:  V=12m/s, 50 days 122,720 km  After refueling, leave L1 on the outward invariant manifold.  Swing by the Moon and exit the E-M L2 throat in time to meld with a heteroclinic orbit leading to the Sun-Earth L2  Take one turn around the Lyapunov orbit and enter the external domain of the Sun-Earth system

7. Sun-Earth System Asteroid Mining Tours: Exterior Realm L1L1 1.Drop off cargo at L1 Station. Leave L1 Lyapunov orbit. Follow heteroclinic orbit to L2 (pink line, left to right) (drop off cargo at Earth-Moon system) 2.Meld into L2 Lyapunov orbit, follow for ¾ of a period, then follow the unstabile manifold (green line, heading down) Sun-Earth Frame L2L2 3.0 million km

8. Through S-E L2 to the Grand Tour of the Exterior Realm Sun 3-2 resonance Apophis 3. Follow the homoclinic, exterior domain orbit (green path issuing from L2 and going clockwise) 4. Mine Atens and Apollos on the way (3 years) Then: see next slide 1 AU

9. Sun-Earth System Heteroclinic Transfer Between Exterior and Interior Realms L1L1 5.Follow homoclinic exterior domain orbit to L2 on the stable manifold (green line, pointing down, left). Refurbish and repair at L2 Station 6.Meld into L2 Lyapunov orbit, follow for ½ of a period, then follow the heteroclinic orbit to L1 (pink line, right to left). 7.Deliver cargo to Earth-Moon system. Meld into L1 Lyapunov orbit, Exchange crew and refuel at L1 Station. 8.Follow Lyapunov orbit for one period, then follow the homoclinic interior domain orbit (blue line heading to the left) L2L2 3.0 million km

10. Through S-E L1 to the Grand Tour of the Interior Realm Sun 3-2 resonance Apophis 9. Follow the homoclinic, interior domain orbit (red path issuing from L1 and going counter clockwise) 10. Mine Atens and Amors on the way (two years) 11. Then follow the stable manifold to L1 (blue line in previous slide, heading to the right). 12. Refuel and exchange crew at L1 station. Go to step 1 and repeat. Forbidden zone