Asteroid Tour Trajectory

D. Hyland

Nov 21, 2012

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)

Planar Circular Restricted Three Body Problem (PCR3BP)

The Jacobi Integral: Five Cases of Possible Motions

Initial Deployment: Spiral out to E-M L1

3385 10 km

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

From E-M L1 to S-E L2: Start of the First grand Tour

Moon

L1 Lyapunov Orbit

Orbit of the Moon

Earth-Moon Frame Sun-Earth Frame

L2

L2

L1

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

Sun-Earth System

Asteroid Mining Tours: Exterior Realm

L1

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

L2

3.0 million km

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

Sun-Earth System

Heteroclinic Transfer Between Exterior and Interior Realms

L1

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)

L2

3.0 million km

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