1. Interplanetary Travel

2. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel2 Interplanetary Travel  Planning for Interplanetary Travel  Planning a Trip through the Solar System  Interplanetary Coordinate Systems  Gravity-assist Trajectories  Helping Spacecraft Move Between Planets

3. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel SECTION 6.13 Planning a Trip Through the Solar System  Using the Hohmann Transfer, we saw how to transfer between two orbits around the same central body, such as Earth.  Interplanetary transfer just extends the Hohmann Transfer.  Central body is the Sun.  Departure and destination planets are vital.

4. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel4 Interplanetary Coordinate Systems  In the two-body problem described earlier in the course:  Only two bodies are acting—the spacecraft and the Earth.  Earth’s gravity is the only force acting on the spacecraft.  We used the geocentric-equatorial coordinate system.

5. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel5 Interplanetary Coordinate Systems (cont’d)  For interplanetary travel, as a spacecraft goes farther away, Earth’s pull becomes secondary to the Sun’s.  Because the Sun is the central body, we must develop a Sun-centered—or heliocentric—coordinate system.

6. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel6 Interplanetary Coordinate Systems (cont’d)  Heliocentric-ecliptic coordinate frame  Origin: the Sun  Basic plane: the ecliptic plane (Earth’s orbital plane around the Sun)  Main direction: fixed with respect to the universe “I” axis points to constellation Aires

7. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel7 Forces Acting on an Interplanetary Spacecraft  Four bodies are involved:  Sun  Departure Planet  Target Planet  Spacecraft

8. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel8 Four-body Problem  Analyzing the forces from all three central bodies on the spacecraft would amount to a “four-body” problem.  Too much to handle—the two-body problem was challenging enough.  What can we do to simplify?  Break into familiar, manageable pieces.  Consider as three two-body problems.

9. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel9 Patched Conic Approximation  Separate four-body problem into three distinct two-body problems.  Deal with gravity between the spacecraft and each large body (Sun and two planets) separately. F Grav(Sun) F Grav(departure planet) F Grav(target planet)

10. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel10 Regions of the “Patched Conic”  Region 1: Heliocentric Transfer Orbit  Origin: Sun  Transfer: Earth to target planet

11. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel11 Regions of the “Patched Conic” (cont’d)  Region 2: Escape from Departure Planet  Origin: Departure planet  Transfer: Earth departure  Patched to region 1

12. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel12 Regions of the “Patched Conic” (cont’d)  Region 3: Arrival at Target Planet  Origin: Target planet  Transfer: Arrival at the target planet  Patched to region 1

13. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel13 Spheres of Influence  A body’s sphere of influence (SOI) is the surrounding volume in which its gravity dominates a spacecraft.  In theory, SOI is infinite.  In practice, as a spacecraft gets farther away, another body’s gravity dominates.

14. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel14 Spheres of Influence (cont’d)  The size of a planet’s SOI depends on:  The planet’s mass  How close the planet is to the Sun (Sun’s gravity overpowers that of closer planets).  Earth’s SOI  About 1,000,000 kilometers radius  If the Earth were a baseball, its SOI would extend 78 times its radius or 7.9 meters (26 feet).

15. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel15 Spheres of Influence Earth’s SOI in Perspective

16. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel16 Frame of Reference An Earth-bound Example  You’re driving along a straight section of highway at 45 m.p.h.  A friend is following in another car going 55 m.p.h.  A stationary observer on the side of the road sees the two cars moving at 45 m.p.h. and 55 m.p.h., respectively.  Your friend’s velocity with respect to you is only 10 m.p.h.

17. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel17 Frame of Reference An Earth-bound Example (cont’d) “V” = Velocity

18. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel18 Frame of Reference An Earth-Bound Example (cont’d)  Your friend throws a water balloon toward your car at 20 m.p.h. How fast is the balloon going?  What your friend sees (ignoring air drag): it’s moving ahead of his car at 20 m.p.h.  What the stationary observer sees: your friend’s car is going 55 m.p.h., and the balloon leaves his car going 75 m.p.h.  What you see: the balloon is moving toward you with a closing speed of 30 m.p.h.

19. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel19 Frame of Reference An Earth-Bound Example (cont’d) “V” = Velocity

20. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel20 Frame of Reference An Earth-bound Example (cont’d)  This example relates to the patched- conic approximation:  Problem 1: A stationary observer watches your friend throw a water balloon.  The observer sees your friend’s car going 55 m.p.h., your car going 45 m.p.h., and a balloon traveling from one car to the other at 75 m.p.h.  The reference frame is a stationary frame at the side of the road.

21. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel21 Frame of Reference An Earth-bound Example (cont’d)  This example relates to the patched- conic approximation:  Problem 2: The water balloon departs your friend’s car with a relative speed of 20 m.p.h.  The reference frame in this case is centered at your friend’s car.  This problem relates to the patched-conic’s Problem 2 (in region 2), where Earth is like your friend’s car, and the balloon is like the spacecraft.

22. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel22 Frame of Reference An Earth-bound Example (cont’d)  This example relates to the patched conic approximation:  Problem 3: water balloon lands in your car!  It catches up to your car at a relative speed of 30 m.p.h. The reference frame is centered at your car.  It’s like the patched-conic’s Problem 3 (in region 3), where the target planet is similar to your car and the balloon is still like the spacecraft.

23. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel SECTION 6.223 Gravity-assist Trajectories  Gravity-assist definition: using a planet’s gravitational field and orbital velocity to “sling shot” a spacecraft, changing its velocity (in magnitude and direction) with respect to the Sun. Spacecraft Passing Behind a Planet

24. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel24 Gravity-assist Trajectories (cont’d)  As a spacecraft enters a planet’s sphere of influence (SOI), it coasts on a hyperbolic trajectory around the planet.  Then, the planet pulls it in the direction of the planet’s motion, increasing (or decreasing) its velocity relative to the Sun. Spacecraft Passing in Front of a Planet

25. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel25 Gravity-assist Trajectories (cont’d)

26. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel26 Summary  Planning for Interplanetary Travel  Planning a Trip through the Solar System  Interplanetary Coordinate Systems  Gravity-assist Trajectories  Helping Spacecraft Move Between Planets

27. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel27 Next  We’ve practiced describing orbits, orbital maneuvers, and interplanetary travel. Next time, we’ll cover ballistic missiles and launch windows and time.