ARO309 - Astronautics and Spacecraft Design

1. ARO309 - Astronautics and Spacecraft Design Winter 2014 Try Lam CalPoly Pomona Aerospace Engineering

2. Introductions Class Materials at http://www.trylam.com/2014w_aro309/ • Course: ARO 309: Astronautics and Spacecraft Design (3 units) • Description: Space mission and trajectory design. Kepler’s laws. Orbits, hyperbolic escape trajectories, interplanetary transfers, gravity assists. Special orbits including geostationary, Molniya, sunsynchronous. [Kepler's equation, orbit determination, attitude dynamics and control.] • Prerequisite: C or better in ME215 (dynamics) • Section 01: 5:30 PM – 6:45 PM MW (15900) Room 17-1211Section 02: 7:00 PM – 8:15 PM MW (15901) Room 17-1211 • Holidays: 1/20 • Text Book:  H. Curtis, Orbital Mechanics for Engineering Students, Butterworth-Heinemann (preference: 2nd Edition) • Grades: 10% Homework, 25% Midterm, 25% Final, 40% Quizzes (4 x 10% each)

3. Introductions • Things you should know (or willing to learn) to be successful in this class • Basic Math • Dynamics • Basic programing/scripting

4. What are we studying?

5. What are we studying?

6. Earth Orbiters

7. Pork Chop Plot

8. High Thrust Interplanetary Transfer

9. Low-Thrust Interplanetary Transfer

10. Low-Thrust Europa End Game

11. Low-Thrust Europa End Game

12. Low-Thrust Europa End Game

13. Orbit Stability Stable for > 100 days Enceladus Orbit

14. Juno

15. Other Missions

16. Other Missions

18. Lecture 01 and 02: Two-Body Dynamics: Conics Chapter 2

19. Equations of Motion

20. Equations of Motion • Fundamental Equations of Motion for 2-Body Motion

21. Conic Equation From 2-body equation to conic equation

22. Angular Momentum Other Useful Equations

23. Energy NOTE: ε = 0 (parabolic), ε > 0 (escape), ε < 0 (capture: elliptical and circular)

24. Conics

25. Circular Orbits

26. Elliptical Orbits

27. Elliptical Orbits

28. Elliptical Orbits

29. Parabolic Orbits • Parabolic orbits are borderline case between an open hyperbolic and a closed elliptical orbit NOTE: as v  180°, then r  ∞

30. Hyperbolic Orbits

31. Hyperbolic Orbits Hyperbolic excess speed

32. Properties of Conics 0 < e < 1

33. Conic Properties

34. Vis-Viva Equation Vis-viva equation Mean Motion

35. Perifocal Frame “natural frame” for an orbit centered at the focus with x-axis to periapsis and z-axis toward the angular momentum vector

36. Perifocal Frame FROM THEN

37. Lagrange Coefficients • Future estimated state as a function of current state Solving unit vector based on initial conditions and Where

38. Lagrange Coefficients • Steps finding state at a future Δθ using Lagrange Coefficients • Find r0 and v0 from the given position and velocity vector • Find vr0 (last slide) • Find the constant angular momentum, h • Find r (last slide) • Find f, g, fdot, gdot • Find r and v

39. Lagrange Coefficients • Example (from book)

40. Lagrange Coefficients • Example (from book)

41. Lagrange Coefficients • Example (from book)

42. Lagrange Coefficients • Example (from book) Since Vr0 is < 0 we know that S/C is approaching periapsis (so 180°<θ<360°) ALSO

43. CR3BP • Circular Restricted Three Body Problem (CR3BP)

44. CR3BP Kinematics (LHS):

45. CR3BP Kinematics (RHS):

46. CR3BP Lyapunov Orbit CR3BP Plots are in the rotating frame DRO Horseshoe Orbit Tadpole Orbit

47. L4 L3 L1 L2 L5 CR3BP: Equilibrium Points Equilibrium points or Libration points or Lagrange points Jacobi Constant