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/ 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 17-1211 Section 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: 2 nd 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?

6. Earth Orbiters

7. Pork Chop Plot

8. High Thrust Interplanetary Transfer

9. Low-Thrust Interplanetary Transfer

10. Low-Thrust Europa End Game

13. Stable for > 100 days Orbit Stability Enceladus Orbit

14. Juno

15. Other Missions

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

19. Equations of Motion

20. 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

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 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 1.Find r 0 and v 0 from the given position and velocity vector 2.Find v r0 (last slide) 3.Find the constant angular momentum, h 4.Find r (last slide) 5.Find f, g, fdot, gdot 6.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 ALSO Since V r0 is < 0 we know that S/C is approaching periapsis (so 180°<θ<360°)

43. CR3BP Circular Restricted Three Body Problem (CR3BP)

44. CR3BP Kinematics (LHS):

45. CR3BP Kinematics (RHS):

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

47. CR3BP: Equilibrium Points Equilibrium points or Libration points or Lagrange points L1L2L3 L4 L5 Jacobi Constant