Download presentation

Presentation is loading. Please wait.

Published byDesiree Wait Modified over 3 years ago

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

Similar presentations

OK

Spacecraft Trajectories You Can Get There from Here! John F Santarius Lecture 9 Resources from Space NEEP 533/ Geology 533 / Astronomy 533 / EMA 601 University.

Spacecraft Trajectories You Can Get There from Here! John F Santarius Lecture 9 Resources from Space NEEP 533/ Geology 533 / Astronomy 533 / EMA 601 University.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google