ARO 309 Astronautics and Spacecraft Design Winter 2014

ARO 309 - Astronautics and Spacecraft Design Winter 2014 Try Lam Cal. Poly Pomona Aerospace Engineering

Introductions Class Materials at http: //www. trylam. com/2014 w_aro 309/ • 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 ME 215 (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)

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

What are we studying?

What are we studying?

Earth Orbiters

Pork Chop Plot

High Thrust Interplanetary Transfer

Low-Thrust Interplanetary Transfer

Low-Thrust Europa End Game

Low-Thrust Europa End Game

Low-Thrust Europa End Game

Orbit Stability Stable for > 100 days Enceladus Orbit

Juno

Other Missions

Other Missions

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

Equations of Motion

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

Conic Equation From 2 -body equation to conic equation

Angular Momentum Other Useful Equations

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

Conics

Circular Orbits

Elliptical Orbits

Elliptical Orbits

Elliptical Orbits

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

Hyperbolic Orbits

Hyperbolic Orbits Hyperbolic excess speed

Properties of Conics 0<e<1

Conic Properties

Vis-Viva Equation Vis-viva equation Mean Motion

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

Perifocal Frame FROM THEN

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

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 vr 0 (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

Lagrange Coefficients • Example (from book)

Lagrange Coefficients • Example (from book)

Lagrange Coefficients • Example (from book)

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

CR 3 BP • Circular Restricted Three Body Problem (CR 3 BP)

CR 3 BP Kinematics (LHS):

CR 3 BP Kinematics (RHS):

CR 3 BP Lyapunov Orbit CR 3 BP Plots are in the rotating frame Tadpole Orbit DRO Horseshoe Orbit

CR 3 BP: Equilibrium Points Equilibrium points or Libration points or Lagrange points L 4 L 3 L 1 L 2 Jacobi Constant L 5