ASTE 280 Spring 2024: Foundations of Astronautical Engineering
3 units
Lectures Mondays and Wednesdays 3:30-4:50 PM, SOS B2
Instructor:
Dan Erwin, OHE 500W, 213-740-5358,
erwin@usc.edu.
Office Hours: Tuesdays 12-3 PM; Wednesdays 10:30 AM-12:30 PM
TA:
TBA
Catalogue Description
Coordinate systems and transformations. Spherical trigonometry. Orientation angles. Spacecraft orbits and orbital maneuvers. Introduction to rocket propulsion, spacecraft attitude dynamics and control and space environment.
Course Description
This course is a broad introduction to basic topics in astronautics. It has four major topics: Mathematics of coordinate systems and transformations; spacecraft orbits and orbital maneuvers; rocket engines and rocket vehicles; rigid body rotation and spacecraft attitude dynamics. A brief introduction to the space environment is given at the end; while ASTE students will have more material on this in later courses, this is the only space course required for AE and many AE students will not see space environment in any other course. This course is required for the B.S. degrees in Aerospace Engineering and Astronautical Engineering, and is typically taken in the second year.
Learning Objectives
After taking this course, the student will:
- Understand the most common coordinate systems used in astronautics: geocentric vs. heliocentric, inertial vs. body-fixed, and when each one is appropriate.
- Transform between these systems using rotational matrices and quaternions.
- Understand basics and applications of spherical trigonometry.
- Understand Keplerian orbits and orbital perturbations. Design spacecraft trajectories such as Hohmann transfers, plane changes, and interplanetary escape and capture.
- Understand the fundamentals of rocket propulsion, and know the basic characteristics of the different kinds of rockets: solid, liquid, electric. Understand rocket vehicle dynamics: Earth launch, trajectories in the atmosphere, delta-V for orbital maneuvers.
- Understand the basics of rigid body rotations: Euler's equations; orientation angles and quaternions.
Prerequisites: MATH 226, PHYS 152L
Recommended preparation: Matlab programming
Required Texts
Course notes, to be published on the class website
Optional Materials
V. L. Pisacane, Fundamentals of Space Systems, 2nd edition. ISBN 978-0195162059
Description and Assessment of Assignments:
- Homework: Written homework assigned weekly and due at midnight on Wednesdays. Homeworks will be graded and returned, generally in one week. Homework solutions will be posted on the class website.
- Midterms: Two midterm exams will be given, on Wednesday of Week 6 and Week 12 respectively. The exams will be in the regular classroom, during the regular class time.
- Final Exam: The final exam will be two hours, in the regular classroom, Friday May 3, 2-4 PM.
Grading Breakdown
Homework, 15%
1st Midterm Exam, 25%
2nd Midterm Exam, 25%
Final Exam, 35%
|
Week
|
Date
|
Topics
|
Notes |
|
1
|
01/08 & 01/10
|
Class organization. Introduction to spacecraft. Length scales: Solar system and astronomical unit. Types of coordinate systems. Spherical trigonometry laws and applications.
|
Ch. 1 |
|
2
|
01/15 & 01/17
|
Rotations and rotation matrices. Spherical polar coordinates. Proofs and applications of spherical trigonometry laws.
|
Ch. 1 |
|
3
|
01/22 & 01/24
|
ECI to ECEF transformation. Azimuth and elevation of planets in sky. Universal time and Julian date. Solar and sidereal time. Gravitational parameter. Solar system data. Circular orbits.
|
Ch. 1, 2 |
|
4
|
01/29 & 01/31
|
Two-body motion: angular momentum; energy and velocity on orbit. Conic sections. Time since periapsis for elliptical orbits. Classical orbital elements. Proof of Kepler's laws. Flight path angle. Geostationary and Molniya orbits. Orbital perturbations: Regression of nodes.
|
Ch. 2 |
|
5
|
02/05 & 02/07
|
Rotation of apsides. Perturbations due to Sun and Moon. Ground track.
|
Ch. 2 |
|
6
|
02/12 & 02/14
|
Review of last year’s first midterm exam. FIRST MIDTERM EXAM.
|
|
|
7
|
02/19 & 02/21
|
Hyperbolic orbits. Oberth maneuver. Determining orbital elements from position and velocity. Spacecraft field of view. Orbital maneuvers. Instantaneous Delta-V.
|
Ch. 2, 3 |
|
8
|
02/26 & 02/28
|
Hohmann transfers. Plane changes. Bielliptic transfers. Fast transfers. Gravity assist. Interplanetary trajectories. Synodic period. Launch windows.
|
Ch. 3 |
|
9
|
03/04 & 03/06
|
Intro to rocket vehicles. Rocket equation. Momentum and pressure thrust. Specific impulse. Liquid-fueled rockets. Thrust coefficient and characteristic velocity.
|
Ch. 4 |
|
|
|
SPRING BREAK
|
|
|
10
|
03/18 & 03/20
|
Optimal nozzle exit area. Solid-fueled rocket motors. Performance of rocket vehicles. Atmospheric drag.
|
Ch. 4 |
|
11
|
03/25 & 03/27
|
Stability of solid rocket combustion. Gravity turn.
|
|
|
12
|
04/01 & 04/03
|
Review. SECOND MIDTERM EXAM.
|
|
|
13
|
04/08 & 04/10
|
Staging. Launch sites. Attitude and orbital control system. Moment of inertia. Parallel axis theorem. Angular velocity and angular momentum. Moment of inertia tensor. Principal axes. Transformation of time derivatives between rotating and inertial frames. Euler's equations. Stability of spin about a principal axis.
|
Ch. 4 |
|
14
|
04/15 & 04/17
|
Rate of change of Euler angles and quaternion. Full equations of motion for rigid body rotation. External torques on spacecraft. Attitude sensing. Gravity-gradient stabilization. Attitude control: Thrusters and reaction wheels. Angular momentum dumping. Gyroscopic forces. Control-moment and rate gyros. Magnetic torque rods.
|
Ch. 4 |
|
15
|
04/22 & 04/24
|
Space environment. Review.
|
Ch. 6 |
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