## AEM 4301: Orbital Mechanics

### Catalog Description

**Syllabus**

**AEM 4301**

Orbital Mechanics

3 Credits

**Catalog Description**:

The two-body problem. Earth-satellite operations, rocket performance, reentry dynamics, space environments, interplanetary trajectories. Numerical simulations. Design project.

**Course Web Address**:

http://www.aem.umn.edu/courses/aem4301/

**Prerequisites by Topic**:

1. Dynamics (AEM 2012)

2. Linear Algebra and Differential Equations (Math 2243)

**Text**:

*Orbital Mechanics for Engineering Students*, Howard C.
Curtis, Elsevier, 2005

**Format of Course**:

3 hours of lecture per week

**Computer Usage**:

MatLab and STK (Systems Toolkit from AGI)

**Course Objectives**:

Develop an understanding of orbital mechanics. Obtain a detailed knowledge of the two-body problem and its solutions with applications to geocentric orbits and interplanetary transfers. Understand the concept of impulsive thrusting and its use in orbital transfers including plane changes. Obtain a knowledge of time-of-flight relations on two-body trajectories, using both classical and universal variables. Understand and be able to apply Lambert’s theorem for the time-of-flight on the parabola and ellipse. Understand the numerical solution of Gauss’ problem using universal variables and MatLab. Understand the concept of “patched conics” and its use in the design of interplanetary transfer trajectories. Introduction to STK, a software package for orbital analysis and design.

**Course Outcomes**:

Students who successfully complete the course will demonstrate the following outcomes

by tests, homework, and written reports

- Ability to apply knowledge of math., science, and engineering. This will be accomplished by applying these disciplines to solve problems regarding space flight.
- An ability to identify, formulate, and solve engineering problems. This will be accomplished through problems from orbital mechanics such as finding characteristics of desired transfer trajectories and the corresponding specific impulses.
- An ability to design a system, component or process to meet desired needs. This will be accomplished through problems requiring the design of interplanetary trajectories.
- An ability to use the techniques, skills, modern engineering tools necessary for engineering practice. This will be accomplished by using MatLab for the numerical solution of Lambert’s problem and Gauss’ problem.

**Relationship of course to program objectives**:

This course develops topics in orbital mechanics, space flight and control of space vehicles. It provides a broad background in aerospace engineering, a background in orbital mechanics, space flight and other space related topics. It introduces essential tools and problem solving techniques and helps produce graduates who can be successful in graduate level work.

**Relationship of course to program outcomes**:

This course provides the following outcomes:

1. Apply mathematics

2. System design

3. Identify engineering problems

4. Communication skills

5. Lifelong learning

6. Engineering tools

7. Orbital mechanics

8. Other space-related topics

__Direct Measures__

Outcome: System Design, Engineering Tools

*Performance Criteria*: Demonstrate
the ability to design basic space missions such as an orbital transfer using
Matlab or STK.

*Assessment Method*: Extended
homework problem

**Course Outline**:

Lecture |
Topic |

3 |
The two-body problem |

3 |
Kepler’s laws, equations of conic sections |

3 |
Geocentric orbits, canonical units |

3 |
Orbital elements, STK |

3 |
Orbital transfers |

3 |
Time of flight |

3 |
Lambert’s theorem |

3 |
Universal variables |

3 |
Numerical methods, MatLab |

3 |
Interplanetary transfers |

3 |
Planetary fly-by, gravity assist |

3 |
The intercept problem |

3 |
Fast transfers |

3 |
Atmospheric entry |

**Outcome Measurement**:

Accomplished through homework, periodic exams and a design project.

**Go-No-Goes:**

The go-no-goes for this course are fundamental questions on last hour exam which must all be answered correctly by the students in order for them to pass the course.

**Student Survey Questions:**

In this course I gained:

1. An ability to apply knowledge of math, science, and engineering.

2. An ability to design a system, component or process to meet desired needs.

3. An ability to identify, formulate, and solve engineering problems.

4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.

Please answer the following questions regarding the course:

5. The text book was clearly written and appropriate for the course.

6. The homework helped me to understand the concepts presented in the course.

7. The tests were appropriate in length and content.

8. The level of work required in this course was appropriate for the credit given.

In this course I acquired the following:

9. A knowledge of orbital mechanics.

10. A knowledge of other space related topics.

11. A knowledge of the two-body problem and the integrals of motion.

12. A knowledge of universal variables.

13. A knowledge of the design of geocentric and interplanetary transfer orbits.

14. A knowledge of numerical methods for orbit determination and their application using MatLab.

**Last modified**:

2012-4-25

** **

*Last Modified: 2008-03-10 at 09:45:28*
-- this is in
International Standard Date and Time Notation