16.346 | Fall 2008 | Graduate



Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Course Description

This course covers the fundamentals of astrodynamics, focusing on the two-body orbital initial-value and boundary-value problems with applications to space vehicle navigation and guidance for lunar and planetary missions, including both powered flight and midcourse maneuvers. Other topics include celestial mechanics, Kepler’s problem, Lambert’s problem, orbit determination, multi-body methods, mission planning, and recursive algorithms for space navigation. Selected applications from the Apollo, Space Shuttle, and Mars exploration programs are also discussed.


Battin, Richard. An Introduction to the Mathematics and Methods of Astrodynamics. Revised ed. Reston, VA: AIAA, 1999. ISBN: 9781563473425.

Special Sections in the Textbook


  • This article appeared in the New York Times on the eve of the Apollo 8 mission. It was reprinted in a special Look magazine issue titled Apollo 8: Voyage to the Moon.
  • Provides a layman’s description of navigating to the moon and how it would be accomplished on the Apollo 8 flight, which was the first time ever that astronauts left the earth for a voyage to another body.


  • Describes some milestones in astrodynamics.
  • Explains the notation used in the book.
  • Gives a list of general references which were used in preparing the textbook.
  • Note: Pay attention to the way in which problems in the textbook are stated. In particular, to what the student is expected to do.


  • Originally published as “Space Guidance Evolution: A Personal Narrative” by the author in the Journal of Guidance, Control, and Dynamics, March-April 1982.
  • It was invited as a history of Key Technologies paper as part of the AIAA’s Fiftieth Anniversary celebration.
  • Describes the work done at MIT from the early 1950s to the development of the Apollo guidance, navigation and control system.

Appendix B

  • Provides a review of vector and matrix algebra in the form of problems to be solved.


  • Originally appeared as Chapter 14 of the book Theory and Application of Kalman Filtering, a publication of the Advisory Group for Aerospace Research and Development of the North Atlantic Treaty Organization, published in February 1970 as AGARDograph 139 and edited by Cornelius T. Leondes. It was prepared at the request of the guidance and control panel of AGARD-NATO. The chapter was entitled “Application of Kalman Filtering Techniques to the Apollo Program” and was co-authored by Richard H. Battin and Gerald M. Levine.
  • Describes the implementation of the navigation software for the onboard guidance computer in the command module. Also provides the experience of the navigation system on Apollo 8, which demonstrated that astronauts could navigate in space without contact with the earth.


There are exercises and problems at the end of each lecture. Some will be collected and graded. The solutions are expected to be your own work.

Grades are determined from the problem sets and three exams. This course has no final exam.

Course Info

As Taught In
Fall 2008
Learning Resource Types
Lecture Notes
Problem Sets with Solutions