615.655.8VL - Orbital and Celestial Mechanics

Expanded Course Description

This introductory course will focus on the study of orbital and celestial mechanics, using many of the methods and formalisms that are covered in a traditional graduate level mechanics course.  We will look primarily at closed form and approximation methods (as opposed to numerical solutions) in a wide variety of problems in orbital and celestial mechanics.  Space engineering and applied physics students who take this class will be well-versed in fundamentals that can then be leveraged in more advanced future space applications. Topics will include Newtonian Mechanics, Newtonian Gravitation, Central Force Orbits (with a focus on Keplerian Orbits), Orbital & Interplanetary Maneuvers, Non-inertial Reference Frames, the Lagrangian Formalism, Rigid Body Rotation, and the Three Body Problem.

Discussions will include the historical figures in physics who contributed significantly to the topics discussed.  Before taking this class students should be proficient in multivariate integral and differential calculus, linear algebra, vector algebra, vector calculus, and special functions.

Course Structure

The course will be divided into 9 different modules, each of which will have a section on the CANVAS page.  Each module will include instructor notes and the slides presented in class.  Most modules will also have a homework assignment.  Class recordings will also be published in each module.

Course Topics

• Class introduction and Math Review
• Newtonian Mechanics
• Newtonian Gravity
• Motion in a Central Force Field and Kepler Orbits
• Orbital and Interplanetary Maneuvers
• Non-inertial Reference Frames
• Lagrangian Formalism
• Rigid Body Rotation
• Three-Body Problem

Course Goals

• To appreciate that, despite the complexity and vastness of the universe, celestial motions are largely stable, predictable, and tractable.
• To develop systematic analytical approaches and confidence in solving complex mechanics problems.
• To prepare the students to study more advanced celestial and orbital mechanics problems.
• To better understand the roles historical scientists played in developing today’s understanding of celestial mechanics.

Textbooks

• An Introduction to Celestial Mechanics, Richard Fitzpatrick (2012). The course’s required text book with good content and lots of problems with varying difficulty.  I recommend that you purchase the hardcopy of this book (because you can read it anywhere, make notes, etc.) but Dr. Fitzpatrick does have an html version of his book available on his website at: https://farside.ph.utexas.edu/teaching/celestial/Celestial/Celestial.html.  Note that some of his links are broken and there are differences between some of the figure/equation numbering compared to the hardcopy, so user beware.  
• Foundations of Celestial Mechanics, Elena Bannikova and Massimo Capaccioli (2022). This is a new, graduate level treatment of celestial mechanics.  It is a very formal mathematical treatment of celestial mechanics.  The treatment is challenging but thorough and makes some nice connections with other physics topics.  The English translation is a bit rough but the historical overview and anecdotes on Celestial Mechanics are very good.
• Orbital Mechanics for Engineering Students, Howard Curtis (2005). An applied approach to orbital mechanics.  Includes good content on orbital and interplanetary maneuvers.  A free PDF of this book is available at www.academia.edu and elsewhere on the web (I make no guarantees about any of the sites.)
• Analytical Mechanics (4th Edition), Grant Fowles (1986). Classic book in Advanced Mechanics for undergraduates.  My copy is very worn.  I believe that this book eventually reached a 7th edition that may now be out of print.
• Classical Mechanics (3rd Edition), Goldstein, Poole, and Safko (2002). Another classic Advanced Mechanics book for graduate students.  The treatment of some topics in this text is quite advanced.
• Theoretical Mechanics of Particles and Continua, Fetter and Walecka (1980). A very Advanced Mechanics book for graduates.  Written very tersely.  Contains some very difficult problems.  This was my graduate mechanics text and I hated it.

An Introduction to Celestial Mechanics by Fitzpatrick will be the course textbook.  Other, more advanced treatments from the other sources will supplement this text but you do not need access to those texts.

Student Coursework Requirements

Homework will be assigned weekly and will comprise 30% of the final grade.  The lowest homework grade of the semester will be dropped.  Homework will generally consist of several assigned problems of various difficulty.  Homework must be submitted into Canvas before the start of the next class and late homework will be corrected but will receive a score of zero (since we will review the homework solutions at the beginning of class).    Partial credit will be given for homework problems.  As such your problem-solving approaches and how you apply what you have learned is more important than getting the exact final answer correct (see Expectations below and Tips for Solving Physics Problems in Module 1.)

I will ask one or two student each week to discuss one of their homework solutions with the rest of the class.    The emphasis of these discussions will be on the approach to solving the problem, and the correct application of the physics principles discussed in class, and not on getting the exact correct answer.

The mid-term and final exam will each comprise 30% of the final grade.  These exams will be designed to test mastery of all the topics presented in the class. They will be take-home exams, will be open-book and open-notes (only, no other resources are permitted), and will consist of several problems with moderate-to-difficult complexity. No collaboration is allowed on these exams.

The class project will account for the remaining 10% of the grade.  For this project students will research a celestial mechanics topic of their choice, using papers published in technical journals.  The project will consist of several milestones, to ensure that consistent progress is being made throughout the semester, and a final presentation with slides.  The topic can be one covered in class or another related topic in celestial mechanics (ideally each student will have a different topic).  The presentation will be approximately 10 minutes in length and cover new or interesting facets of the topic not covered previously, or a previously covered topic covered in more detail.  The emphasis should be on new or recent developments in the field.  All milestones should be uploaded into CANVAS. 

Grading Policy

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

Course Policies

Students are expected to attend each class and participate actively. Students are expected to do their own work.  You may certainly consult with your fellow students and discuss your general ideas at a high level (on homework only, not exams) but your submitted assignments should be your own product.  All work should be well-written, legible, neat & well-organized, and free of spelling and grammatical errors.  Please do not make it difficult for the grader to follow your solution; your thought process and approach should be clearly clear to the grader.  Work should be submitted on-time unless other arrangements have been previously discussed with the instructor.  Generally, late-submitted work will not be eligible for full credit.  

The use of on-line services such as Chegg for homework assignments is strictly prohibited and will be reported as academic misconduct.   

There are a variety of other problem solutions posted on line, such as those in published academic papers and on class websites for Physics classes at other universities.   Strictly speaking, the use of these references is not considered academic misconduct, although it is in a gray area that requires the following clarification.  You may use these, with the following guidance, provided that you reference the resource and do not present it as your own work.  Note however: 

• Sometimes posted solutions have errors in them
• The use of these resources is not the best way to develop good problem-solving skills
• It takes time to search the web to find them, time better spent working on the problems yourself
• They will not help you on exams (where I use original problems)

Also, please:

• Try to resist the urge to search for and use these external sources
• If you must, do not copy the solutions and present them as your own, which is academic misconduct and will be reported as such. It is recommended that you use the bare minimum content necessary from these sources, perhaps just to get started or get over a step that you are having trouble with
• If you use any portion of an external reference, you MUST acknowledge it in your solution and attach the reference

If you use an external reference, I will deduct a number of points proportional to the amount of content that you utilized from that reference.  And once again, to be clearly clear, if you use an external reference and present any of its content as your own work without providing the reference it will be considered to be an academic violation and reported as such.

A final word on symbolic manipulators.  As an old-skool guy I’m not a big fan of symbolic manipulator programs as an aide in homework.  All the homework and exam problems in this class have closed form or approximate closed form solutions that can be solved without symbolic manipulators.  As such they should not be used as an aide in homework.  However, you may use them to check the final answers of your homework, provided that you acknowledge that you did so.  You may also use symbolic manipulators for any matrix operations, including the determination of eigenvalues and eigenvectors. 

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.