675.734.8VL - Fundamentals of Celestial and Orbital Mechanics

Course Structure

Weekly modules will be released at 12am Friday morning ET to allow students the weekend to preview content prior to the virtual live course meeting on Monday evenings. Please refer to individual assignments in Canvas for details on submission and due dates.

The course materials are divided into modules which can be accessed by clicking Modules on the Canvas course menu. A module will have several sections including the learning path, lecture content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting.

The lecture content presented during class is available on Canvas pages to allow students to use a variety of accessibility tools built into the Canvas learning management system. Information on accessibility tools is available on the Canvas at JHU webpage Accessibility Resources for Students.

Course Topics

Module Topics

Module 1 - Course Introduction & Math Review
Module 2 - Newtonian Mechanics
Module 3 - Newtonian Gravity, Part 1
Module 4 - Newtonian Gravity, Part 2
Module 5 - Motion in a Central Force Field & Kepler Orbits, Part 1
Module 6 - Motion in a Central Force Field & Kepler Orbits, Part 2
Module 7 - Orbital and Interplanetary Maneuvers
Module 8 - Midterm Exam Discussion
Module 9 - Non-Inertial Reference Frames
Module 10 - Lagrangian Formalism
Module 11 - Rigid Body Rotation, Part 1
Module 12 - Rigid Body Rotation, Part 2 (Course Project Due)
Module 13 - Spherical Harmonic Representation of the Earth & Introduction to the Three Body Problem (Final Exam Due)
Module 14 - Course Project Peer Feedback & Final Exam Solutions

Course Goals

Equip students with the skills to analyze and model the motion of celestial bodies, including planetary orbits and satellite trajectories, using gravitational laws and principles of orbital mechanics. Provide students with the ability to derive and interpret the six orbital parameters of orbiting bodies, leveraging Kepler’s laws and gravitational mechanics to understand orbital dynamics over time. Enable students to apply concepts of rigid body rotation, precession, and nutation to model the Earth’s rotation, and understand the dynamics of satellite motion, particularly in proximity to Lagrange points in multi-body systems.

Course Learning Outcomes (CLOs)

• Analyze the motion of the planets around the sun and the motion of satellites around celestial bodies, such as Earth, using mathematical and physical principles of gravity.
• Derive the six orbital parameters of orbiting bodies as a function of time using gravitational principles and their relationship to Kepler’s equations of motion.
• Apply the knowledge of fixed body rotation to model the Earth's rotational motion including rotation, precession, and nutation.
• Model satellite motion around the Lagrange points that are derived from a small object such as a satellite orbiting in the vicinity of 2 large bodies, i.e. the Earth and the Moon.

Textbooks

Fitzpatrick, R. (2012). An introduction to celestial mechanics. Cambridge University Press.

Required Software

There are no specific software tools required for the course. Students have access to the Microsoft Office suite of tools through MyJH.

Technical Skills and Digital Information Literacy Skills Expected

This course requires proficiency in digital information literacy and technical skills. Students should be comfortable using Microsoft Office applications, particularly Word, PowerPoint, and introductory-level Excel.

Student Coursework Requirements

Assignment Weighting

• Problem Sets: 40%
• Midterm Exam: 20%
• Final Exam: 20%
• Course Project: 20%

Problem Sets
Problem Sets will generally be assigned weekly and will comprise 40% of the final grade. The lowest Problem Set grade of the semester will be dropped.

Problem sets consist of several assigned problems of various difficulty. Problem Sets submitted late may receive feedback, however, these will receive a score of zero since we will review the homework solutions at the beginning of class. Partial credit will be given for 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.

I will ask one or two students 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 principles discussed in class, and not on getting the exact correct answer.

Midterm and Final Exams
The midterm and final exam will each comprise 20% of the final grade.

These exams will be designed to test mastery of 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.

Course Project
The course project will account for the remaining 20% of the grade.  

For this project students will research a celestial mechanics topic of their choice, using papers published in technical journals. The topic can be one covered in class or another related topic in celestial mechanics. 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. See Canvas course site for full details, deliverables, and due dates.

Grading Policy

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

Course Policies

Students should attend each class and actively participate whenever possible. The class will be recorded for those that can't be there or for review at a later time.

Students are expected to do their own work. The use of on-line services such as Chegg for homework assignments is strictly prohibited and will be reported as academic misconduct.  

You may consult with your fellow students and discuss your general ideas at a high level on the Problem Sets and Course Project only, not exams, but your submitted assignments should be your own product.

All work should be legible, neat & well-organized.  Please do not make it difficult for the grader to follow your solution; your thought process and approach should be 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 because we will go over solutions during class.

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.