ASTR310 – Course Information

Under Construction

WARNING: This page is still under construction. Even though I did not put in false information deliberately, some things here are subject to change. I will add more material and clarify some points as they become definite. Feel free to ask, if in doubt. At this point I only copy-pasted a previous syllabus and edited a few parts.

Some Questions with Answers

Can we change the scheduled time and day? No. I have other responsibilities so there are very few possible slots. In any case, it takes a very big effort to make a change, and in fact it might be impossible to find a time that works for me and vast majority is happy with. We can attempt at the first meeting but it probably will not work.

Will this be an online course? No. I will provide some online material, but it is mostly face-to-face.

Do I need to attend the course? Will you take attendance? Is it a problem (i.e., “sıkıntı olur mu?”) if I miss the classes? Yes. I expect you to attend the class. This is an elective course, if you cannot attend, take another course.

I did not take the prerequisites for this course, is there anything you can do? Yes. The consent of the department (i.e., me) is sufficient. If you do not satisfy the formal requirements, then you need to demonstrate that you know coding in some way.

Is my mathematical background sufficient for this course? This is very subjective, so it is hard to answer. You need to have basic familiarity with differential equations and linear algebra. Some of it you can learn on the way, but not all of it. The main audience for this course is Physics major juniors, if you are a sophomore, I suggest to wait a year.

Is my physics/astronomy background sufficient for this course? Probably, yes. I will not assume much beyond freshman level physics and almost no astronomy. The textbook assumes that you are familiar with a few subjects beyond that level, but I will provide resources for those topics.

Basic Course Information

Code, name, semester: This document contains information on ASTR310 (8640310), “Celestial Mechanics”, for the fall semester of 2025-26 academic year.

Time and place: The class will be held on Wednesdays 9:40-12:30, Room P350 (3rd floor). This may change, me may move to the “smart classroom” during the semester.

Webpage: The course has a page on ODTUClass, where I will be posting all essential information.

Prerequisites: The course has a number of prerequisites. It is mainly to assure that you have some familiarity with coding.

Content: The course will be an introduction to celestial mechanics. This is perhaps the oldest branch of mathematical physics going back to Newton, Laplace, Lagrange etc. The problems introduced will be old, but we will also have some modern solutions using computers. Analytical and numerical approaches can complement each other, so we will deal with both.

Textbook and Additional Resources

We will be using

Richard Fitzpatrick’s Introduction to Celestial Mechanics (Cambridge University Press, 2nd edition 2012, ISBN: 1107023815) and
John M. A. Danby’s Fundamentals of Celestial Mechanics (Willmann-Bell, 2nd Revised & Enlarged Edition 1988, ISBN: 0943396204) as our main textbooks. In addition, we will refer to
Moving Planets Around, Javier Roa, Adrian S. Hamers, Maxwell X. Cai and Nathan W. C. Leigh; MIT Press, 2020, 9780262539340.
Dynamics of Planetary Systems, Scott Tremaine; Princeton, 2023, 9780691207124.
Solar System Dynamics, Carl D. Murray, Stanley F. Dermott; Cambridge University Press, 2000, 9781139174817.

There are also useful videos on YouTube on various topics. I will post them here, as I encounter them.

Course Course Coverage and Objectives

The course will cover the following topics, roughly 1 week for each. This is a lot to cover, so in some cases, the coverage will be very brief. This is the first time I am attempting something this ambitious, I may adapt during the semester.

Introduction to Newtonian mechanics and universal gravitation. Derivation of the equations of motion for two-body systems.
The Kepler problem: general properties and solutions. Classification of orbits (elliptic, parabolic, hyperbolic) using conic sections. Simple numerical solutions.
Derivation and physical meaning of conserved quantities in gravitational two-body problem: energy, angular momentum, and the Runge-Lenz vector. The hodograph and orbital geometry.
Anomalies in orbital motion: true, eccentric, and mean anomalies. Kepler’s equation and its numerical solution via root finding and iteration methods.
Universal variables. Coordinate systems in celestial mechanics: inertial, barycentric, heliocentric, and Jacobi coordinates. Transformations between them
Orbital elements, Delaunay and Milankovitch variables, and their geometric interpretation. Impulses and associated changes.
Numerical integration of orbits: introduction to symplectic and Runge-Kutta methods. Hamiltonian and Hamilton’s equations of motion. Simple perturbations. Midterm examination and summary of two-body dynamics.
Restricted three-body problem: equations of motion, Lagrange points, stability and zero-velocity curves. Circular and elliptic restricted cases.
von Zeipel-Kozai-Lidov mechanism: physical origin, analytical treatment, and applications in hierarchical systems. Refined treatment via Hamiltonian formalism.
More applications of Hamiltonian formalism. Resonant and secular terms in Hamiltonian.
Mean motion resonances: resonance conditions, examples from the solar system, capture into resonance, and long-term orbital effects.
Chaotic motion in celestial mechanics: overview of chaos indicators, resonance overlap, and phase space structure.

Instructor

Mehmet Atakan Gürkan (I use Atakan), email: agurkan@metu.edu.tr, Office: P411 (Physics Building 4th floor), Office phone: 3294.

Email is the best way to reach me. Please do not contact me with WhatsApp, Twitter, Instagram etc. (all of these happened). When contacting me by email, please pay attention to these points. These may seem crude or harsh, but they all stemmed from my past experience.

Your email can be in English or Turkish.
Your message should begin with a greeting and end with your name. As greeting, you can use “Merhaba”, “Hi”, “Hocam”, “Atakan hocam”, “Dear Atakan hocam”, etc. You do not need to be very formal, but remember that you are not sending a WhatsApp message to a buddy.
Please observe proper grammar, punctuation and capitalization in your message.
Adding your student ID at the very end is useful if I need to check my records to answer your question.
Unless you are really replying to something I wrote in an email, do not use reply-to feature of your email client to send me a message. Use a fresh subject line appropriate to your message content. If I cannot track your message, I cannot answer it.
All other things being equal, the shorter the answer you require, the faster I will respond.
Please do not send me Microsoft Word, Excel etc. documents. I cannot open them, at least not easily, since I do not have MS Windows or MacOS. If you send me photos, make sure they are not too small, blurred etc.
The best time to email me is weekday mornings. If you email me on weekends or outside 9am-4pm, your message has a higher chance of being read but not replied to; since once it gets marked as read, it will not necessarily draw my attention in the morning.
If your message does not really require a response, I probably will not reply at all. However, if it does require a response, and I did not provide one in a few days, feel free to re-email me.

Lecture structure

This will be a face-to-face course, supported by a number of online tools. We will use ODTUClass (for many purposes), perusall (for some reading assignments, not firm on this yet; in any case, it will not be graded), GradeScope (for exams).

I expect you to attend the lectures and participate in the discussions, if you regularly fail to do so, you will receive an NA grade.

Office Hours

I will not be holding office hours for this class this semester. I will be available for your questions after the lecture, and alvo via email. If there is a big demand, I will consider setting up office hours.

Other Guidelines

Students and faculty each have responsibility for maintaining an appropriate learning environment. Students who fail to adhere to such behavioral standards may be subject to discipline. Faculty have the professional responsibility to treat all students with understanding, dignity and respect, to guide classroom discussion and to set reasonable limits on the manner in which they and their students express opinions. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, language, age, culture, religion, politics, sexual orientation, gender variance, and nationalities. Class rosters are provided to the instructor with the student’s legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. My preferred gender pronouns are he/him/his.

If you have specific physical, psychiatric, or learning disabilities and require accommodations, please contact me as soon as possible (preferably by the second week of the semester, but it is better late than never). You can also contact our Disability Support Office to see if you can benefit from their services http://engelsiz.metu.edu.tr/en/services.

Homework Assignments

There will be a homework assignment about every two weeks (I expect a total of 5-6 homeworks). You will have about two weeks to complete each. There will be no make-ups for these. Late submissions will be accepted but be subject to a penalty.

Using Gradescope

You will be scanning and uploading your homeworks to Gradescope. You are fully responsible for providing a legible copy of your homework, on time. One of the email addresses you have at Gradescope needs to be your email address in the course’s website at ODTUClass. If you use another address, even if it is an alias, you will not be able to access this course on Gradescope. You will register for this course automatically once I upload the class roster. I am waiting the end of add/drop period to do that.

Written exams

There will be two in-class written exams. The midterm exam will be after we finish topic 7 above, and the final exam will be at the end of the term (covering everything, but with more emphasis on later topics).

Grading

You will be graded on homework problems, a midterm exam, and a final exam. Discussion participation will be considered in borderline cases.

Homework assignments	20%
Midterm exam	40%
Final exam	40%
Discussion participation	xx

The letter grades will be assigned according to:

90 or above	AA
85-89	BA
80-84	BB
75-79	CB
70-74	CC
65-69	DC
60-64	DD
50-59	FD
49 or below	FF

I reserve the right to lower these limits, but I will not raise them. In particular, it will be possible for everyone to get an AA.

General Disclaimer

The above schedule, policies, procedures, and assignments in this course are subject to change in the event of extenuating circumstances, by mutual agreement, and/or to ensure better student learning.