ASTC25 Astrophysics of Planetary Systems (2024, in-person)
The page you are reading ( together with the syllabus and other subpages are the only official source of information on this course. It provides lecture notes, home assignments, prelim. results and other material. Check it regularly.
In addition to this page, Quercus will provide audiovisual recordings of lectures, and will be used for sending messages and/or reminders via email and for your submissions of assignment sets and our feedback on them.
We have lectures Thu 13:00-15:00. Tutorials come after lectures & a lunch break, 16:00-17:00. Between lectures & tutorial there is a hour, the 1st 1/2 hr of which is office hour. To answer all the remaining questions we likewise transfer to my office after the tutorial for 1/2 hr office "hour".


Dates given in syllabus take priority over any other documents, including the course web page (should there be a mistake in the web page):
Syllabus including topics & dates of lectures, assignments, and exams

Please check both this page and syllabus every week; they will keep being updated. In case some dates are in disagreement in different places on these pages, please notify the lecturer. Normally the syllabus takes precedence.
Urgent messages will be sent to you via Quercus, as well as comments on your submitted assignments. However Quercus does not provide updates. Only this page and the syllabus spell out all the rules & the conduct of this course. Please make a bookmark for this webpage.

General information

Welcome to an upper-undergraduate overview of planetary astrophysics at a level appropriate for science students. Topics include: Orbital mechanics from 2-Body problem to more complicated cases (tides, restricted 3-Body problem, etc.). Planets as a by-product of star formation. Protostellar/protoplanetary disks. Planetesimals. Protoplanet migration. Solar system. Giant planets, terrestrial planets, dwarf planets and minor bodies in the Solar System: astrophysical and other perspectives. Extrasolar planetary systems: types of exoplanets we find so far. Habitability, ETIs.

LEFT: The first known visitor from interstellar space known as 1I/2017 U1 (Oumuamua). 1I stands for 1st Interstellar. Discovered in 2017 by a military Pan-STARRS 1 telescope in Hawaii at a distance of 0.22 AU from Earth, the object came from the direction of the constellation Lyra, cruising through interstellar space at 26.33 km/s. Its classification as a small comet vs. asteroid ejected from another planetary system has changed over time: c,a,c,neither.
RIGHT: A visitor from Oort Cloud has been spotted in March 2022 by Californian astronomers. The Green Comet or C/2022 E3 (ZTF) flew closest to us on 1 Feb 2023, at a safe distance of 0.28 AU. Green light was due to a complex interaction of UV sunlight with C2 molecules it ejected (among others). This comet was initially classified as an asteroid, and may or may not become interstellar after this passage through the inner Solar System.

As indicated above, this course deals with the origin, structure and lives of planets, the latter both in our solar and the other (extrasolar) planetary systems. In fact, we know 100s more of the latter kind, although not so intimately. Starting from basic physical principles and utilizing mathematics as a language, we will build a basic understanding of how planets form, function, and evolve. We will confront the presented theories with assorted observational facts, including some of the newest discoveries. Yet we put emphasis not on the observational but the theoretical and conceptual astrophysical aspects of such current issues as: mechanisms of formation of the solar and extrasolar planetary systems, physics of dusty circumstellar disks etc. At the end of the course, we will consider basic astrobiology issues such as our chances to meet extraterrestrial civilizations.

Course and textbook

The planetary system science is developing quickly. Appropriate, all-encompassing, textbooks at the upper undergraduate level are very few and far between. Therefore I mostly teach from own notes. Implicitly (behind the scenes) I use a textbook I have published in 1995, which has no English language edition or an electronic form. Almost everything I want you to know, I put into lectures+recordings and lecture notes (in PDF form). What you learn in the lectures should partially prepare you for the written problems found in the homeworks (assignment sets 1-4) and the exams. I very strongly encourage attendance at lectures, taking your own notes, and asking questions during lectures - please feel free to interrupt me. If you don't participte in this way, you may find it difficult to undestand the lecture notes I provide.
I also mix in some material from a widely-accessible textbook.

"Fundamental Planetary Science: Physics, Chemistry and Habitability" by Jack J. Lissauer and Imke de Pater (2013, 2019). I will mention where to find the book in the tutorial.
Be careful not to confuse it with the book "Planetary Sciences" (by the same authors), which is a different, graduate-level, version of the book I mention in the section on other books.
You don't have to read the whole book. Several chapters might give you another angle on or another wording of issues than Lectures, but they are not required reading. Only Chapter 15 is obligatory, please read it.

There are some other books worth reading listed on a subpage. They are not obligatory but some you may find them interesting, and can be good choices for extra book reading (activity points, see next subsection).

Marking Scheme:

4 sets of home assignments: 32% (8% ea. set)
midterm: 20% (10% problems + 10% quiz)
final exam: 44% (22% problems + 22% test)
class/tutorial partic. & activity*: 4%
MAX. SCORE: 100%

Grading is standard: minimum percentage marks for letter grades (for orientation only, since grades are reported as percentages)
A+ 90%, A 85%, A- 80%, B+ 77%, B 73%, B- 70%, C+ 67%, C 63%, C- 60%, D+ 57%, D 53%, D- 50%, F 49% or less.

*)- the activity points are awarded for participation in lectures and tutorials, and asking questions. Full points will be awarded for coming to office hour and sharing the knowledge gained from reading an optional book, if the level of the book is appropriate, subject concerns planetary systems, and I find that you understood the book. Examples of appropriate books are linked in the previous section. Email me the author and title of a book that is not on the list of recommended books, or show it in person. It will need to be approved (scope, level).

Email and TA contact

Please mention ASTC25 in subject line, or your mail may get lost.
Lecturer: Pawel Artymowicz, email: pawel AT
TA (marking & email answering): Hamid Moezzi-Rafie (h.moezzi AT

If you want to make sure I get your mail promptly, please always verify that you send mail to the address above or alternatively to pawel.artymowicz AT, include ASTC25 in the subject line. and please mention your student number in the text, since e.g. temporary results file does not contain your name, only 3 last digits of student number.

Do not send email or comments to me via Quercus, I rarely check things posted there, and it's impossible for me to reply to a message forwarded via Quercus. We encourage you to use your UofT mail address in correspondence with us, to avoid the possible redirection to spam folder and for quick verification that you are UofT student.

Homework problems

General info

The format and the way of submission of solutions is electronic: take readable snapshots or scans of *neatly* hand-written, numbered pages, indicating your student number. Convert to one .pdf document. (If you hate handwriting, you can typeset your solutions and upload them as .pdf or .doc but then you will have to spend extra time doing the sketches/diagrams which you'd otherwise quickly do by hand.) You submit your term work to Quercus/Assignments before the deadline posted in the syllabus. Your TA will be an authority on this process. Contact him/her if you are unsure where to submit. Your solutions may be checked for possible plagiarism (i.e., overlap with fellow student's work or with internet pages; if you quote online resources, clearly reference the source).

Please remember to number the pages and sign all of them with your name and last 3 digits of student number, say, "...123". Write legibly; very messy homeworks cannot be graded. Please give enough details IN WORDS of the solution procedure. It's as important as the correct final answer. And don't forget to follow the guidelines on what a decent solution must contain (below) soch as physical units checks.

Everything you submit and the comments by the marking TA will be visible on Quercus. It will allow multiple submission of the files before deadline, so if you have corrections to your solution please post an updated file before the deadline (so it's not marked as late). You will be able to see and check a computational/calculational solution against a published one. This will make long explanations by the marker (TA) unnecessary, so don't expect very detailed comments on Quercus. Individual problems will have a nominal point value displayed, abd the TA will summarize your marks relative to these max scores. But the eventual "out of" or maximum score for a given task will be decided by the lecturer, and sometimes slightly re-adjusted toward the end of the course in your favor. Check the preliminary results file on this web page for your results vs. the "out of" scores for each task.


You have 9 days to solve problem sets really meant for 1 week solution time. But don't put the work away until the last days (read on why!). In addition, please plan ahead for a timely submission of solutions. Quercus flags late submissions and tells us exactly when you submitted the work.
Late by 10 minutes? We will accept it, assuming technical problems. But start submitting sufficiently early, especially if your network has problems. Much later submission will not be accepted. More precisely, they will be accepted only in medical or personal emergency, and you'll need to substantiate it. It is both because of the fairness to all those who respect deadlines, and the need (sometimes immediately after the deadline) to post and/or discuss solutions in the tutorial.
Likewise, a special treatment will also be extended to justified absences at midterm (there are no deferred midterms in ASTC25; points will be transferred to final exam).
Please do not ask for extension a few days before the deadline - it will be denied if it's not a justified exception outlined above. Other midterms and other courses are known ahead of the time, so plan ahead, use the long solution period of 9 and sometimes even more days to your advantage.

🤔   Four problem sets

If there are misprints or anything else unclear about the problem set and/or access to it, please ask immediately and allow up to a day for an answer. It is too late to ask one day before the due date.

Remember that a fully solved problem may require all of the following steps:

  1. A sketch of the situation
  2. Analytical part - manipulation of symbols to find the required relationships between quantities
  3. Units checks
  4. If units are ok (then & only then) substitute the constants and values, calculate the results
  5. Decide whether results make sense (e.g., is the order of magnitude ok?)
  6. Write up final version clearly, putting student # on 1st page. Explain in a few words what you're doing, don't just write equations.
The same applies to written problems in exams. Of course, some problems may not require pts. 1, 3, 4.

Set A1. Due Thu 1 Feb. . Published 22 Jan. Formulation Prob. set 1, PDF . Solutions: see this PDF .
Set A2. Due Thu 15 Feb at 1pm. Published 6 Feb. Formulation: In this PDF . Use summary of facts on orbital motion from A1. Solutions: cf. this PDF.
Set A3. Due Thu 14 March at 1pm Problem formulation (publ. 5 March): In this PDF. Solutions of A3: this PDF
Set A4. Due Thu 28 March. Last set (avail. 19 March): this PDF. Solutions: this PDF

😞   Note on plagiarism

Plagiarism and cheating do happen, sometimes by ignorance. When we notice strange non-sequiturs in your written problem solution, or close similarity of your solution to your fellow student's or some web page (wiki, google, chatGPT, etc.), it will be up to you to orally convince us that *you* originally wrote and understand what you submitted. (Plagiarism is to misrepresent as your work something that isn't.) Failing that, the usual, sometimes harsh, procedures and/or penalties UofT mandates will have to be applied. Read more in offical docs.

Lectures (pdf + animations)

The lecture numbers mostly correspond to the lecture number in syllabus.
L01_02-ASTC25-2024.pdf ,   L03_04-ASTC25-2024.pdf ,   L05_06-ASTC25-2024.pdf ,
     Phobos 1. (mpeg) ,
     Phobos 2. (mpeg),
     Phases & Libration of the Moon in 2012 (youtube),
L07_08-ASTC25-2024.pdf ,   L09_10-ASTC25-2024.pdf ,
     Disk formation. (mpg) ,
     Cluster formation. (avi),
     Hydrodynamic instability in a disk near the black hole. (mpg) ,
     MHD (magnetohydrodynamical) calculation of MRI (magnetorotational instability). (mpg) ,
L11_12-ASTC25-2024.pdf ,   L13_14-ASTC25-2024.pdf ,   L15-ASTC25-2024.pdf ,   L16_18-ASTC25-2024.pdf ,
     Brown dwarf opens a gap in a gas+dust disk, (mp4)
     Dust avalanche simulation. (mp4)
     Irradiation instability, gas disk. (mpg)
     Irradiation instability in gas disk. Modal growth. (mpg)
     Irradiation instability, particle disk, tau=4. (mp4)
     Irradiation instability, particle disk, tau=12. (mp4)
L19_23-ASTC25-2024.pdf ,
     Beta Pictoris planet orbiting (2013-2018). (gif)
     51 Eridani planet orbiting (2014-2018). (gif)
     HR 8799 planets orbiting (2009-2016). (gif)
     Jupiter opens a gap. (r,phi) coordinates, (mp4)
     Jupiter-mass protoplanet migrates. (mp4)
     Migration, type III - outward migration.
     Migration, type III - inward migration.
     Saturn's mass protoplanet - migration type III.
     One of 4 vortices generated by a 5-Earth mass planet.
     Planet migration page by Ph. Armitage
L24-ASTC25-2024.pdf .


See this page. Tutorials are important for preparation to written parts of exams.

Brief FAQ

Q: What do I need to write an exam?
A: Calculator, pens. (Exam booklets will be supplied.)

Q: What is the format of the final exam?
A: Exactly the same as midterm, just longer. The level of difficulty is also the same. 2/3 of final are from the post-midterm material, 1/3 from pre-midterm material.

Q: Are exams open-book?
A: No they are not. Electronic devices except calculator are also prohibited.

Q: Are own notes allowed at exams?
A: YES, own handwritten (not photocopied) notes are allowed: 4 pages at midterm, 8 pages at the final. That's pages not sheets! You decide if the notes are single-sided or double-sided, and what to write in them. (There is no need to copy tables of planetary data, since all the constants needed for the solution will be provided in the exam.)

Q: Until when can I drop the course without academic penalty?
A: In 2024 until 25 March.

Q: Is my presence at *all* lectures and tutorials required?
A: It isn't enforced or mandatory but it's VERY HELPFUL to attend both the lectures and the tutorials. Since the lectures DO NOT follow literally any books, except for sometimes quoting the assorted fragments of our textbook 1 (book no.1 above), your advantages are many: (i) the points for participation (see Marking section), (ii) you get information beyond what's in the textbook and posted materials, some of which may be *very* valuable at test/exam. I strongly encourage and expect you to engage and take own notes (I do write some things on the blackboard or whiteboard). For example, most of the (exo)planetary system theory is not yet found in any undergraduate textbooks, so hearing it presented in our meetings will be helpful. We will be discussing solutions to home assignments and solving new problems during the tutorials.

Q: Will there be recordings of lectures made available and can't I just use them instead of coming to in-person meetings (lectures, tutorials)?
A: Recordings of 2022/2023 lectures will be posted in Media Gallery on Quercus. There were occasional glitches when the session was not recorded at full length. The course is in-person, so you should not primarily rely on recordings but attend the lectures. You will also have the current PDF lecture notes below. Re-download them every week, since a few percent of each file is normally updated or expanded shortly before and sometimes after each lecture.

Q: Is this page going to be always visible or should I download things I need from it to my computer?
A: It did happen once that our server was unavailable 2 days before the exam. The networking problem was solved in the last minute but put a stress on those who did not download the preperatory material ahead of time. We advise to download or refresh lecture notes and other files you need every week.

Midterm exam - general info & preparation

The exam is in person. It starts 16:05 and ends 17:00 on 29 Feb (in class). You do the Quiz on the supplied exam (please do not list quiz answers in the exam booklet!) Mark the correctness of the sentence (Y/N) in front of the sentence. If you answer N, please also circle at least one word or number which is incorrect, otherwise your answer will be treated as a guess (no penalty but no credit, either).
Written part requires calculations. If you need scratch paper for that, use the blank pages of the exam booklet. We won't mark those. Your final solution must be found legibly written on lined pages.

Everything that was in the lectures and tutorials (and assignments) up to day 6 can be the subject of midterm exam, so study the notes up to and including L10 and days 1-6 of recordings, including tutorials.

Midterm Quiz will be testing notions and facts discussed in Lectures. The texbook can provide additional clarifications but is not required for the midterm. (This may not be the case in the final exam, so don't throw the Lissauer/de Pater book away!)

Own handwritten notes and calculators will be allowed at midterm. Nothing else is allowed, no electronic devices during the exam. Quiz usually takes about 20 min. You decide what to do first, quiz or written part. But remember that they carry approximately the same weight, so probably doing Quiz first makes more sense.

A training set of quiz questions is provided below. This version has about 50% of answers provided. Not sure if the scope exatly covers all lectures up to the SPH simulation of star cluster formation in L10 (the required material are all lectures up to this point). PDF.
Next I provide a set of sample written problems . Just like the Quiz, to prepare well for the exam, please solve the unsolved items with or without the lecture notes and texbook in hand. Problems without solutions . And here is the set of the problems with most answers or hints provided, but you should use it after you find your own solutions: problems-with-solutions .

Remember that a fully solved problem (in exam or assignment) may require all 6 points listed earlier in the section on homeworks.

Midterm on 29 Feb 2024

Solutions are in this PDF  

Instructions and preparation for the final exam on 13 April

The exam will take place on Saturn's day (Saturday) in MW160, 9am-12 (see syllabus if in doubt). Format of the final exam is the same as midterm.

For the quiz, review the files of lecture notes, your own notes, and/or recordings of lectures. As for the Lissauer+DePater textbook, please only read chapter 15. Read it thoroughly.
Sample quiz questions, many solved, is before the exam in this PDF file. For credit, remember to circle incorrect word(s) in case you choose N as answer. No attempt to cover all the lectures equally is made in this file.

As far as the written problems are concerned, please also remember to check the preparatory material for the midterm and all the posted homeworks & their solutions. I'm not including those things in the problems below, although I have covered most of the course material in preparation file for the Quiz.
The problems WITHOUT solutions, PDF file . The problems WITH solutions, PDF file .

Final exam 2024

PDF file .

Sample of Ostlie & Carroll

Annotated copy of chapter 2 of Ostlie and Carroll's book can be downloaded from here (pdf 5MB), to help you improve your knowledge of the Kepler problem, Newtonian physics etc.

Your points

preliminary (text file).

Interesting links

To the local home page of Pawel Artymowicz
Last modified: March 2024