Course Delivery: Our class will be "remote". All lectures will be via zoom (and will be recorded, so can be reviewed any time). Office hours will be via zoom and will be "walk in". The links for lectures and office hours will be at the blackboard page Tools->zoom
Community: The only real advantage of "in person" classes is that it makes it more convenient to form a communities and subgroups of students. You could look at videos and read books by yourself to your hearts content, but it is generally difficult to find others doing the same thing to talk to and work with. Such groups have the potential to both make the experience of the class more fun and more effective.
So I strongly encourage you to get to know others in the class. You automatically have topic of conversation (this class!). Working in groups or teams is the norm in most professions that involve this material and it is more and more the case that the team will have members that are physically distant, so treat this semester as part of your training.
Academic Conduct: Your conduct in this course, as with all BU courses, is governed by the BU Academic Conduct Code. Copies of the code are available from the CAS Dean's office (CAS 105) or here.. Specifics rules for specific assignments will be discussed in lecture.
The "Golden Rule" of academic conduct is to "Give Credit Where Credit is Due". That is, if you use or consult a source, including a book, journal, web page or person, then cite that source (i.e., give sufficient information so that someone reading your work could determined what information you used and be able to find the source). The details of the form necessary in citation vary greatly from subject to subject, but the basic rule is universal.
If you have any doubt about any aspect of proper citation or academic conduct in general, ask!.
This is a one-time only "topics" class. It is a treat for me to be able to offer it and I hope you enjoy it. Celestial Mechanics ranks as one of the oldest areas of mathmeatics--people have been looking at the stars for at least as long as they could count. Those who have worked on and contributed to the field form a "Who's-who" in the history of mathematics. Many of the things you've had to learn were included in your earlier classes because they are used in Celestial Mechanics (and it isn't unlikely they were developed to answer questions in Celestial Mechanics)
Celestial Mechanics, in its modern form, is the study of solutions of a particular system of differential equations that arise from Newton's Laws of motion and Law of universal attraction of gravity. This is different from other classes since we are not looking for general theorems or techniques that apply to many problems, we are looking solutions of just one specific system--and we are willing to do what needs to be done in order to learn about those solutions.
Who should take this class? (Prerequisites): We will use ideas from Calculus--particularly MA 225--including some of those arcane vector identities that you were forced to learn but wondered why... In addition, we'll use ideas from differential equations (particularly what it means to be a solution) and occasionally details on behavior of solutions. Otherwise the class should be "self contained"--i.e., no knowledge of physics or astronomy will be assumed.
Books:I am writing up course notes that will be the basis of (but different from) lecture notes, so in theory, you won't need a text. There are, however, lots of good books, if you like buying books. The course notes will, at least for the first few weeks and off and on after that be mainly drawn from two books:
The Szebehely book is a good starting point--it is easy to follow and has examples and exercises. It also has interesting chapters on spacecraft dynamics and rocket science. Expensive, but available on the used book market
The Pollard book is very thin little book, but it is very dense and covers enough for a begining graduate course, however, it starts from scratch. It is out of print, but is available as an ebook from the MAA
Technology: I will send any course announcement via the registrar's course list (so your BU email account). Make sure you check this account regularly (once a day is sufficient) so that you are up to date with any course announcements.
Grades: I hate grading. I hate it with a passion that is hard to even put into words. The only situation in which grading is not torture for me is when what I am grading is both correct and well written. So, I am arranging the grading of this class so that I have a minimal amount of unpleasant grading to do.
Weights for components of the course work are as follows:
Notes:
Miscellaneous:
Study groups: I encourage you to form study groups and to spend some (not all) of your study time with your group. Make absolutely sure that you abide by the requirements of the Academic Conduct Code and the rules for each assignment. In particular, you should write up your assignment on your own. Papers which are too similar will be subject to action under the Academic Conduct Code porcedures. Also, if you get a significant idea or assistance from a tutor or a classmate, BE SURE to reference them ("Thank you to So A. So for suggesting I integrate by parts on problem 3.").
Pedagogy: I have heard it said that students learn approximately 5 percent of the material for a class in lecture. This is usually quoted to justify doing away with lectures. However, about 5 percent of my body is my head and I would not want to do without that.
In fact, I think that the 5 percent figure is about right. You learn mathematics by doing mathematics, doing exercises and writing up solutions carefully so that your answers can be easily understood. On the exams, you will be asked to do problems, and your ability to do so will be what determines your grade.
Seeing examples and hearing the important points discussed before trying to do the problems yourself is much more efficient than reconstructing all the mathematics for yourself (the mathematics we will cover took literally hundreds of years to develope). So think of the lectures as how you prepare to do the real work of learning the material which is doing the exercises yourself.
Final comment: Too many students consider their courses hoops that they must jump through in order to reach a degree. This philosophy implies that you only need to keep the material in your head until the final. This is just wrong.
Celestial Mechanics involves many hard computations. You should go through these computations carefully with the goal of getting to the point that you could reproduce them. It is all in the details!
Celestial Mechanics has always strattled the boundary between pure and applied mathematics...All the giants of math (Newton, Euler, Gauss, Laplace, Lagrange, Cauchy, Poincare,...) thought about problems in celestial mechanics. While the goal is to understand the solutions of just one system of differential equations, the astounding complexity and variety of those solutions is still an active area of research today with amazing new discoveries appearing regularly. Celestial Mechanics is so hard that that it often seems impossible, but still progress is made, step by step, over the centuries. Have fun!