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How to learn celestial mechanics

  1. Feb 17, 2010 #1
    Good morning,

    (I'm not sure if this is the right place for this question.)
    I want to learn about the Physics of orbits and how to calculate planets' position, velocity, etc. Basically, the only source I have is Internet, but the majority of the sites give incomplete and fragmented information (there is no sequence from basic to advanced and it is not well explained). I have no idea what sequence to follow or even where I should start, because I don't know what is important to know first.
    My current knowledge comes from high-school Physics and a collection of university introductory-level books (two by Paul Tipler and one from Resnick, Halliday and Krane). I'm still not in college; so, the knowledge from these college books is self-taught. I also have a basic knowledge of calculus, which is also self-taught (from the internet).
    My question is: how should I proceed? Is my current Physics/math knowledge proper so that I can already look for an introductory book on celestial mechanics? Or is there some other thing I should learn first?

    Thank you in advance.
  2. jcsd
  3. Feb 17, 2010 #2
    Last edited by a moderator: Apr 24, 2017
  4. Feb 17, 2010 #3
    Thanks for asking this question, pc2-brazil. I was about post a similar one. And thanks Matt for the recommendation. From the reviews it looks to be widely respected. Does anyone have any suggestions for a (non-astronomically priced) introductory book that fills in some the gaps mentioned by some of the amazon reviewers:

    "Admittedly, the mathematical treatment is a bit dated, geared toward a 1970's engineer with a slide rule."

    "It does not cover more advanced topics such as rotational dynamics, gravity models, or navigation & control systems."

    "However, it does not deal with spacecraft rotations, which are an important part of spacecraft motion."

    "Don't be fooled, however, it's not a book on orbital mechanics, since there is a lot more mathematics to orbital mechanics than is shown in this book (e.g. numerical methods, perturbations and averaging methods)."

    "As the title suggests, it presents the **fundamentals** of astrodynamics (not attitude control, not propulsion, not advanced mechanics, etc.)."

    "Sure, it leaves out chaos [...]"
  5. Feb 17, 2010 #4
    Thank you for the answer.

    I have two doubts:
    - What are the Physics/maths-related prerequisites for reading this book (or any other book introducing the subject)? This and other books seem to use vector calculus, with which I'm not familiar.
    - From what I've read on-line (and noticed from the book preview in Google Books http://books.google.com/books?id=g7...ent=opera&hl=pt-BR&cd=1#v=onepage&q=&f=false"), this book seems really good, but the problem is that I don't know if Astrodynamics is quite what I'm looking for, as it is specifically applied to artificial satellites (cf. Wikipedia), and not celestial bodies in general.

    Thank you in advance.
    Last edited by a moderator: Apr 24, 2017
  6. Feb 17, 2010 #5
    You have to know and understand vector calculus in order to understand the quantities you are interested in calculating. Sorry, there is no getting around this.

    The only
    requirement is that you can hold the book open and turn the pages. LOL

  7. Feb 17, 2010 #6
    Thank you for your answer.

    I have two other questions:

    1) Regarding the study of orbits, how far can I go knowing just Calculus I (Limits, Differentiation and Integration)?

    2) From what I can see in some Physics books, new mathematical subjects are generally covered in the book itself as the need arises. For example, in the general Physics books from Paul Tipler that I have, dot product (scalar product) is introduced along with work and vector product is introduced along with the discussion about the vectorial nature of rotations. Since I haven't studied vector calculus yet, I probably don't have the appropriate "foundations" yet. When is vector calculus introduced in Physics?
  8. Feb 17, 2010 #7
    I've been recommended The Physical Universe by Frank Shu. I don't have the book, but it comes higly recommended from a professor that I respect and admire. I just finished reading Astronomy: The Evolving Universe and while I like the text and found it informative, I think there is just not as much mathematics as I was hoping for, thus, I was told to get Shu's book.
  9. Feb 20, 2010 #8
    Elecromagnetism is trial by fire in vector calculus.
  10. Feb 20, 2010 #9
    Celestial motion was first studies by Henry Poincare, and interestingly he found that such kind of dynamics is chaotic. Your basic knowledge about classical mechanics is enough to studies the chaotic dynamics.
    Book "Introduction to the analysis of non-linear dynamics"
  11. Feb 24, 2010 #10

    This is some question, one whose answer I have been seeking for quite a while. Basically, you've got to know your calculus rock solid and understand polar coordinates calculus etc... Everytime I find one explanation I then find other more advanced ones, it's a deeper and deeper rabbit hole. The above book is a book on learning vector calculus so with your basic calc I think you'll do just fine in it.

    My advice, which I am currently following :p, it to keep studying until you find the most satisfactory explanation.

    If you get your math up a bit, a man named Meus wrote a book called Astronomical Algorithms which has a crazy amount of detail of the positions of planets etc... to use real calculatable figures. I've seen this book and was scared away lol, it's saved for the future.

    My link, the book linked above in a previous post & similar books of these kinds are the best hope of getting a satisfactory explanation.
    Last edited by a moderator: May 4, 2017
  12. Feb 24, 2010 #11
    The book Matt recommended, Bate, Mueller & White: Fundamentals of Astrodynamics, has a 9-page appendix that covers the basics of vector algebra and calculus, but if you're completely new to the subject you'll want a more detailed introduction too. I began with Davis & Snider: Introduction to Vector Analysis, which is quite visual and emphasises the geometric aspects. But there are many other textbooks and online resources at various levels.

    The Khan Academy is good. It has loads of short (mostly about 10 minutes) videos, starting at a very basis level and working up to more advance topics. Vectors are introduced in the physics section, in the context of mechanics and elecromagnetism, and gone in to in more detail in the linear algebra section. The calculus section includes videos on multivariable and vector calculus, including the concepts of gradient, curl and divergence.

    Among the lectures at MIT open courseware, basic vector algebra is introduced in lecture 3 of 8.01 Physics I: Classical Mechanics, and is covered in the first section of 18.02 Multivariable Calculus and explored in more detail and with more abstract background in 18.06 Linear Algebra.
  13. Feb 24, 2010 #12


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    One note about Bate, Mueller and White: It uses archaic units. Everything is in feet and pounds, with some stuff in nautical miles! For me, this is one of the more frustrating and annoying parts about the book. Other than that, cheap and good.
  14. Feb 24, 2010 #13
    Ah, so that's what "nm" stands for! I knew it wasn't nanometres...
  15. Mar 11, 2012 #14
    Our of curiosity I wondered if the Khan Academy dealt with celestial mechanics. Google picked up this. Although the post is 2 years old, I'll provide a good source anyone who wants to delve into this.

    <http://orca.phys.uvic.ca/~tatum/celmechs.html>. [Broken] It's free, current and well done.
    Last edited by a moderator: May 5, 2017
  16. Mar 12, 2012 #15
  17. Mar 12, 2012 #16
    This book seems to be very comprehensive. What would you say about the mathematical requirements for reading it?

    Thank you in advance.
  18. Mar 12, 2012 #17
    The first class I had which it was required for was a galactic astronomy class. The prerequisites were a semester of mechanics, which I think presumes you have taken the full high-school math workload (algebra, geometry, and precalculus/trigonometry).

    If you understand that math well, you should be able to follow the math in a good chunk of the book, especially since it goes over the proofs in pretty good detail. However, if you want to understand all of it (mainly following the proofs and doing all the problems), you probably need the full lower-division math sequence (three semesters of calculus and differential equations).

    It is kind of like the astronomer's/astrophysicist's bible. It covers 90% of the main topics in astronomy and is a good starting place for any advanced problem (the suggested reading is very helpful to continue research) that is not sufficiently covered in the book.
  19. Mar 13, 2012 #18

    Filip Larsen

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  20. Mar 13, 2012 #19
    $149.00 on Amazon. Unfortunately, it doesn't have a Look Inside, so you could read part of it, but you could look at the reader comments.

    If you are really uncertain about a book, have your library borrow it through a inter-library loan, and examine it yourself.
  21. Mar 13, 2012 #20

    This should show you the nearest libraries with the book.
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