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Textbook on Numerical Celestial Mechanics

  1. May 1, 2004 #1
    I'm seeking for a good textbook on numerical celestial mechanics. My current level of proficiency is:
    1- understanding of classical mechanics is at the level of Goldstein's textbook
    2- understanding of numerical analysis is at the level that I can easily pick up an algorithm from the "numerical recipes" and rewrite it in my preferred language(s)
    Virtually all of the books I've seen so far do not fit my requirements for one or more of the following reasons:
    1- too introductory (e.g., start explaining Newton's laws)
    2- no numerical approach
    3- focused on other applications (e.g., satellite control)
    Of course, a cheap textbook would be appreciated ... ;-)
  2. jcsd
  3. May 1, 2004 #2


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    You may need to find a good Numerical Methods book and then apply the general methods to Celestial Mechanics.
    I find Elementary Numerical Analysis by Conte and de Boor very useful. Also the 2 volume set A Survey of Numerical Mathematics by Young and Gregory is good.
  4. May 1, 2004 #3
    thanks for you reply. However, I understand that Celestial Mechanics has some peculiar idiosyncracies (long integration time, need to conserve energy, precision balancing between numerical integration and function evaluation) that seem to require a very specialized approach.
    From you reply I understand that I was not very clear on my background: I have some years experience in technical/scientific computing so an introductory text on Numerical Analysis is likely to be of little use. But'll be glad to have a look at the books you reference.
  5. May 2, 2004 #4


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    Neither of those texts are a "recipe" style books. I used them in grad level Numerical Analysis Math courses, I believe that this differers from a CS course in that a large emphasis is placed on understanding the inherent errors. If you cannot find a canned set of recipes to do what you need. These books may be of some help in designing your own programs. Though it may not be easy to dig out the information you need.
  6. May 2, 2004 #5


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    Hi Coelum,

    It's not cheap, but http://www.talkroot.com/cgi-bin/shop-item_id-1881883124-search_type-AsinSearch-locale-us.html [Broken] is the book which is used in my school for two semesters of orbital mechanics. It has quite a few pseudocode algorithms for various topics, and covers pretty much any topic you can think of.

    Downside is: It's poorly organized, IMO. It has everything, but needs an editor badly.
    Last edited by a moderator: May 1, 2017
  7. May 25, 2004 #6
    what do you want to know?

    modelling an orbit is just a matter of integrating some equations. one can easily make numerical equations from written ones.

    or are there other things you want to do?
  8. Jun 6, 2004 #7


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    I liked A.D. Dubyago's THE DETERMINATION OF ORBITS, translated from the Russian by the Rand Corporation. The Method of Gauss to determine an orbit by three angle-only observations is in Chapter Five.

    Jerry Abbott
  9. Nov 2, 2008 #8
    Here's my solution to the ephemeris problem. Yahoo Answers staff didn't like it, but it's a correct general solution with a worked example for Jupiter's position on a given date.

    Here's a BASIC program I wrote (with double precision) to evolve a heliocentric state vector with a small time increment for a given period of time. It's basically a numerical check on a two-body Keplerian solution for my transfer orbit procedure.

    Hyperbolic transfer orbit calculation.

    Predicting lunar eclipses.

    Determining an orbit with three geocentric angular positions by the method of Gauss.

    Elliptical transfer orbit calculation.

    The Case of the Mischievous Astronaut (probably somebody's homework problem).

    Orbital elements for solar system planets.

    Hohmann transfer orbits (worked examples).

    Jerry Abbott
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