Skip to main content Accessibility help
×
Home

An Optimum Method for Calculating Restricted Three-Body Orbits

  • Marc A. Murison (a1)

Abstract

The restricted three-body problem (RTBP) has in the past played an essential role in many different areas of dynamical astronomy, and indications are that this will continue. As the state of the art in computing becomes more advanced, larger numbers of integrations and longer durations are attempted. Thus, computational efficiency and accuracy are becoming more important. Also, the use of the RTBP in many different areas leads to the desire for a general integration method. In order to maximize the efficiency of orbit calculations, comparisons are made of different methods of integration. The results can be summarized as follows: 1. The Bulirsch-Stoer extrapolation method is extremely fast and accurate, and is the method of choice. 2. Regularization of the equations of motion is essential. 3. When applicable, a manifold correction algorithm, originally due to Nacozy (1971), reduces numerical errors to the limits of machine accuracy, and at a cost of only 1 to 3 percent in cpu time.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      An Optimum Method for Calculating Restricted Three-Body Orbits
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      An Optimum Method for Calculating Restricted Three-Body Orbits
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      An Optimum Method for Calculating Restricted Three-Body Orbits
      Available formats
      ×

Copyright

References

Hide All
Bettis, D.G. and Szebehely, V. (1971). Astrophys. Space Sci. 14, 133.
Henon, M. (1969). Quart. Appl. Math. 27, 291.
Huang, T.-Y. and Innanen, K.A. (1983). Astron. J. 88, 1537.
Murison, M.A. (1988). Ph.D. Thesis, Univ. of Wisconsin-Madison.
Nacozy, P.E. (1971). Astrophys. Space Sci. 14, 40.
Press, W. H., Flanner-y, B.P., Teukolsky, S. A. and Vetterling, W. T. (1986). Numerical Recipes: The Art of Scientific Computing. Cambridge Univ. Press.
Stiefel, E. and Scheifele, G. (1970). Linear and Regular Celestial Mechanics. Springer-Verlag.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed