Skip to main content
SpringerLink
Log in

Comments on the application of power series solutions to problems in celestial mechanics

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

The author relates his experiences in utilizing the power series method to generate trajectories for orbital and sub-orbital vehicles and for then-body problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Broucke, R.: 1971,Celes. Mech. 4, 110–115.

    Google Scholar 

  • Danby, J. M. A.: 1972,Celes. Mech. 5, 311–316.

    Google Scholar 

  • Deprit, A. and Price, J. F.: 1965,Astron. J. 70, 836–846.

    Google Scholar 

  • Deprit, A. and Zahar, R. V. M.: 1965, ‘Numerical Integration of an Orbit and Its Concomitant Variations by Recurrent Power Series’, Boeing Scientific Research Laboratories, Mathematical Note No. 445.

  • DeWitt, R. N.: 1962, ‘Derivations of Expressions Describing the Gravitational Field of the Earth’, U.S. Naval Weapons Laboratory, Technical Memorandum No. K-35/62, Dahlgren, Virginia.

    Google Scholar 

  • Fehlberg, E.: 1964, ‘Numerical Integration of Differential Equations by Power Series Expansions, Illustrated by Physical Examples’, NASN TN D-2356.

  • Hartwell, J. G.: 1967a, ‘Taylor Series Solution of the Analysis and Integration of Orbits for Apollo Ships’, D. Brown Associates, Inc., Melbourne, Florida, 1967.

    Google Scholar 

  • Hartwell, J. G.: 1967b,J. Astron. Sci. 14, 173–177.

    Google Scholar 

  • Hartwell, J. G.: 1968, ‘A Power Series Solution for the Motion of an Artificial Satellite and Its Concomitant Variational Equations’, D. Brown Associates, Inc., Melbourne, Florida.

    Google Scholar 

  • Moore, R. E. and Greenspan, D.: 1972, ‘The Perihelion of Mercury’, University of Wisconsin, Computer Science Department, Technical Report No. 161.

  • Rabe, E.: 1961,Astron. J. 66, 500–513.

    Google Scholar 

  • Roberts, C. E.: 1968, Engineering Analysis Technical Memo No. 103, PAFB, Florida.

    Google Scholar 

  • Roberts, C. E.: 1969, ‘A Power Series Solution the Equations of Motion and the Associated Variational Equations for Spherical Harmonic Geopotential Models’, Engineering Analysis Technical Memo No. 108, PAFB, Florida.

    Google Scholar 

  • Saari, D. G.: 1970,Celes. Mech. 1, 331–342.

    Google Scholar 

  • Sconzo, P. and Hale, M.: 1964, ‘Convergence and Truncation Error Study in Time Series Expansions’, Mission and Mathematical Analysis Report 12-010, IBM Federal Systems Division, Houston, Texas.

    Google Scholar 

  • Sconzo, P., LeSchack, A. R., and Tobey, R.: 1965,Astron. J. 70, 269–271.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indiana State University, Terre Haute, Ind., USA

    Charles E. Roberts Jr.

Authors
  1. Charles E. Roberts Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roberts, C.E. Comments on the application of power series solutions to problems in celestial mechanics. Celestial Mechanics 12, 397–407 (1975). https://doi.org/10.1007/BF01595387

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01595387

Keywords

Search

Navigation