Skip to main content
SpringerLink
Log in

'On Solving Kepler's Equation For Nearly Rectilinear Hyperbolic Orbits'

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

We deal here with efficient starting points for Kepler's equation in a special case of nearly rectilinear hyperbolic orbits, that is these ones with the eccentricities e ≫ 1. These orbits appear in stellar dynamics when considering encounters of stars. We test efficiency of these starters for the method for successive approximation (MSA) in its two often applied variants, that is the Newton's method with the quadratic convergence (NM) and in the fixed point method (FPM). Moreover, we determine a dynamical domain of Kepler's equation for this motion.

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

  • Garcia-Sanchez, J., Preston, R. A., Jones, D. L., Weissman, P. R., Lestrade, J. F., Latham, D.W. and Stefanik, P. R.: 1999, 'Stellar encounters with the Oort cloud based on Hipparcos data', A. J. 117, 1042.

    Article  Google Scholar 

  • Kantorovich, L. V. and Akilov, G. P.: 1964, Functional Analysis in Normed Spaces, Pergamon Press, Oxford.

    Google Scholar 

  • Prussing, J. E.: 1977, 'Bounds on the solution to Kepler's problem', J. Astronaut. Sci. 25, No. 2, 123.

    Google Scholar 

  • Serafin, R. A.: 1997, 'On solving Kepler's equation for nearly parabolic orbits', Celest. Mech. & Dyn. Astr. 65, 389.

    Google Scholar 

  • Serafin, R. A.: 1998, 'Bonds on the solution to Kepler's equation, II, Universal and optimal starting points', Celest. Mech. & Dyn. Astr. 70, 131.

    Google Scholar 

  • Serafin, R. A.: 2001, 'On the rectilinear non-collision motion', Celest. Mech. & Dyn. Astr. 90, 87.

    Google Scholar 

  • Smith, G. R.: 1979, 'A simple efficient starting values for the iterative solution of Kepler's equation', Celest. Mech. 19, 163.

    Article  Google Scholar 

  • Smith, O. K.: 1968, 'Terminating the iterative solution of Kepler's equation', Amer. Rocket Soc. J. 31, 1598.

    Google Scholar 

  • Taylor, E. J.: 1988, Solution and Iteration Surfaces for Kepler's Equation, MSc Paper, Department of Mathematics, Iowa State University, Ames IA.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Uhlandstraβe 46, D-46047, Oberhausen, Germany

    Richard A. Serafin

Authors
  1. Richard A. Serafin
    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

Serafin, R.A. 'On Solving Kepler's Equation For Nearly Rectilinear Hyperbolic Orbits'. Celestial Mechanics and Dynamical Astronomy 82, 363–373 (2002). https://doi.org/10.1023/A:1015283119522

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015283119522

Search

Navigation