# The solution of Kepler's equation, III

@article{Danby1987TheSO, title={The solution of Kepler's equation, III}, author={J. M. Anthony Danby}, journal={Celestial mechanics}, year={1987}, volume={40}, pages={303-312} }

Recently proposed methods of iteration and initial guesses are discussed, including the method of Laguerre-Conway. Tactics for a more refined initial guess for use with universal variables over a small time interval are described.

## 44 Citations

Bounds on the solution to Kepler's equation

- Mathematics
- 1986

For Kepler's equation two general linear methods of the bounds determination forE0 root are presented. The methods based on elementary properties of convex functions allow an approach toE0 root…

Procedures for solving Kepler's equation

- Mathematics
- 1986

We review starting formulae and iteration processes for the solution of Kepler's equation, and give details of two complete procedures. The first has been in use for a number of years, but the second…

Appropriate Starter for Solving the Kepler's Equation

- Physics
- 2014

This article focuses on the methods that have been used for solving the Kepler’s equation for thirty years, then Kepler's equation will be solved by Newton-Raphson's method, and one appropriate choice first guesses that increase the isotropy and decrease the time of Implementation of solving is introduced.

The solution of the generalized Kepler's equation

- Physics
- 2018

In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or…

Numerical solution of the two-body problem for orbital motion is heavily dependent on efficient solution of Kepler's Equation

- Mathematics
- 1995

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four…

On solving Kepler's equation for nearly parabolic orbits

- Physics
- 1996

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these…

Kepler Equation solver

- Computer Science
- 1995

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation, and requires only four transcendental function evaluations.

The hyperbolic Kepler equation (and the elliptic equation revisited)

- Physics, Mathematics
- 1988

A procedure is developed that, in two iterations, solves the hyperbolic Kepler's equation in a very efficient manner, and to an accuracy that proves to be always better than 10−20 (relative…

An improved algorithm due to laguerre for the solution of Kepler's equation

- Physics
- 1986

A root-finding method due to Laguerre (1834–1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several…

The Convergence of Newton–Raphson Iteration with Kepler's Equation

- Physics
- 1997

Conway (Celest. Mech. 39, 199–211, 1986) drew attention to the circumstance that when the Newton–Raphson algorithm is applied to Kepler's equation for very high eccentricities there are certain…

## References

SHOWING 1-4 OF 4 REFERENCES

The solution of Kepler's equation, I

- Physics
- 1983

Methods of iteration are discussed in relation to Kepler's equation, and various initial ‘guesses’ are considered, with possible strategies for choosing them. Several of these are compared; the…

The solution of Kepler's equation, II

- Physics, Mathematics
- 1983

Starting values for the iterative solution of Kepler's equation are considered for hyperbolic orbits, and for generalized versions of the equation, including the use of universal variables.

Procedures for solving Kepler's equation

- Mathematics
- 1986

We review starting formulae and iteration processes for the solution of Kepler's equation, and give details of two complete procedures. The first has been in use for a number of years, but the second…

An improved algorithm due to laguerre for the solution of Kepler's equation

- Physics
- 1986

A root-finding method due to Laguerre (1834–1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several…