# The solution of Kepler's equation, II

@article{Burkardt1983TheSO, title={The solution of Kepler's equation, II}, author={T. M. Burkardt and J. M. Anthony Danby}, journal={Celestial mechanics}, year={1983}, volume={31}, pages={317-328} }

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.

## 38 Citations

Homotopy Solutions of Kepler's Equations

- Physics
- 1996

Kepler's Equation is solved using an integrative algorithm developed using homotropy theory. The solution approach is applicable to both elliptic and hyperbolic forms of Kepler's Equation. The…

The solution of Kepler's equation, III

- Physics
- 1987

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…

A new simple method for the analytical solution of Kepler's equation

- Physics
- 1985

A new simple method for the closed-form solution of nonlinear algebraic and transcendental equations through integral formulae is proposed. This method is applied to the solution of the famous Kepler…

A cubic approximation for Kepler's equation

- Mathematics, Physics
- 1987

We derive a new method to obtain an approximate solution for Kepler's equation. By means of an auxiliary variable it is possible to obtain a starting approximation correct to about three figures. A…

Solving Kepler's equation with high efficiency and accuracy

- Physics
- 1991

We present a method for solving Kepler's equation for elliptical orbits that represents a gain in efficiency and accuracy compared with those currently in use. The gain is obtained through a starter…

Robust resolution of Kepler’s equation in all eccentricity regimes

- Physics, Mathematics
- 2013

In this paper we discuss the resolution of Kepler’s equation in all eccentricity regimes. To avoid rounding off problems we find a suitable starting point for Newton’s method in the hyperbolic case.…

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.

KEPLER’S EQUATIONS a kinematical deduction

- Physics
- 2005

Kepler’s equations are considered as central to Celestial Mechanics since their solutions permit ’to find the position of a body for a given time’. To obtain a kinematical deduction of them, only one…

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 1-9 OF 9 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…

A simple, efficient starting value for the iterative solution of Kepler's equation

- Physics
- 1979

A simple starting value for the iterative solution of Kepler's equation in the elliptic case is presented. This value is then compared against five other starting values for 3750 test cases. In…

An exact analytical solution of Kepler's equation

- Physics
- 1972

Complex-variable analysis is used to develop an exact solution to Kepler's equation, for both elliptic and hyperbolic orbits. The method is based on basic properties of canonical solutions to…

A general algorithm for the solution of Kepler's equation for elliptic orbits

- Physics
- 1979

An efficient algorithm is presented for the solution of Kepler's equationf(E)=E−M−e sinE=0, wheree is the eccentricity,M the mean anomaly andE the eccentric anomaly. This algorithm is based on simple…

Analysis of Numerical Methods

- Mathematics
- 1966

Keywords: analyse ; methodes : numeriques ; equations : lineaires ; calcul : integral ; equations : differentielles Reference Record created on 2005-11-18, modified on 2016-08-08