The solution of Kepler's equation, II

  title={The solution of Kepler's equation, II},
  author={T. M. Burkardt and J. M. Anthony Danby},
  journal={Celestial mechanics},
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. 
Homotopy Solutions of Kepler's Equations
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
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
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
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
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Robust resolution of Kepler’s equation in all eccentricity regimes
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Kepler Equation solver
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
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
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


The solution of Kepler's equation, I
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
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
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
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Analysis of Numerical Methods
Keywords: analyse ; methodes : numeriques ; equations : lineaires ; calcul : integral ; equations : differentielles Reference Record created on 2005-11-18, modified on 2016-08-08