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

@article{Ng1979AGA, title={A general algorithm for the solution of Kepler's equation for elliptic orbits}, author={Edward W. Ng}, journal={Celestial mechanics}, year={1979}, volume={20}, pages={243-249} }

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 initial approximations that are cubics inM, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20 000 pairs of values ofe andM show that for single precision (∼10−8…

## 24 Citations

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

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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…

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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…

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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…

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This work attacks Kepler's equation with the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions.

A new method for obtaining approximate solutions of the hyperbolic Kepler's equation

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- 2015

We provide an approximate zero S̃(g, L) for the hyperbolic Kepler’s equation S − g arcsinh(S)−L = 0 for g ∈ (0, 1) and L ∈ [0,∞). We prove, by using Smale’s α-theory, that Newton’s method starting at…

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- 2006

This paper defines Kepler’s equation for the elliptical case and describes existing solution methods, and presents the dynamic discretization method and shows the results of a comparative analysis, demonstrating that, for the conditions of the tests, dynamicDiscretization performs the best.

Appropriate Starter for Solving the Kepler's Equation

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- 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.

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- 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…

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…

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