Appropriate Starter for Solving the Kepler's Equation
@article{Esmaelzadeh2014AppropriateSF, title={Appropriate Starter for Solving the Kepler's Equation}, author={Reza Esmaelzadeh and Hossein Ghadiri}, journal={International Journal of Computer Applications}, year={2014}, volume={89}, pages={31-38} }
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. For increasing the stability of Newton’s method, various guesses studied and the best of them introduced base on minimum number repetition of algorithm. At the end, after studying various guesses base on time of Implementation, one appropriate choice first guesses that increase the isotropy and decrease the time of…
Figures and Tables from this paper
6 Citations
Re-Evaluation Solution Methods for Kepler's Equation of an Elliptical Orbit
- PhysicsIraqi Journal of Science
- 2019
An evaluation was achieved by designing a matlab program to solve Kepler’s equation of an elliptical orbit for methods (Newton-Raphson, Danby, Halley and Mikkola). This involves calculating the…
A new analytical solution of the hyperbolic Kepler equation using the Adomian decomposition method
- Physics
- 2017
Improved First Estimates to the Solution of Kepler's Equation
- Physics, Geology
- 2017
The manuscripts provides a novel starting guess for the solution of Kepler's equation for unknown eccentric anomaly E given the eccentricity e and the mean anomaly M of an elliptical orbit.
Improvement of the Accuracy of the Perturbed Orbital Elements for LEO Satellite by Improving 4th Order Runge–Kutta’s Method
- Physics
- 2020
Background/objectives: To study the motion equation under all perturbations effect for Low Earth Orbit (LEO) satellite. Predicting a satellite’s orbit is an important part of mission exploration.…
Determination the optimum orbit for low Earth satellites by changing the eccentricity
- Physics, Geology
- 2020
The main objective of this paper is to determine an acceptable value of eccentricity for the satellites in a Low Earth Orbit LEO that are affected by drag perturbation only. The method of converting…
References
SHOWING 1-10 OF 27 REFERENCES
On solving Kepler's equation
- Physics, Geology
- 1989
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.
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…
Dynamic discretization method for solving Kepler’s equation
- Computer Science
- 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.
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…
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 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 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…
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…
A Solution of Kepler’s Equation
- Physics
- 2014
The
present study deals with a traditional physical problem: the solution of the
Kepler’s equation for all conics (ellipse,
hyperbola or parabola). Solution of the universal Kepler’s equation in…
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…