# Fast Procedure Solving Universal Kepler's Equation

@article{Fukushima1999FastPS, title={Fast Procedure Solving Universal Kepler's Equation}, author={Toshio Fukushima}, journal={Celestial Mechanics and Dynamical Astronomy}, year={1999}, volume={75}, pages={201-226} }

We developed a procedure to solve a modification of the standard form of the universal Kepler’s equation, which is expressed as a nondimensional equation with respect to a nondimensional variable. After reducing the domain of the variable and the argument by using the symmetry and the periodicity of the equation, the method first separates the case where the solution is so small that it is given an inverted series. Second, it separates the cases where the elliptic, parabolic, or hyperbolic…

## 11 Citations

A Solution of Kepler’s Equation

- Physics
- 2014

The
present study deals with a traditional physical problem: the solution of the
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hyperbola or parabola). Solution of the universal Kepler’s equation in…

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- 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…

Solving Kepler's equation CORDIC-like

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- 2018

This work presents an algorithm to compute the eccentric anomaly and even its cosine and sine terms without usage of other transcendental functions at run-time with slight modifications for the hyperbolic case.

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- Computer Science, PhysicsAstronomy & Astrophysics
- 2018

An algorithm to compute the eccentric anomaly and even its cosine and sine terms without usage of other transcendental functions at run-time without using trigonometric or root functions is presented.

Fast Switch and Spline Function Inversion Algorithm with Multistep Optimization and k-Vector Search for Solving Kepler’s Equation in Celestial Mechanics

- Physics
- 2020

Obtaining the inverse of a nonlinear monotonic function f(x) over a given interval is a common problem in pure and applied mathematics, the most famous example being Kepler’s description of orbital…

Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic

- Mathematics
- 2008

In order to accelerate the numerical evaluation of torque-free rotation of triaxial rigid bodies, we present a fast method to compute various kinds of elliptic functions for a series of the elliptic…

Optimal starters for solving the elliptic Kepler’s equation

- Computer Science, Physics
- 2013

The highly accurate starter given by Markley is considered in proposing an improvement of it for low to medium eccentricities and new optimal starters with respect to these measures are derived.

Gravitational Few-Body Dynamics

- Physics
- 2020

This volume explains the methodology of the subject for graduate students and researchers in celestial mechanics and astronomical dynamics with an interest in few-body dynamics and the regularization of the equations of motion.

Numerical Comparison of Two-Body Regularizations

- Physics
- 2007

We numerically compare four schemes to regularize a three-dimensional two-body problem under perturbations: the Sperling-Burdet (S-B), Kustaanheimo-Stiefel (K-S), and Burdet-Ferrandiz (B-F)…

AN ORBITAL ELEMENT FORMULATION WITHOUT SOLVING KEPLER'S EQUATION

- Physics, Geology
- 2008

Starting from a standard orbital element formulation adopting the mean anomaly or longitude as the element related to time, changing its independent variable from the physical time to the…

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