SOLVING KEPLER'S EQUATION WITH HIGH EFFICIENCY AND ACCURACY

被引：26

作者：

Nijenhuis, Albert ^{[1
,2
]}

机构：

[1] Univ Penn, Dept Math, Philadelphia, PA 19103 USA

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 1991年 / 51卷 / 04期

关键词：

Two-body problem; Kepler's equation; numerical method;

D O I：

10.1007/BF00052925

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

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 algorithm which uses Mikkola's ideas in a critical range, and less costly methods elsewhere. A higher-order Newton method is used thereafter. Our method requires two trigonometric evaluations.

引用

页码：319 / 330

页数：12

共 10 条

[1] Abramowitz M., 1965, HDB MATH FUNCTIONS
[2] CARLSON B, 1943, RATIONAL APPROXIMATI
[3] AN IMPROVED ALGORITHM DUE TO LAGUERRE FOR THE SOLUTION OF KEPLER EQUATION
CONWAY, BA
[J]. CELESTIAL MECHANICS, 1986, 39 (02): : 199 - 211
[4] THE SOLUTION OF KEPLER EQUATION .1.
DANBY, JMA
BURKARDT, TM
[J]. CELESTIAL MECHANICS, 1983, 31 (02): : 95 - 107
[5] THE HYPERBOLIC KEPLER EQUATION (AND THE ELLIPTIC EQUATION REVISITED)
Gooding, R. H.
Odell, A. W.
[J]. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 1988, 44 (03) : 267 - 282
[6] A CUBIC APPROXIMATION FOR KEPLER EQUATION
MIKKOLA, S
[J]. CELESTIAL MECHANICS, 1987, 40 (3-4): : 329 - 334
[7] GENERAL ALGORITHM FOR THE SOLUTION OF KEPLERS EQUATION FOR ELLIPTIC ORBITS
NG, EW
[J]. CELESTIAL MECHANICS, 1979, 20 (03): : 243 - 249
[8] PROCEDURES FOR SOLVING KEPLER EQUATION
ODELL, AW
GOODING, RH
[J]. CELESTIAL MECHANICS, 1986, 38 (04): : 307 - 334
[9] TAFF LG, 1991, CELEST MECH IN PRESS
[10] Traub JF., 1964, ITERATIVE METHODS SO

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