scholarly journals Corrigendum to “A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion”

2016 ◽  
Vol 2016 ◽  
pp. 1-1
Author(s):  
José Antonio López Ortí ◽  
Francisco José Marco Castillo ◽  
María José Martínez Usó
Keyword(s):  
Numerical Integration ◽  
Orbital Motion

scholarly journals A Study about the Integration of the Elliptical Orbital Motion Based on a Special One-Parametric Family of Anomalies

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
José Antonio López Ortí ◽  
Francisco José Marco Castillo ◽  
María José Martínez Usó
Keyword(s):  
Linear Combination ◽  
Numerical Integration ◽  
Body Problem ◽  
Numerical Solutions ◽  
Orbital Motion ◽  
Planetary Motion ◽  
Two Body Problem ◽  
New Family ◽  
Analytical Development ◽  
Convex Linear Combination

This paper aimed to address the study of a new family of anomalies, called natural anomalies, defined as a one-parameter convex linear combination of the true and secondary anomalies, measured from the primary and the secondary focus of the ellipse, and its use in the study of analytical and numerical solutions of perturbed two-body problem. We take two approaches: first, the study of the analytical development of the basic quantities of the two-body problem to be used in the analytical theories of the planetary motion and second, the study of the minimization of the errors in the numerical integration by an appropriate choice of parameters in our family for each value of the eccentricity. The use of an appropriate value of the parameter can improve the length of the developments in the analytical theories and reduce the errors in the case of the numerical integration.

scholarly journals Comparison of ELP-2000 to a JPL Numerical Integration

1981 ◽  
Vol 63 ◽  
pp. 257-264
Author(s):  
Jean Chapront ◽  
Michelle Chapront-Touzé
Keyword(s):  
Analytical Solution ◽  
Numerical Integration ◽  
Orbital Motion ◽  
Complete Solution ◽  
Analytical Theory ◽  
The Moon ◽  
Full Paper ◽  
Lunar Laser ◽  
Lunar Ephemeris

This contribution is an outline of the main results obtained by the authors in comparing their solution ELP-2000, to a JPL numerical integration, LE-51. A full paper containing discussions and comments on the results will be proposed to Astronomy ’ Astrophysics.A solution for the orbital motion of the Moon has been built by the authors. It is named ELP-2000, the epoch of reference being J2000. It is a semi-analytical solution, its structure being quite similar to Brown-Eckert’s one, as it appears in the Improved Lunar Ephemeris, ILE, j=2, (Eckert et al., 1954). The main purpose of this work is to present the results of a comparison of a provisional but complete solution, to an external numerical integration, LE-51, built at JPL (Williams, 1980), and fitted to lunar laser rangings. The JPL numerical integration is regarded as an “observational model”. It is a first attempt to compare as a whole, a new lunar ephemeris, derived from a semi-analytical theory, to observations, via a numerical integration.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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