On the general planetary perturbations in rectangular coordinates

Musen, P.; Carpenter, L.

doi:10.1029/jz068i009p02727

Cited by 14 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this purpose at the U. S. Naval Observatory, in cooperation with other organizations, the preparation of new general theories, particularly for the inner planets, are being undertaken. The methods of Musen and Carpenter are being applied to determine numerical general theories (Musen and Carpenter 1963, Carpenter 1963, 1965. Numerical integrations of all the planets of the solar system are "being planned and observations for all the planets are being collected and reduced to the FKU system.…”

Section: Present Statusmentioning

confidence: 99%

Planetary Theories and Observational Data

Duncombe¹,

Seidelmann²

1978

International Astronomical Union Colloquium

View full text Add to dashboard Cite

show abstract

Section: Present Statusmentioning

confidence: 99%

Planetary Theories and Observational Data

Duncombe¹,

Seidelmann²

1978

International Astronomical Union Colloquium

View full text Add to dashboard Cite

show abstract

“…This method thus removes the influence of the variability of the elements on the coefficients of the disturbing force components from the differential equations and shifts this influence to the modified disturbing force. In the present paper we express this modified disturbing force in terms of Fad De Bruno [1857] differential operators, as we did in a planetary theory of different form [Musen, 1963[Musen, , 1965. The perturbation effects of higher orders are transferred from the elements to these operators.…”

Section: This Form Requires the Computation Of Lagrange And Poisson Bmentioning

confidence: 99%

“…A further extension of this idea is due to Brouwer [1944], and works in which different approaches to the problem are used have recently been published by Danby [1962] and Musen [1963Musen [ , 1965. The central idea of Brouwer's theory is one form of variation of astronomical elements.…”

Section: Introductionmentioning

confidence: 99%

Some possible modifications of Brouwer's theory of the general perturbations in rectangular coordinates

Musen¹

1966

J. Geophys. Res.

Self Cite

View full text Add to dashboard Cite

The method of general perturbations in rectangular coordinates is the most direct of all methods of expansion of the perturbations into series because it is intimately associated with the computation of ephemerides. In addition, unlike the method of variation of elliptic elements, the method of coordinates does not have the zero eccentricity as a singularity. In Brouwer's theory of the general perturbations in rectangular coordinates the variation of elements in the canonical form is used. However, if the perturbations are being developed into trigonometric series with purely numerical coefficients, the use of canonical elements is not of any advantage. This fact was recognized by Davis, who rewrote Brouwer's formulas in terms of the standard elliptic elements. Davis's formula contains two terms of order −1 in the eccentricity. The presence of these terms causes considerable numerical inconvenience in the study of nearly circular orbits. We suggest here the use of the Eckert‐Brouwer formula for the orbit correction as a foundation of a planetary theory. The application of this formula leads directly to a vectorial expression for perturbations which is free from the disadvantages mentioned above and is also convenient for the numerical computations. The method of iteration is suggested for computing the effects of higher orders. The inclusion of the higher‐order terms is important not only in the planetary case but also in the case of artificial celestial bodies moving in orbits in cislunar space, far away from the earth. Such bodies in their motions resemble planets or comets more than satellites.

show abstract

“…They used the methodology of Musen and Carpenter [26] and assumed a trigonometric series for the perturbations and numerically determined the coefficients such that a periodic solution can be found [26,27].…”

Section: Introductionmentioning

confidence: 99%