# On Broucke's velocity-related series expansions in the two-body problem

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

1975-12

AUTHORS ABSTRACT

This short article supplements a recent paper by Dr R. Broucke on velocity-related series expansions in the two-body problem. The derivations of the Fourier and Legendre expansions of the functionsF(v),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {F(\upsilon )}$$ \end{document} and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\sqrt {{1 \mathord{\left/ {\vphantom {1 {F(\upsilon )}}} \right. \kern-\nulldelimiterspace} {F(\upsilon )}}}$$ \end{document} are given, where\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$F(\upsilon ) = (1 - e^2 )/(1 + 2e\cos \upsilon + e^2 ), e< 1$$ \end{document} In the two-body problem,v is identified with the true anomaly,e the eccentricity andF(v) equals (an/V)2.Some interesting relations involving Legendre polynomials are also noted. More... »

PAGES

513-518

### References to SciGraph publications

• 1974-12. A note on velocity-related series expansions in the two-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01595394

DOI

http://dx.doi.org/10.1007/bf01595394

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001743077

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