The problem of the critical inclination revisited

Ontology type: schema:ScholarlyArticle

Article Info

DATE

1975-05

AUTHORS ABSTRACT

The behaviour of the argument of the pericentre is investigated for the orbit of an artificial satellite which is moving under the potential when the inclination of the orbit is close to thecritical value tan−1 2. The theory is developed to first order and it is applicable to all values of the eccentricity, with the exception of those in the neighbourhood of zero and unity. Four principal types of behaviour are noted and these are illustrated in appropriate phase-plane diagrams. It is shown that the two types which exhibit double libration in the argument of the pericentre are restricted to a relatively small domain in the (a, e)-plane of possible motions. Moreover, it is demonstrated that for double libration to occur it is necessary, but not sufficient, that\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$e > \sqrt 6/13$$ \end{document}. The ranges of values of the inclination for which libration of the pericentre is a possibility are given for the more important cases.The general results are applied to the specific case of artificial Earth satellites whose orbits are inclined to the equator at angles close to the value of the critical inclination. More... »

PAGES

361-378

References to SciGraph publications

• 1973-01. The perturbed ideal resonance problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1973-08. The global solution of the problem of the critical inclination in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1972-09. Normality condition in the ideal resonance problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
• 1969-03. How critical is the critical inclination? in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01228812

DOI

http://dx.doi.org/10.1007/bf01228812

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046339924

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