The two-body problem with a decreasing gravitational constant

Details The two-body problem with a decreasing gravitational constant The two-body problem with a decreasing gravitational constant

Dec 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976mnras.177..545h&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 177, Dec. 1976, p. 545-549.

Mathematics

Logic

5

Cosmology, Gravitational Constant, Secular Variations, Two Body Problem, Asymptotic Methods, Celestial Mechanics, Differential Equations, Double Cusps, Eddington Approximation, Equations Of Motion

Scientific paper

Starting with equations given by Hadjidemetriou (1967), it is possible to present the equations for the osculating elements of the two-body problem with monotonically decreasing gravitational 'constant' G and to derive equations for the secular variation of the mean motion and longitude. The results contain, as a special case, the equations derived by Vinti (1974) and produce more precise estimates. Using the theory of asymptotic approximations, expressions are given for the behavior of the true longitude; if G behaves as a singular Jeans-Eddington function, a remarkable simplification of the results is found. Using observational data, some cosmological implications are discussed.

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