Other
Scientific paper
Sep 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16...77n&link_type=abstract
Celestial Mechanics, vol. 16, Sept. 1977, p. 77-86. NSF-supported research.
Other
12
Jupiter (Planet), Orbital Mechanics, Saturn (Planet), Solar Orbits, Three Body Problem, Axes (Reference Lines), Eccentricity, Planetary Mass, Solar System, Truncation Errors
Scientific paper
The results of several numerical integration methods applied to calculating the 100,000-year evolution of the semi-major axes, eccentricities, and inclinations of the orbits of Jupiter and Saturn are compared and analyzed. The methods included a recurrent power series method with variable order and step size with Levi-Civita regularization of the closest pair, and an 8th-order variable step-size Runge-Kutta-Fehlberg method with K-S regularization of the closest pair. The sensitivity of the results to initial conditions was studied. The range of values of the mass parameter which yielded bounded motions was determined. Two solutions with two slightly different local truncation errors did not significantly deviate from each other, which indicates orbital stability of the Jupiter-Saturn-sun system.
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