Literal solution for Hill's lunar problem

Details Literal solution for Hill's lunar problem Literal solution for Hill's lunar problem

Apr 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19..279s&link_type=abstract

Celestial Mechanics, vol. 19, Apr. 1979, p. 279-289.

Statistics

Computation

3

Computer Techniques, Hill Lunar Theory, Power Series, Convergence, Earth Orbits, Earth-Moon System, Variational Principles, Sun, Motion, Moon, Orbits, Three Body Problem, Distance, Earth, Rotation

Scientific paper

A computer program for the manipulation of power series in several variables is used to find the first order solution of Hill's lunar problem. The ratio m of the mean motion of the sun to that of the moon is kept as a formal parameter. The series in m are known to converge very poorly. It is shown how efficient algorithms among them the Lie transformation allow computation of the series in m as far as they are needed. When the series are evaluated at Brown's numerical value for m the results achieve or exceed his accuracy.

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