Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac. Volume 12. Coordinates of the Five Outer Planets,
NAUTICAL ALMANAC OFFICE WASHINGTON D C
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This volume contains the heliocentric coordinates of Jupiter, Saturn, Uranus, Neptune, and Pluto, at forty-day intervals from 1653 to 2060. They were obtained by numerical integration on the IBM Selective Sequence Electronic Calculator. These coordinates will be useful in discussing the motions of the planets themselves and in computing their effects on comets and other objects. All the mutual attractions of the five planets and the Sun were included and the resulting set of simultaneous non-linear differential equations of the thirtieth order was solved numerically with an accuracy of fourteen decimals. This accuracy is more than ample to give the desired accuracy at the two extremes of the four-hundred-year interval covered. The attractions of the inner planets, which are scarcely perceptible, can best be applied as small corrections to these values. The relativity-effect, which is smaller and is easily applied as a small correction, has also been omitted. The starting positions and velocities for the integration were determined from all available observations. Approximately 25,000 observations from about 1780 to 1940 were used. Two preliminary integrations were made to determine the constants for the final definitive one. The final integration was continued back to 1653 because observations of eclipses of Jupiters satellites near that date are still of value.