A4 Planetary Positions

(1) The Tuckerman Tables.

Tuckerman, Bryant. 1962. Planetary, Lunar, and Solar Positions 601 B.C. to A.D. 1 at Five-Day and Ten-Day Intervals (Philadelphia: The American Philosphical Society). The Amer. Phil. Soc. Memoirs, No. 56. Tuckerman, Bryant. 1964. Planetary, Lunar, and Solar Positions A.D. 2 to A.D. 1649 at Five-Day and Ten-Day Intervals (Philadelphia: The American Philosphical Society). The Amer. Phil. Soc. Memoirs, No. 59.

in these two volumes, Tuckerman uses improved theories and ephemerides and attention to roundoff error to present the geocentric ecliptic longitude and latitude positions of the naked-eye planets for an important segment of history; as a check, he compares them to the earlier work of P.V. Neugebauer (1914,1929) and investigates the differences between them. See the Introduction to the 1962 volume for a discussion of error. He gives estimated uncertainties in celestial longitude (p. 12) of 0.011°, 0.016°, 0.006°, 0.016°, 0.025°, 0.155°, 0.22° for Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the Moon, respectively; but also see Stephenson and Houlden (1981) for a discussion of the precision and Houlden and Stephenson (1986) for a discussion of the accuracy and for corrections, which can amount to as much as 0.7° (for longitudes of Mars), when Stephenson's positions are compared with those provided by numerical integration techniques. The positions of the Moon, Mercury, and Venus are given at 5-day intervals, and those of the Sun and outer planets at 10-day intervals.

(2) Supplement to the Tuckerman Tables.

Houlden, M.A., and Stephenson, F.R. 1986. A Supplement to the Tuckerman Tables. (Philadelphia: The American Philosphical Society). The Amer. Phil. Soc. Memoirs, No. 170.

This is an important update to the Tuckerman tables for the longitude positions of the outer planets for the full interval 601 b.c. to 1649 a.d. Tables are explicitly given for Mars, and graphs of the corrections are given for Jupiter and Saturn. The predicted brightnesses of all naked-eye planets in magnitude measure are also tabulated.

(3) Stahlman, W., and Gingerich, O. 1963. Solar and Planetary Longitudes for Years -2500 to +2000 by Ten-Day Intervals. (Madison: Univ. of Wisconsin Press).

(4) United States Naval Observatory almanacs (and corresponding sources in other countries).

The positions of planets can be calculated for modern epochs to good precision by software packages such as the "Floppy Almanac" and the annual Astronomical Almanac, available from the U.S. Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, D.C. 204029328. Certain astronomy supply houses also carry them.

(5) Orbital calculations can be carried out given observations, or given the elements of an orbit, predicted positions can be computed. Several resources are available: (a) Schlosser et al. (1991/1994) have a section on celestial mechanics in which planetary positions can be calculated; tables are provided as shortcuts. Ch. 14 and App. E are suitable for finding approximate positions of planets.

(b) Danby, J.M.A. 1988. Fundamentals of Celestial Mechanics, 2nd ed. (Richmond: Willmann-Bell, Inc.) available with floppy disks containing celestial mechanics programs.

(c) Boulet, D. 1992. Methods of Orbit Determination for the Micro Computer. (Richmond: Willmann-Bell, Inc.) with optional program listings in BASIC.

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