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Formulas are developed for the transformation of ecliptical orbital elements from B 1950 to J 2000. The results are compared with those recommended by IAU Commission 20. Some drawbacks to the Commission 20 formulation are pointed out and we develop procedures which are consistent with standard precessional formulations.

Solar eclipse timings measured between A.D. 1672 and 1806 are analyzed to study the variation of Delta T (= ET - UT) over this interval. These solar eclipse observations confirm the results of Brouwer (1952), Martin (1969), and Stephenson and Morrison (1969) which were obtained from the analysis of occultations in this period. It is believed that Goldstein's (1985) analysis inadequately represents the changes in Delta T.

The techniques and data used in previous determinations of the orbital evolution of the Galilean satellites of Jupiter are reviewed, and a new analysis is developed on the basis of Lieske's (1986) collection of 15,711 eclipse observations from the period 1652-1983, photographic observations, and Voyager optical-navigation images (Synnott et al., 1982). The data and results are presented in tables, and the secular changes in the satellite mean motions are found to be smaller than previously determined: e.g., (-7.4 + or - 8.7) x 10 to the -10th/yr for Io and (+8 + or - 42) x 10 to the -9th/yr for the relative evolution between Io and Europa.

The most complete collection of extant Galilean satellite eclipse observations since 1652 has been assembled. Since many of the old data exist only in manuscript form or in archaic forms (e.g., apparent time, local time, sidereal time, Julian calendar, etc.), they have been reduced to a modern proleptic Universal Time (UT) system (where the day begins at midnight) on the Gregorian calendar. Many of the data had been presumed to be lost for more than a century and since they are very valuable for discussion of long-term effects on the satellites, they are presented here for present as well as future generations of astronomers. The data are invaluable for long-term studies of Galilean satellite motion and for the determination of physical parameters.

Properties of astronomical time scales (ET and UT) are considered, with particular emphasis on correctly determining of-date longitude as the sum of inertial mean longitude of the sun relative to the mean equinox of a fixed epoch (1950.0), and the general precession in longitude accumulated since the epoch. The inertial mean longitude and motion (relative to the mean equinox) are derived from tabular ephemerides such as the Jet Propulsion Laboratories' DE 102 and DE 96, by comparisons with subroutines based on Newcomb's perturbation theory. An unresolved inconsistency of approximately 1 second per century among the mean inertial motion of DE 102, IAU precession speed (1976), and the classical Newcomb of-date mean motion is found. Interpretation difficulties arising from the use of different systems of Ephemeris Time are also discussed.

A method is developed by which Sampson's theory of motion of Jupiter's Galilean satellites can be revitalized by use of algebraic manipulation software on a digital computer. The technique seeks (1) to remove algebraic errors existing in the current Sampson theory, (2) to introduce some neglected effects due to solar interactions and the 3-7 commensurability between the outer two satellites, (3) to allow for nonzero amplitude and phase of the libration, (4) to allow future revision of the arbitrary constants of integration, (5) to express the final results as analytic functions of variations in the numerous arbitrary constants of integration and arbitrary parameters, and (6) to provide analytic partial derivatives by means of which the numerical values of coefficients in the expressions for the coordinates can be adjusted. The level of precision desired is one arc second (Jovicentric) for the coordinates (2, 3.3, 5.2, and 9.1 km, respectively, for satellites I through IV).

Over 4800 earth-based observations of Jupiter's Galilean satellites have been analyzed in order to develop improved ephemerides of the satellites for the Voyager mission, using the new theory of motion of the Galilean satellites. Included are over 1700 eclipses of the satellites by Jupiter spanning the interval 1878-1974, 85 mutual events (eclipses and occultations) observed in 1973, and over 2900 exposures on photographic plates from 1967-1978. The resulting ephemerides (labeled E-2) were employed for the Voyager I encounter and are in error by less than 200 km at the time of Jupiter close approach. A very small (0.066 deg) amplitude of the Laplacian free libration is indicated by the data.

Simplified expressions for the poles of Jupiter's Galilean satellites are derived, assuming that the satellites' poles are normal to their orbits. The resulting short trigonometric series depend upon the nodal motions of the satellites and librate about the pole of Jupiter. The precision of the final expressions is better than 0.01 degrees.

The excellent series of photometric eclipses of the Galilean satellites observed at Harvard from 1878 to 1903, which formed the basis for Sampson's study of the Galilean satellites, have been combined with the relatively few available post-1903 photometric eclipse observations in order to evaluate the satellite parameters which occur in the new theory of motion of the satellites. After obtaining values for the epsilon-beta parameters, the mutual eclipses and occultations observed in 1973 are compared with the new theory in order to assess the degradation which might occur in the 84 years which have elapsed since the mean epoch of the photometric eclipses. The results indicate that the new theory satisfactorily can predict ephemeris positions of the Galilean satellites over spans of nearly a century and that it will be a useful tool for analyzing future observations.

The structure of the expressions usually employed in calculating the effects of precession is examined, and a method is outlined for revising the expressions to account for changes in the fundamental astronomical constants. It is shown that the basic set of parameters, upon which depend the lengthy polynomials for computing the mean obliquity of data and the elements of the precession matrix, consists of the mean obliquity, the speed of general precession in longitude at a fixed epoch, and the system of planetary masses. Special attention is given to the motion of the ecliptic pole, formulations for a basic epoch as well as an arbitrary epoch, and ecliptic motion relative to the basic epoch. Numerical precession quantities at epoch J2000.0 (JED 2451545.0) are presented which result from the revision of astronomical constants adopted at the XVI General Assembly of the IAU.

Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.

The 3-7 commensurability between Jupiter's outer two Galilean satellites is investigated. The solution is developed in a manner which enables its adoption to any subsequent revision of Sampson's theory of their motion. A comparison with the results of de Heardtl is used to demonstrate the validity of the final expressions. The effect of the commensurability is to introduce periodic perturbations in longitude on the order of 20-40 km.