Excerpt from Celestial Mechanics: A Survey of the Status of the Determination of the General Perturbations of the Minor Planets

Exhaustive researches are available only for a very limited number of planets. Among these are (4) Vesta, (13) Egeria and (447) Valen tine. The researches on (4) Vesta are due to Leveau, whose extraordi nary investigations extend approximately over a complete century of oppositions. In connection with his work on the motion of Vesta, Leveau has aimed at a determination of the masses of Jupiter'and Mars. His final value is larger than the best available mass of Jupiter by approximately one one-thousandth. On account of the moderate perturbations, the motion of Vesta does not lend itself as well to a determination of the mass of Jupiter as the motion of other minor planets with very large perturba tions. Any slight departure from the true mass of Jupiter, et cetera, can reveal itself through the motion of Vesta only in long intervals of time, which accounts for Leveau's gradual improvement of his adopted mass by successively including longer periods of observation. For the present his results may be considered funda mental and final, so far as this planet is concerned. No other case has been studied so exhaustively. Later predictions are well within the errors of observation, and not the slightest departure from the New tonian law is noticeable. It remains, however, to establish the same result for planets with large perturbations, particularly for such planets as have a mean motion commensurable with that of Jupiter. To avoid the necessity of gradually improving the Jupiter mass by means of subsequent observations of Vesta, it appears advisable to base further predictions on the best determined values of the masses of the major planets. Vesta also furnishes an example of the weight to be assigned to observations in the early part of the last century.

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